YES(O(1), O(n^2)) 240.57/77.11 YES(O(1), O(n^2)) 240.85/77.14 240.85/77.14 240.85/77.14 240.85/77.14 240.85/77.14 240.85/77.14 Runtime Complexity (innermost) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml.xml 240.85/77.14 240.85/77.14 240.85/77.14
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240.85/77.14
240.85/77.14
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(n^2)).

0 CpxTRS
240.85/77.14 
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳2 CdtProblem
240.85/77.14 
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳4 CdtProblem
240.85/77.14 
↳5 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳6 CdtProblem
240.85/77.14 
↳7 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
240.85/77.14 
↳8 CdtProblem
240.85/77.14 
↳9 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳10 CdtProblem
240.85/77.14 
↳11 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳12 CdtProblem
240.85/77.14 
↳13 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳14 CdtProblem
240.85/77.14 
↳15 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳16 CdtProblem
240.85/77.14 
↳17 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳18 CdtProblem
240.85/77.14 
↳19 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳20 CdtProblem
240.85/77.14 
↳21 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳22 CdtProblem
240.85/77.14 
↳23 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳24 CdtProblem
240.85/77.14 
↳25 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳26 CdtProblem
240.85/77.14 
↳27 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳28 CdtProblem
240.85/77.14 
↳29 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳30 CdtProblem
240.85/77.14 
↳31 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳32 CdtProblem
240.85/77.14 
↳33 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳34 CdtProblem
240.85/77.14 
↳35 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳36 CdtProblem
240.85/77.14 
↳37 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳38 CdtProblem
240.85/77.14 
↳39 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳40 CdtProblem
240.85/77.14 
↳41 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳42 CdtProblem
240.85/77.14 
↳43 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳44 CdtProblem
240.85/77.14 
↳45 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳46 CdtProblem
240.85/77.14 
↳47 CdtUnreachableProof (⇔)
240.85/77.14 
↳48 CdtProblem
240.85/77.14 
↳49 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳50 CdtProblem
240.85/77.14 
↳51 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳52 CdtProblem
240.85/77.14 
↳53 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
240.85/77.14 
↳54 CdtProblem
240.85/77.14 
↳55 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
240.85/77.14 
↳56 CdtProblem
240.85/77.14 
↳57 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
240.85/77.14 
↳58 CdtProblem
240.85/77.14 
↳59 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
240.85/77.14 
↳60 CdtProblem
240.85/77.14 
↳61 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
240.85/77.14 
↳62 CdtProblem
240.85/77.14 
↳63 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
240.85/77.14 
↳64 CdtProblem
240.85/77.14 
↳65 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))
240.85/77.14 
↳66 CdtProblem
240.85/77.14 
↳67 SIsEmptyProof (BOTH BOUNDS(ID, ID))
240.85/77.14 
↳68 BOUNDS(O(1), O(1))
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240.85/77.14

(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

active(app(nil, YS)) → mark(YS) 241.17/77.24
active(app(cons(X, XS), YS)) → mark(cons(X, app(XS, YS))) 241.17/77.24
active(from(X)) → mark(cons(X, from(s(X)))) 241.17/77.24
active(zWadr(nil, YS)) → mark(nil) 241.17/77.24
active(zWadr(XS, nil)) → mark(nil) 241.17/77.24
active(zWadr(cons(X, XS), cons(Y, YS))) → mark(cons(app(Y, cons(X, nil)), zWadr(XS, YS))) 241.17/77.24
active(prefix(L)) → mark(cons(nil, zWadr(L, prefix(L)))) 241.17/77.24
active(app(X1, X2)) → app(active(X1), X2) 241.17/77.24
active(app(X1, X2)) → app(X1, active(X2)) 241.17/77.24
active(cons(X1, X2)) → cons(active(X1), X2) 241.17/77.24
active(from(X)) → from(active(X)) 241.17/77.24
active(s(X)) → s(active(X)) 241.17/77.24
active(zWadr(X1, X2)) → zWadr(active(X1), X2) 241.17/77.24
active(zWadr(X1, X2)) → zWadr(X1, active(X2)) 241.17/77.24
active(prefix(X)) → prefix(active(X)) 241.17/77.24
app(mark(X1), X2) → mark(app(X1, X2)) 241.17/77.24
app(X1, mark(X2)) → mark(app(X1, X2)) 241.17/77.24
cons(mark(X1), X2) → mark(cons(X1, X2)) 241.17/77.24
from(mark(X)) → mark(from(X)) 241.17/77.24
s(mark(X)) → mark(s(X)) 241.17/77.24
zWadr(mark(X1), X2) → mark(zWadr(X1, X2)) 241.17/77.24
zWadr(X1, mark(X2)) → mark(zWadr(X1, X2)) 241.17/77.24
prefix(mark(X)) → mark(prefix(X)) 241.17/77.24
proper(app(X1, X2)) → app(proper(X1), proper(X2)) 241.17/77.24
proper(nil) → ok(nil) 241.17/77.24
proper(cons(X1, X2)) → cons(proper(X1), proper(X2)) 241.17/77.24
proper(from(X)) → from(proper(X)) 241.17/77.24
proper(s(X)) → s(proper(X)) 241.17/77.24
proper(zWadr(X1, X2)) → zWadr(proper(X1), proper(X2)) 241.17/77.24
proper(prefix(X)) → prefix(proper(X)) 241.17/77.24
app(ok(X1), ok(X2)) → ok(app(X1, X2)) 241.17/77.24
cons(ok(X1), ok(X2)) → ok(cons(X1, X2)) 241.17/77.24
from(ok(X)) → ok(from(X)) 241.17/77.24
s(ok(X)) → ok(s(X)) 241.17/77.24
zWadr(ok(X1), ok(X2)) → ok(zWadr(X1, X2)) 241.17/77.24
prefix(ok(X)) → ok(prefix(X)) 241.17/77.24
top(mark(X)) → top(proper(X)) 241.17/77.24
top(ok(X)) → top(active(X))

Rewrite Strategy: INNERMOST
241.17/77.24
241.17/77.24

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

Converted CpxTRS to CDT
241.17/77.24
241.17/77.24

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 241.17/77.24
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.17/77.24
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.17/77.24
active(zWadr(nil, z0)) → mark(nil) 241.17/77.24
active(zWadr(z0, nil)) → mark(nil) 241.17/77.24
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.17/77.24
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.17/77.24
active(app(z0, z1)) → app(active(z0), z1) 241.17/77.24
active(app(z0, z1)) → app(z0, active(z1)) 241.17/77.24
active(cons(z0, z1)) → cons(active(z0), z1) 241.17/77.24
active(from(z0)) → from(active(z0)) 241.17/77.24
active(s(z0)) → s(active(z0)) 241.17/77.24
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.17/77.24
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.17/77.24
active(prefix(z0)) → prefix(active(z0)) 241.17/77.24
app(mark(z0), z1) → mark(app(z0, z1)) 241.17/77.24
app(z0, mark(z1)) → mark(app(z0, z1)) 241.17/77.24
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.17/77.24
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.17/77.24
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.17/77.24
from(mark(z0)) → mark(from(z0)) 241.17/77.24
from(ok(z0)) → ok(from(z0)) 241.17/77.24
s(mark(z0)) → mark(s(z0)) 241.17/77.24
s(ok(z0)) → ok(s(z0)) 241.17/77.24
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.17/77.24
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.17/77.24
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.17/77.24
prefix(mark(z0)) → mark(prefix(z0)) 241.17/77.24
prefix(ok(z0)) → ok(prefix(z0)) 241.17/77.24
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.17/77.24
proper(nil) → ok(nil) 241.17/77.24
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.17/77.24
proper(from(z0)) → from(proper(z0)) 241.17/77.24
proper(s(z0)) → s(proper(z0)) 241.17/77.24
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.17/77.24
proper(prefix(z0)) → prefix(proper(z0)) 241.17/77.24
top(mark(z0)) → top(proper(z0)) 241.17/77.24
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(cons(z0, z1), z2)) → c1(CONS(z0, app(z1, z2)), APP(z1, z2)) 241.17/77.24
ACTIVE(from(z0)) → c2(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0)) 241.17/77.24
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c5(CONS(app(z2, cons(z0, nil)), zWadr(z1, z3)), APP(z2, cons(z0, nil)), CONS(z0, nil), ZWADR(z1, z3)) 241.17/77.24
ACTIVE(prefix(z0)) → c6(CONS(nil, zWadr(z0, prefix(z0))), ZWADR(z0, prefix(z0)), PREFIX(z0)) 241.17/77.24
ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.17/77.24
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.17/77.24
ACTIVE(cons(z0, z1)) → c9(CONS(active(z0), z1), ACTIVE(z0)) 241.17/77.24
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 241.17/77.24
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 241.17/77.24
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.17/77.24
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.17/77.24
ACTIVE(prefix(z0)) → c14(PREFIX(active(z0)), ACTIVE(z0)) 241.17/77.24
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.17/77.24
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.17/77.24
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.17/77.24
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.17/77.24
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.17/77.24
FROM(mark(z0)) → c20(FROM(z0)) 241.17/77.24
FROM(ok(z0)) → c21(FROM(z0)) 241.17/77.24
S(mark(z0)) → c22(S(z0)) 241.17/77.24
S(ok(z0)) → c23(S(z0)) 241.17/77.24
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.17/77.24
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.17/77.24
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.17/77.24
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.17/77.24
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.17/77.24
PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.24
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.24
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.17/77.24
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.17/77.24
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.24
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.17/77.24
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.17/77.24
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0))
S tuples:

ACTIVE(app(cons(z0, z1), z2)) → c1(CONS(z0, app(z1, z2)), APP(z1, z2)) 241.17/77.24
ACTIVE(from(z0)) → c2(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0)) 241.17/77.24
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c5(CONS(app(z2, cons(z0, nil)), zWadr(z1, z3)), APP(z2, cons(z0, nil)), CONS(z0, nil), ZWADR(z1, z3)) 241.17/77.24
ACTIVE(prefix(z0)) → c6(CONS(nil, zWadr(z0, prefix(z0))), ZWADR(z0, prefix(z0)), PREFIX(z0)) 241.17/77.24
ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.17/77.24
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.17/77.24
ACTIVE(cons(z0, z1)) → c9(CONS(active(z0), z1), ACTIVE(z0)) 241.17/77.24
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 241.17/77.24
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 241.17/77.24
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.17/77.24
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.17/77.24
ACTIVE(prefix(z0)) → c14(PREFIX(active(z0)), ACTIVE(z0)) 241.17/77.24
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.17/77.24
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.17/77.24
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.17/77.24
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.17/77.24
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.17/77.24
FROM(mark(z0)) → c20(FROM(z0)) 241.17/77.24
FROM(ok(z0)) → c21(FROM(z0)) 241.17/77.24
S(mark(z0)) → c22(S(z0)) 241.17/77.24
S(ok(z0)) → c23(S(z0)) 241.17/77.24
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.17/77.24
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.17/77.24
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.17/77.24
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.17/77.24
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.17/77.24
PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.24
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.24
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.17/77.24
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.17/77.24
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.24
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.17/77.24
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.17/77.24
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c1, c2, 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, c31, c32, c33, c34, c35, c36, c37

241.17/77.24
241.17/77.24

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

Removed 5 trailing tuple parts
241.17/77.24
241.17/77.24

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 241.17/77.24
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.17/77.24
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.17/77.24
active(zWadr(nil, z0)) → mark(nil) 241.17/77.24
active(zWadr(z0, nil)) → mark(nil) 241.17/77.24
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.17/77.24
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.17/77.24
active(app(z0, z1)) → app(active(z0), z1) 241.17/77.24
active(app(z0, z1)) → app(z0, active(z1)) 241.17/77.24
active(cons(z0, z1)) → cons(active(z0), z1) 241.17/77.24
active(from(z0)) → from(active(z0)) 241.17/77.24
active(s(z0)) → s(active(z0)) 241.17/77.24
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.17/77.24
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.17/77.24
active(prefix(z0)) → prefix(active(z0)) 241.17/77.24
app(mark(z0), z1) → mark(app(z0, z1)) 241.17/77.24
app(z0, mark(z1)) → mark(app(z0, z1)) 241.17/77.24
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.17/77.24
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.17/77.24
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.17/77.24
from(mark(z0)) → mark(from(z0)) 241.17/77.24
from(ok(z0)) → ok(from(z0)) 241.17/77.24
s(mark(z0)) → mark(s(z0)) 241.17/77.24
s(ok(z0)) → ok(s(z0)) 241.17/77.24
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.17/77.24
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.17/77.24
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.17/77.24
prefix(mark(z0)) → mark(prefix(z0)) 241.17/77.24
prefix(ok(z0)) → ok(prefix(z0)) 241.17/77.24
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.17/77.24
proper(nil) → ok(nil) 241.17/77.24
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.17/77.24
proper(from(z0)) → from(proper(z0)) 241.17/77.24
proper(s(z0)) → s(proper(z0)) 241.17/77.24
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.17/77.24
proper(prefix(z0)) → prefix(proper(z0)) 241.17/77.24
top(mark(z0)) → top(proper(z0)) 241.17/77.24
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(cons(z0, z1), z2)) → c1(CONS(z0, app(z1, z2)), APP(z1, z2)) 241.17/77.24
ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.17/77.24
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.17/77.24
ACTIVE(cons(z0, z1)) → c9(CONS(active(z0), z1), ACTIVE(z0)) 241.17/77.24
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 241.17/77.24
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 241.17/77.24
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.17/77.24
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.17/77.24
ACTIVE(prefix(z0)) → c14(PREFIX(active(z0)), ACTIVE(z0)) 241.17/77.24
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.17/77.24
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.17/77.24
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.17/77.24
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.17/77.24
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.17/77.24
FROM(mark(z0)) → c20(FROM(z0)) 241.17/77.24
FROM(ok(z0)) → c21(FROM(z0)) 241.17/77.24
S(mark(z0)) → c22(S(z0)) 241.17/77.24
S(ok(z0)) → c23(S(z0)) 241.17/77.24
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.17/77.24
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.17/77.24
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.17/77.24
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.17/77.24
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.17/77.24
PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.24
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.24
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.17/77.24
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.17/77.24
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.24
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.17/77.24
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.17/77.24
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.17/77.24
ACTIVE(from(z0)) → c2(S(z0)) 241.17/77.24
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c5(APP(z2, cons(z0, nil)), CONS(z0, nil), ZWADR(z1, z3)) 241.17/77.24
ACTIVE(prefix(z0)) → c6(PREFIX(z0))
S tuples:

ACTIVE(app(cons(z0, z1), z2)) → c1(CONS(z0, app(z1, z2)), APP(z1, z2)) 241.17/77.24
ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.17/77.24
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.17/77.24
ACTIVE(cons(z0, z1)) → c9(CONS(active(z0), z1), ACTIVE(z0)) 241.17/77.24
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 241.17/77.24
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 241.17/77.24
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.17/77.24
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.17/77.24
ACTIVE(prefix(z0)) → c14(PREFIX(active(z0)), ACTIVE(z0)) 241.17/77.24
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.17/77.24
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.17/77.24
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.17/77.24
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.17/77.29
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.17/77.29
FROM(mark(z0)) → c20(FROM(z0)) 241.17/77.29
FROM(ok(z0)) → c21(FROM(z0)) 241.17/77.29
S(mark(z0)) → c22(S(z0)) 241.17/77.29
S(ok(z0)) → c23(S(z0)) 241.17/77.29
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.17/77.29
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.17/77.29
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.17/77.29
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.17/77.29
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.17/77.29
PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.29
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.29
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.17/77.29
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.17/77.29
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.29
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.17/77.29
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.17/77.29
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.17/77.29
ACTIVE(from(z0)) → c2(S(z0)) 241.17/77.29
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c5(APP(z2, cons(z0, nil)), CONS(z0, nil), ZWADR(z1, z3)) 241.17/77.29
ACTIVE(prefix(z0)) → c6(PREFIX(z0))
K tuples:none
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c1, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c2, c5, c6

241.17/77.29
241.17/77.29

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

Split RHS of tuples not part of any SCC
241.17/77.29
241.17/77.29

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 241.17/77.29
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.17/77.29
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.17/77.29
active(zWadr(nil, z0)) → mark(nil) 241.17/77.29
active(zWadr(z0, nil)) → mark(nil) 241.17/77.29
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.17/77.29
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.17/77.29
active(app(z0, z1)) → app(active(z0), z1) 241.17/77.29
active(app(z0, z1)) → app(z0, active(z1)) 241.17/77.29
active(cons(z0, z1)) → cons(active(z0), z1) 241.17/77.29
active(from(z0)) → from(active(z0)) 241.17/77.29
active(s(z0)) → s(active(z0)) 241.17/77.29
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.17/77.29
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.17/77.29
active(prefix(z0)) → prefix(active(z0)) 241.17/77.29
app(mark(z0), z1) → mark(app(z0, z1)) 241.17/77.29
app(z0, mark(z1)) → mark(app(z0, z1)) 241.17/77.29
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.17/77.29
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.17/77.29
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.17/77.29
from(mark(z0)) → mark(from(z0)) 241.17/77.29
from(ok(z0)) → ok(from(z0)) 241.17/77.29
s(mark(z0)) → mark(s(z0)) 241.17/77.29
s(ok(z0)) → ok(s(z0)) 241.17/77.29
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.17/77.29
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.17/77.29
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.17/77.29
prefix(mark(z0)) → mark(prefix(z0)) 241.17/77.29
prefix(ok(z0)) → ok(prefix(z0)) 241.17/77.29
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.17/77.29
proper(nil) → ok(nil) 241.17/77.29
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.17/77.29
proper(from(z0)) → from(proper(z0)) 241.17/77.29
proper(s(z0)) → s(proper(z0)) 241.17/77.29
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.17/77.29
proper(prefix(z0)) → prefix(proper(z0)) 241.17/77.29
top(mark(z0)) → top(proper(z0)) 241.17/77.29
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.17/77.29
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.17/77.29
ACTIVE(cons(z0, z1)) → c9(CONS(active(z0), z1), ACTIVE(z0)) 241.17/77.29
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 241.17/77.29
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 241.17/77.29
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.17/77.29
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.17/77.29
ACTIVE(prefix(z0)) → c14(PREFIX(active(z0)), ACTIVE(z0)) 241.17/77.29
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.17/77.29
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.17/77.29
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.17/77.29
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.17/77.29
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.17/77.29
FROM(mark(z0)) → c20(FROM(z0)) 241.17/77.29
FROM(ok(z0)) → c21(FROM(z0)) 241.17/77.29
S(mark(z0)) → c22(S(z0)) 241.17/77.29
S(ok(z0)) → c23(S(z0)) 241.17/77.29
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.17/77.29
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.17/77.29
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.17/77.29
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.17/77.29
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.17/77.29
PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.29
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.29
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.17/77.29
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.17/77.29
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.29
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.17/77.29
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.17/77.29
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.17/77.29
ACTIVE(from(z0)) → c2(S(z0)) 241.17/77.29
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.17/77.29
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.17/77.29
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.17/77.29
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.17/77.29
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.17/77.29
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.17/77.29
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.17/77.29
ACTIVE(cons(z0, z1)) → c9(CONS(active(z0), z1), ACTIVE(z0)) 241.17/77.29
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 241.17/77.29
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 241.17/77.29
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.17/77.29
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.17/77.29
ACTIVE(prefix(z0)) → c14(PREFIX(active(z0)), ACTIVE(z0)) 241.17/77.29
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.17/77.29
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.17/77.29
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.17/77.29
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.17/77.29
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.17/77.29
FROM(mark(z0)) → c20(FROM(z0)) 241.17/77.29
FROM(ok(z0)) → c21(FROM(z0)) 241.17/77.29
S(mark(z0)) → c22(S(z0)) 241.17/77.29
S(ok(z0)) → c23(S(z0)) 241.17/77.29
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.17/77.29
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.17/77.29
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.17/77.29
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.17/77.29
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.17/77.29
PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.29
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.29
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.17/77.29
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.17/77.29
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.29
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.17/77.29
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.17/77.29
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.17/77.29
ACTIVE(from(z0)) → c2(S(z0)) 241.17/77.29
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.17/77.29
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.17/77.29
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.17/77.29
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.17/77.29
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.17/77.29
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3))
K tuples:none
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c2, c6, c

241.17/77.29
241.17/77.29

(7) CdtPolyRedPairProof (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)) → c36(TOP(proper(z0)), PROPER(z0))
We considered the (Usable) Rules:

app(mark(z0), z1) → mark(app(z0, z1)) 241.17/77.29
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.17/77.29
app(z0, mark(z1)) → mark(app(z0, z1)) 241.17/77.29
active(app(nil, z0)) → mark(z0) 241.17/77.29
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.17/77.29
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.17/77.29
active(zWadr(nil, z0)) → mark(nil) 241.17/77.29
active(zWadr(z0, nil)) → mark(nil) 241.17/77.29
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.17/77.29
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.17/77.29
active(app(z0, z1)) → app(active(z0), z1) 241.17/77.29
active(app(z0, z1)) → app(z0, active(z1)) 241.17/77.29
active(cons(z0, z1)) → cons(active(z0), z1) 241.17/77.29
active(from(z0)) → from(active(z0)) 241.17/77.29
active(s(z0)) → s(active(z0)) 241.17/77.29
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.17/77.29
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.17/77.29
active(prefix(z0)) → prefix(active(z0)) 241.17/77.29
prefix(mark(z0)) → mark(prefix(z0)) 241.17/77.29
prefix(ok(z0)) → ok(prefix(z0)) 241.17/77.29
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.17/77.29
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.17/77.29
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.17/77.29
s(mark(z0)) → mark(s(z0)) 241.17/77.29
s(ok(z0)) → ok(s(z0)) 241.17/77.29
from(mark(z0)) → mark(from(z0)) 241.17/77.29
from(ok(z0)) → ok(from(z0)) 241.17/77.29
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.17/77.29
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.17/77.29
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.17/77.29
proper(nil) → ok(nil) 241.17/77.29
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.17/77.29
proper(from(z0)) → from(proper(z0)) 241.17/77.29
proper(s(z0)) → s(proper(z0)) 241.17/77.29
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.17/77.29
proper(prefix(z0)) → prefix(proper(z0))
And the Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.17/77.29
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.17/77.29
ACTIVE(cons(z0, z1)) → c9(CONS(active(z0), z1), ACTIVE(z0)) 241.17/77.29
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 241.17/77.29
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 241.17/77.29
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.17/77.29
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.17/77.29
ACTIVE(prefix(z0)) → c14(PREFIX(active(z0)), ACTIVE(z0)) 241.17/77.29
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.17/77.29
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.17/77.29
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.17/77.29
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.17/77.29
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.17/77.29
FROM(mark(z0)) → c20(FROM(z0)) 241.17/77.29
FROM(ok(z0)) → c21(FROM(z0)) 241.17/77.29
S(mark(z0)) → c22(S(z0)) 241.17/77.29
S(ok(z0)) → c23(S(z0)) 241.17/77.29
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.17/77.29
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.17/77.29
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.17/77.29
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.17/77.29
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.17/77.29
PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.29
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.29
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.17/77.29
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.17/77.29
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.29
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.17/77.29
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.17/77.29
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.17/77.29
ACTIVE(from(z0)) → c2(S(z0)) 241.17/77.29
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.17/77.29
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.17/77.29
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.17/77.29
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.17/77.29
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.17/77.29
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3))
The order we found is given by the following interpretation:
Polynomial interpretation : 241.17/77.29

POL(ACTIVE(x1)) = 0    241.17/77.29
POL(APP(x1, x2)) = 0    241.17/77.29
POL(CONS(x1, x2)) = 0    241.17/77.29
POL(FROM(x1)) = 0    241.17/77.29
POL(PREFIX(x1)) = 0    241.17/77.29
POL(PROPER(x1)) = 0    241.17/77.29
POL(S(x1)) = 0    241.17/77.29
POL(TOP(x1)) = [4]x1    241.17/77.29
POL(ZWADR(x1, x2)) = 0    241.17/77.29
POL(active(x1)) = x1    241.17/77.29
POL(app(x1, x2)) = [1] + [4]x1 + x2    241.17/77.29
POL(c(x1)) = x1    241.17/77.29
POL(c10(x1, x2)) = x1 + x2    241.17/77.29
POL(c11(x1, x2)) = x1 + x2    241.17/77.29
POL(c12(x1, x2)) = x1 + x2    241.17/77.29
POL(c13(x1, x2)) = x1 + x2    241.17/77.29
POL(c14(x1, x2)) = x1 + x2    241.17/77.29
POL(c15(x1)) = x1    241.17/77.29
POL(c16(x1)) = x1    241.17/77.29
POL(c17(x1)) = x1    241.17/77.29
POL(c18(x1)) = x1    241.17/77.29
POL(c19(x1)) = x1    241.17/77.29
POL(c2(x1)) = x1    241.17/77.29
POL(c20(x1)) = x1    241.17/77.29
POL(c21(x1)) = x1    241.17/77.29
POL(c22(x1)) = x1    241.17/77.29
POL(c23(x1)) = x1    241.17/77.29
POL(c24(x1)) = x1    241.17/77.29
POL(c25(x1)) = x1    241.17/77.29
POL(c26(x1)) = x1    241.17/77.29
POL(c27(x1)) = x1    241.17/77.29
POL(c28(x1)) = x1    241.17/77.29
POL(c29(x1, x2, x3)) = x1 + x2 + x3    241.17/77.29
POL(c31(x1, x2, x3)) = x1 + x2 + x3    241.17/77.29
POL(c32(x1, x2)) = x1 + x2    241.17/77.29
POL(c33(x1, x2)) = x1 + x2    241.17/77.29
POL(c34(x1, x2, x3)) = x1 + x2 + x3    241.17/77.29
POL(c35(x1, x2)) = x1 + x2    241.17/77.29
POL(c36(x1, x2)) = x1 + x2    241.17/77.29
POL(c37(x1, x2)) = x1 + x2    241.17/77.29
POL(c6(x1)) = x1    241.17/77.29
POL(c7(x1, x2)) = x1 + x2    241.17/77.29
POL(c8(x1, x2)) = x1 + x2    241.17/77.29
POL(c9(x1, x2)) = x1 + x2    241.17/77.29
POL(cons(x1, x2)) = x1    241.17/77.29
POL(from(x1)) = [4] + [4]x1    241.17/77.29
POL(mark(x1)) = [1] + x1    241.17/77.29
POL(nil) = 0    241.17/77.29
POL(ok(x1)) = x1    241.17/77.29
POL(prefix(x1)) = [4] + [4]x1    241.17/77.29
POL(proper(x1)) = x1    241.17/77.29
POL(s(x1)) = x1    241.17/77.29
POL(zWadr(x1, x2)) = [4] + [2]x1 + [4]x2   
241.17/77.29
241.17/77.29

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 241.17/77.29
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.17/77.29
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.17/77.29
active(zWadr(nil, z0)) → mark(nil) 241.17/77.29
active(zWadr(z0, nil)) → mark(nil) 241.17/77.29
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.17/77.29
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.17/77.29
active(app(z0, z1)) → app(active(z0), z1) 241.17/77.29
active(app(z0, z1)) → app(z0, active(z1)) 241.17/77.29
active(cons(z0, z1)) → cons(active(z0), z1) 241.17/77.29
active(from(z0)) → from(active(z0)) 241.17/77.29
active(s(z0)) → s(active(z0)) 241.17/77.29
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.17/77.29
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.17/77.29
active(prefix(z0)) → prefix(active(z0)) 241.17/77.29
app(mark(z0), z1) → mark(app(z0, z1)) 241.17/77.29
app(z0, mark(z1)) → mark(app(z0, z1)) 241.17/77.29
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.17/77.29
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.17/77.29
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.17/77.29
from(mark(z0)) → mark(from(z0)) 241.17/77.29
from(ok(z0)) → ok(from(z0)) 241.17/77.29
s(mark(z0)) → mark(s(z0)) 241.17/77.29
s(ok(z0)) → ok(s(z0)) 241.17/77.29
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.17/77.29
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.17/77.29
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.17/77.29
prefix(mark(z0)) → mark(prefix(z0)) 241.17/77.29
prefix(ok(z0)) → ok(prefix(z0)) 241.17/77.29
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.17/77.29
proper(nil) → ok(nil) 241.17/77.29
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.17/77.29
proper(from(z0)) → from(proper(z0)) 241.17/77.29
proper(s(z0)) → s(proper(z0)) 241.17/77.29
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.17/77.29
proper(prefix(z0)) → prefix(proper(z0)) 241.17/77.29
top(mark(z0)) → top(proper(z0)) 241.17/77.29
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.17/77.29
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.17/77.29
ACTIVE(cons(z0, z1)) → c9(CONS(active(z0), z1), ACTIVE(z0)) 241.17/77.29
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 241.17/77.29
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 241.17/77.29
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.17/77.29
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.17/77.29
ACTIVE(prefix(z0)) → c14(PREFIX(active(z0)), ACTIVE(z0)) 241.17/77.29
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.17/77.29
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.17/77.29
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.17/77.29
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.17/77.29
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.17/77.29
FROM(mark(z0)) → c20(FROM(z0)) 241.17/77.29
FROM(ok(z0)) → c21(FROM(z0)) 241.17/77.29
S(mark(z0)) → c22(S(z0)) 241.17/77.29
S(ok(z0)) → c23(S(z0)) 241.17/77.29
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.17/77.29
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.17/77.29
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.17/77.29
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.17/77.29
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.17/77.29
PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.29
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.29
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.17/77.29
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.17/77.29
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.29
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.17/77.29
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.17/77.29
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.17/77.29
ACTIVE(from(z0)) → c2(S(z0)) 241.17/77.29
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.17/77.29
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.17/77.29
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.17/77.29
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.17/77.29
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.17/77.29
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.17/77.29
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.17/77.29
ACTIVE(cons(z0, z1)) → c9(CONS(active(z0), z1), ACTIVE(z0)) 241.17/77.29
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 241.17/77.29
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 241.17/77.29
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.17/77.29
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.17/77.29
ACTIVE(prefix(z0)) → c14(PREFIX(active(z0)), ACTIVE(z0)) 241.17/77.29
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.17/77.29
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.17/77.29
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.17/77.29
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.17/77.29
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.17/77.29
FROM(mark(z0)) → c20(FROM(z0)) 241.17/77.29
FROM(ok(z0)) → c21(FROM(z0)) 241.17/77.29
S(mark(z0)) → c22(S(z0)) 241.17/77.29
S(ok(z0)) → c23(S(z0)) 241.17/77.29
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.17/77.29
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.17/77.29
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.17/77.29
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.17/77.29
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.17/77.29
PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.29
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.17/77.29
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.17/77.29
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.17/77.29
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.59/77.34
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.59/77.34
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.59/77.34
ACTIVE(from(z0)) → c2(S(z0)) 241.59/77.34
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.59/77.34
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.59/77.34
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.59/77.34
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.59/77.34
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.59/77.34
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c2, c6, c

241.59/77.34
241.59/77.34

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

Use narrowing to replace ACTIVE(cons(z0, z1)) → c9(CONS(active(z0), z1), ACTIVE(z0)) by

ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.59/77.34
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.59/77.34
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.59/77.34
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.59/77.34
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.59/77.34
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.59/77.34
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.59/77.34
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.59/77.34
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.59/77.34
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.59/77.34
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.59/77.34
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.59/77.34
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.59/77.34
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.59/77.34
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0)))
241.59/77.34
241.59/77.34

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 241.59/77.34
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.59/77.34
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.59/77.34
active(zWadr(nil, z0)) → mark(nil) 241.59/77.34
active(zWadr(z0, nil)) → mark(nil) 241.59/77.34
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.59/77.34
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.59/77.34
active(app(z0, z1)) → app(active(z0), z1) 241.59/77.34
active(app(z0, z1)) → app(z0, active(z1)) 241.59/77.34
active(cons(z0, z1)) → cons(active(z0), z1) 241.59/77.34
active(from(z0)) → from(active(z0)) 241.59/77.34
active(s(z0)) → s(active(z0)) 241.59/77.34
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.59/77.34
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.59/77.34
active(prefix(z0)) → prefix(active(z0)) 241.59/77.34
app(mark(z0), z1) → mark(app(z0, z1)) 241.59/77.34
app(z0, mark(z1)) → mark(app(z0, z1)) 241.59/77.34
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.59/77.34
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.59/77.34
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.59/77.34
from(mark(z0)) → mark(from(z0)) 241.59/77.34
from(ok(z0)) → ok(from(z0)) 241.59/77.34
s(mark(z0)) → mark(s(z0)) 241.59/77.34
s(ok(z0)) → ok(s(z0)) 241.59/77.34
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.59/77.34
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.59/77.34
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.59/77.34
prefix(mark(z0)) → mark(prefix(z0)) 241.59/77.34
prefix(ok(z0)) → ok(prefix(z0)) 241.59/77.34
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.59/77.34
proper(nil) → ok(nil) 241.59/77.34
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.59/77.34
proper(from(z0)) → from(proper(z0)) 241.59/77.34
proper(s(z0)) → s(proper(z0)) 241.59/77.34
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.59/77.34
proper(prefix(z0)) → prefix(proper(z0)) 241.59/77.34
top(mark(z0)) → top(proper(z0)) 241.59/77.34
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.59/77.34
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.59/77.34
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 241.59/77.34
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 241.59/77.34
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.59/77.34
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.59/77.34
ACTIVE(prefix(z0)) → c14(PREFIX(active(z0)), ACTIVE(z0)) 241.59/77.34
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.59/77.34
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.59/77.34
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.59/77.34
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.59/77.34
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.59/77.34
FROM(mark(z0)) → c20(FROM(z0)) 241.59/77.34
FROM(ok(z0)) → c21(FROM(z0)) 241.59/77.34
S(mark(z0)) → c22(S(z0)) 241.59/77.34
S(ok(z0)) → c23(S(z0)) 241.59/77.34
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.59/77.34
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.59/77.34
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.59/77.34
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.59/77.34
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.59/77.34
PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.59/77.34
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.59/77.34
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.59/77.34
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.59/77.34
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.59/77.34
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.59/77.34
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.59/77.34
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.59/77.34
ACTIVE(from(z0)) → c2(S(z0)) 241.59/77.34
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.59/77.34
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.59/77.34
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.59/77.34
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.59/77.34
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.59/77.34
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.59/77.34
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.59/77.34
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.59/77.34
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.59/77.34
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.59/77.34
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.59/77.34
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.59/77.34
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.59/77.34
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.59/77.34
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.59/77.34
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.59/77.34
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.59/77.34
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.59/77.34
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.59/77.34
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.59/77.34
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0)))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.59/77.34
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.59/77.34
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 241.59/77.34
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 241.59/77.34
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.59/77.34
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.59/77.34
ACTIVE(prefix(z0)) → c14(PREFIX(active(z0)), ACTIVE(z0)) 241.59/77.34
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.59/77.34
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.59/77.34
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.59/77.34
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.59/77.34
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.59/77.34
FROM(mark(z0)) → c20(FROM(z0)) 241.59/77.34
FROM(ok(z0)) → c21(FROM(z0)) 241.59/77.34
S(mark(z0)) → c22(S(z0)) 241.59/77.34
S(ok(z0)) → c23(S(z0)) 241.59/77.34
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.59/77.34
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.59/77.34
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.59/77.34
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.59/77.34
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.59/77.34
PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.59/77.34
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.59/77.34
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.59/77.34
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.59/77.34
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.59/77.34
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.59/77.34
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.59/77.34
ACTIVE(from(z0)) → c2(S(z0)) 241.59/77.34
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.59/77.34
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.59/77.34
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.59/77.34
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.59/77.34
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.59/77.34
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.59/77.34
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.59/77.34
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.59/77.34
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.59/77.34
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.59/77.34
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.59/77.34
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.59/77.34
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.59/77.34
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.59/77.34
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.59/77.34
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.59/77.34
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.59/77.34
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.59/77.34
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.59/77.36
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.59/77.36
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0)))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c7, c8, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c2, c6, c, c9

241.59/77.36
241.59/77.36

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

Use narrowing to replace ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) by

ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.59/77.36
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.59/77.36
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.59/77.36
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.59/77.36
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.59/77.36
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.59/77.36
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.59/77.36
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.59/77.36
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.59/77.36
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.59/77.36
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.59/77.36
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.59/77.36
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.59/77.36
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.59/77.36
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0)))
241.59/77.36
241.59/77.36

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 241.59/77.36
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.59/77.36
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.59/77.36
active(zWadr(nil, z0)) → mark(nil) 241.59/77.36
active(zWadr(z0, nil)) → mark(nil) 241.59/77.36
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.59/77.36
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.59/77.36
active(app(z0, z1)) → app(active(z0), z1) 241.59/77.36
active(app(z0, z1)) → app(z0, active(z1)) 241.59/77.36
active(cons(z0, z1)) → cons(active(z0), z1) 241.59/77.36
active(from(z0)) → from(active(z0)) 241.59/77.36
active(s(z0)) → s(active(z0)) 241.59/77.36
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.59/77.36
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.59/77.36
active(prefix(z0)) → prefix(active(z0)) 241.59/77.36
app(mark(z0), z1) → mark(app(z0, z1)) 241.59/77.36
app(z0, mark(z1)) → mark(app(z0, z1)) 241.59/77.36
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.59/77.36
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.59/77.36
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.59/77.36
from(mark(z0)) → mark(from(z0)) 241.59/77.36
from(ok(z0)) → ok(from(z0)) 241.59/77.36
s(mark(z0)) → mark(s(z0)) 241.59/77.36
s(ok(z0)) → ok(s(z0)) 241.59/77.36
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.59/77.36
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.59/77.36
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.59/77.36
prefix(mark(z0)) → mark(prefix(z0)) 241.59/77.36
prefix(ok(z0)) → ok(prefix(z0)) 241.59/77.36
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.59/77.36
proper(nil) → ok(nil) 241.59/77.36
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.59/77.36
proper(from(z0)) → from(proper(z0)) 241.59/77.36
proper(s(z0)) → s(proper(z0)) 241.59/77.36
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.59/77.36
proper(prefix(z0)) → prefix(proper(z0)) 241.59/77.36
top(mark(z0)) → top(proper(z0)) 241.59/77.36
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.59/77.36
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.59/77.36
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 241.59/77.36
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.59/77.36
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.59/77.36
ACTIVE(prefix(z0)) → c14(PREFIX(active(z0)), ACTIVE(z0)) 241.59/77.36
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.59/77.36
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.59/77.36
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.59/77.36
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.59/77.36
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.59/77.36
FROM(mark(z0)) → c20(FROM(z0)) 241.59/77.36
FROM(ok(z0)) → c21(FROM(z0)) 241.59/77.36
S(mark(z0)) → c22(S(z0)) 241.59/77.36
S(ok(z0)) → c23(S(z0)) 241.59/77.36
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.59/77.36
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.59/77.36
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.59/77.36
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.59/77.36
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.59/77.36
PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.59/77.36
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.59/77.36
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.59/77.36
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.59/77.36
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.59/77.36
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.59/77.36
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.59/77.36
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.59/77.36
ACTIVE(from(z0)) → c2(S(z0)) 241.59/77.36
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.59/77.36
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.59/77.36
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.59/77.36
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.59/77.36
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.59/77.36
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.59/77.36
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.59/77.36
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.59/77.36
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.59/77.36
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.59/77.36
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.59/77.36
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.59/77.36
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.59/77.36
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.59/77.36
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.59/77.36
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.59/77.36
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.59/77.36
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.59/77.36
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.59/77.36
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.59/77.36
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.59/77.36
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.59/77.36
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.59/77.36
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.59/77.36
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.59/77.36
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.59/77.36
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.59/77.36
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.59/77.36
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.59/77.36
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.59/77.36
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.59/77.36
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.59/77.36
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.59/77.36
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.59/77.36
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.59/77.36
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0)))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.59/77.36
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.59/77.36
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 241.59/77.36
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.59/77.36
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.59/77.36
ACTIVE(prefix(z0)) → c14(PREFIX(active(z0)), ACTIVE(z0)) 241.59/77.36
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.59/77.36
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.59/77.36
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.59/77.36
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.59/77.36
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.59/77.36
FROM(mark(z0)) → c20(FROM(z0)) 241.59/77.36
FROM(ok(z0)) → c21(FROM(z0)) 241.59/77.36
S(mark(z0)) → c22(S(z0)) 241.59/77.36
S(ok(z0)) → c23(S(z0)) 241.59/77.36
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.59/77.36
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.59/77.36
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.59/77.36
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.59/77.36
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.59/77.36
PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.59/77.36
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.59/77.36
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.59/77.36
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.59/77.36
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.59/77.36
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.59/77.36
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.59/77.36
ACTIVE(from(z0)) → c2(S(z0)) 241.59/77.36
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.59/77.36
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.59/77.36
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.59/77.36
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.59/77.36
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.59/77.36
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.59/77.36
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.59/77.36
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.59/77.36
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.59/77.36
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.59/77.36
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.59/77.36
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.59/77.36
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.59/77.36
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.59/77.36
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.59/77.36
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.59/77.36
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.59/77.36
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.59/77.36
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.59/77.36
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.59/77.36
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.59/77.36
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.59/77.36
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.59/77.36
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.59/77.36
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.59/77.36
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.59/77.36
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.59/77.36
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.59/77.36
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.59/77.36
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.59/77.36
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.59/77.36
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.59/77.36
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.59/77.36
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.59/77.36
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.59/77.36
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0)))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c7, c8, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c2, c6, c, c9, c10

241.95/77.44
241.95/77.44

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

Use narrowing to replace ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) by

ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0)))
241.95/77.44
241.95/77.44

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 241.95/77.44
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.95/77.44
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.95/77.44
active(zWadr(nil, z0)) → mark(nil) 241.95/77.44
active(zWadr(z0, nil)) → mark(nil) 241.95/77.44
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.95/77.44
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.95/77.44
active(app(z0, z1)) → app(active(z0), z1) 241.95/77.44
active(app(z0, z1)) → app(z0, active(z1)) 241.95/77.44
active(cons(z0, z1)) → cons(active(z0), z1) 241.95/77.44
active(from(z0)) → from(active(z0)) 241.95/77.44
active(s(z0)) → s(active(z0)) 241.95/77.44
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.95/77.44
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.95/77.44
active(prefix(z0)) → prefix(active(z0)) 241.95/77.44
app(mark(z0), z1) → mark(app(z0, z1)) 241.95/77.44
app(z0, mark(z1)) → mark(app(z0, z1)) 241.95/77.44
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.95/77.44
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.95/77.44
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.95/77.44
from(mark(z0)) → mark(from(z0)) 241.95/77.44
from(ok(z0)) → ok(from(z0)) 241.95/77.44
s(mark(z0)) → mark(s(z0)) 241.95/77.44
s(ok(z0)) → ok(s(z0)) 241.95/77.44
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.95/77.44
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.95/77.44
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.95/77.44
prefix(mark(z0)) → mark(prefix(z0)) 241.95/77.44
prefix(ok(z0)) → ok(prefix(z0)) 241.95/77.44
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.95/77.44
proper(nil) → ok(nil) 241.95/77.44
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.95/77.44
proper(from(z0)) → from(proper(z0)) 241.95/77.44
proper(s(z0)) → s(proper(z0)) 241.95/77.44
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.95/77.44
proper(prefix(z0)) → prefix(proper(z0)) 241.95/77.44
top(mark(z0)) → top(proper(z0)) 241.95/77.44
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.44
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.44
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.44
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.44
ACTIVE(prefix(z0)) → c14(PREFIX(active(z0)), ACTIVE(z0)) 241.95/77.44
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.44
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.44
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.44
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.44
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.44
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.44
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.44
S(mark(z0)) → c22(S(z0)) 241.95/77.44
S(ok(z0)) → c23(S(z0)) 241.95/77.44
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.44
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.44
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.44
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.44
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.44
PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.44
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.44
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.95/77.44
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.95/77.44
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.44
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.44
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.95/77.44
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.44
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.44
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.44
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.44
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.44
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.44
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.44
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.44
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0)))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.44
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.44
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.44
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.44
ACTIVE(prefix(z0)) → c14(PREFIX(active(z0)), ACTIVE(z0)) 241.95/77.44
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.44
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.44
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.44
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.44
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.44
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.44
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.44
S(mark(z0)) → c22(S(z0)) 241.95/77.44
S(ok(z0)) → c23(S(z0)) 241.95/77.44
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.44
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.44
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.44
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.44
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.44
PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.44
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.44
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.95/77.44
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.95/77.44
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.44
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.44
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.44
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.44
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.44
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.44
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.44
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.44
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.44
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.44
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0)))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c7, c8, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c2, c6, c, c9, c10, c11

241.95/77.44
241.95/77.44

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

Use narrowing to replace ACTIVE(prefix(z0)) → c14(PREFIX(active(z0)), ACTIVE(z0)) by

ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0)))
241.95/77.44
241.95/77.44

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 241.95/77.44
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.95/77.44
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.95/77.44
active(zWadr(nil, z0)) → mark(nil) 241.95/77.44
active(zWadr(z0, nil)) → mark(nil) 241.95/77.44
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.95/77.44
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.95/77.44
active(app(z0, z1)) → app(active(z0), z1) 241.95/77.44
active(app(z0, z1)) → app(z0, active(z1)) 241.95/77.44
active(cons(z0, z1)) → cons(active(z0), z1) 241.95/77.44
active(from(z0)) → from(active(z0)) 241.95/77.44
active(s(z0)) → s(active(z0)) 241.95/77.44
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.95/77.44
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.95/77.44
active(prefix(z0)) → prefix(active(z0)) 241.95/77.44
app(mark(z0), z1) → mark(app(z0, z1)) 241.95/77.44
app(z0, mark(z1)) → mark(app(z0, z1)) 241.95/77.44
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.95/77.44
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.95/77.44
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.95/77.44
from(mark(z0)) → mark(from(z0)) 241.95/77.44
from(ok(z0)) → ok(from(z0)) 241.95/77.44
s(mark(z0)) → mark(s(z0)) 241.95/77.44
s(ok(z0)) → ok(s(z0)) 241.95/77.44
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.95/77.44
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.95/77.44
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.95/77.44
prefix(mark(z0)) → mark(prefix(z0)) 241.95/77.44
prefix(ok(z0)) → ok(prefix(z0)) 241.95/77.44
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.95/77.44
proper(nil) → ok(nil) 241.95/77.44
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.95/77.44
proper(from(z0)) → from(proper(z0)) 241.95/77.44
proper(s(z0)) → s(proper(z0)) 241.95/77.44
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.95/77.44
proper(prefix(z0)) → prefix(proper(z0)) 241.95/77.44
top(mark(z0)) → top(proper(z0)) 241.95/77.44
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.44
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.44
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.44
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.44
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.44
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.44
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.44
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.44
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.44
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.44
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.44
S(mark(z0)) → c22(S(z0)) 241.95/77.44
S(ok(z0)) → c23(S(z0)) 241.95/77.44
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.44
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.44
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.44
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.44
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.44
PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.44
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.44
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.95/77.44
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.95/77.44
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.44
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.44
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.95/77.44
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.44
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.44
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.44
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.44
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.44
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.44
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.44
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.44
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0)))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.44
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.44
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.44
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.44
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.44
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.44
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.44
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.44
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.44
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.44
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.44
S(mark(z0)) → c22(S(z0)) 241.95/77.44
S(ok(z0)) → c23(S(z0)) 241.95/77.44
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.44
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.44
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.44
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.44
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.44
PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.44
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.44
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.95/77.44
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.95/77.44
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.44
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.44
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.44
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.44
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.44
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.44
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.44
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.44
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.44
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.44
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0)))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c7, c8, c12, c13, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c2, c6, c, c9, c10, c11, c14

241.95/77.44
241.95/77.44

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

Use narrowing to replace PROPER(app(z0, z1)) → c29(APP(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.44
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 241.95/77.44
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.44
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.44
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.44
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.44
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.44
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.44
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 241.95/77.44
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.44
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.44
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.44
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.44
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1))
241.95/77.44
241.95/77.44

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 241.95/77.44
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.95/77.44
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.95/77.44
active(zWadr(nil, z0)) → mark(nil) 241.95/77.44
active(zWadr(z0, nil)) → mark(nil) 241.95/77.44
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.95/77.44
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.95/77.44
active(app(z0, z1)) → app(active(z0), z1) 241.95/77.44
active(app(z0, z1)) → app(z0, active(z1)) 241.95/77.44
active(cons(z0, z1)) → cons(active(z0), z1) 241.95/77.44
active(from(z0)) → from(active(z0)) 241.95/77.44
active(s(z0)) → s(active(z0)) 241.95/77.44
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.95/77.44
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.95/77.44
active(prefix(z0)) → prefix(active(z0)) 241.95/77.44
app(mark(z0), z1) → mark(app(z0, z1)) 241.95/77.44
app(z0, mark(z1)) → mark(app(z0, z1)) 241.95/77.44
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.95/77.44
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.95/77.44
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.95/77.44
from(mark(z0)) → mark(from(z0)) 241.95/77.44
from(ok(z0)) → ok(from(z0)) 241.95/77.44
s(mark(z0)) → mark(s(z0)) 241.95/77.44
s(ok(z0)) → ok(s(z0)) 241.95/77.44
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.95/77.44
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.95/77.44
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.95/77.44
prefix(mark(z0)) → mark(prefix(z0)) 241.95/77.44
prefix(ok(z0)) → ok(prefix(z0)) 241.95/77.44
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.95/77.44
proper(nil) → ok(nil) 241.95/77.44
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.95/77.44
proper(from(z0)) → from(proper(z0)) 241.95/77.44
proper(s(z0)) → s(proper(z0)) 241.95/77.44
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.95/77.44
proper(prefix(z0)) → prefix(proper(z0)) 241.95/77.44
top(mark(z0)) → top(proper(z0)) 241.95/77.44
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.44
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.44
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.44
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.44
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.44
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.44
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.44
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.44
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.44
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.44
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.44
S(mark(z0)) → c22(S(z0)) 241.95/77.44
S(ok(z0)) → c23(S(z0)) 241.95/77.44
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.44
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.44
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.44
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.44
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.44
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.44
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.95/77.44
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.95/77.44
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.44
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.44
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.95/77.44
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.44
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.44
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.44
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.44
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.44
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.44
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.44
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.44
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.44
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.44
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.44
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.44
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.44
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.44
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.44
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.44
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.44
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.44
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.44
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.44
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.44
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 241.95/77.44
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.44
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.45
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.45
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.45
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.45
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.45
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 241.95/77.45
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.45
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.45
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.45
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.45
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.45
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.45
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.45
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.45
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.45
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.45
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.45
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.45
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.45
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.45
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.45
S(mark(z0)) → c22(S(z0)) 241.95/77.45
S(ok(z0)) → c23(S(z0)) 241.95/77.45
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.45
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.45
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.45
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.45
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.45
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.45
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.95/77.45
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.95/77.45
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.45
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.45
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.45
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.45
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.45
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.45
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.45
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.45
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.45
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.45
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.45
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.45
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.45
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.45
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.45
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.45
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.45
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.45
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.45
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.45
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.45
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.45
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.45
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.45
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.45
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.45
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.45
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.45
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.45
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.45
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.45
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.45
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.45
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.45
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.45
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.45
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.45
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.45
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.45
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.45
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 241.95/77.45
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.45
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.45
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.45
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.45
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.45
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.45
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 241.95/77.45
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.45
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.45
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.45
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.45
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c7, c8, c12, c13, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c31, c32, c33, c34, c35, c36, c37, c2, c6, c, c9, c10, c11, c14, c29

241.95/77.45
241.95/77.45

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

Removed 2 trailing tuple parts
241.95/77.45
241.95/77.45

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 241.95/77.45
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.95/77.45
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.95/77.45
active(zWadr(nil, z0)) → mark(nil) 241.95/77.45
active(zWadr(z0, nil)) → mark(nil) 241.95/77.45
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.95/77.45
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.95/77.45
active(app(z0, z1)) → app(active(z0), z1) 241.95/77.45
active(app(z0, z1)) → app(z0, active(z1)) 241.95/77.45
active(cons(z0, z1)) → cons(active(z0), z1) 241.95/77.45
active(from(z0)) → from(active(z0)) 241.95/77.45
active(s(z0)) → s(active(z0)) 241.95/77.45
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.95/77.45
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.95/77.45
active(prefix(z0)) → prefix(active(z0)) 241.95/77.45
app(mark(z0), z1) → mark(app(z0, z1)) 241.95/77.45
app(z0, mark(z1)) → mark(app(z0, z1)) 241.95/77.45
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.95/77.45
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.95/77.45
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.95/77.45
from(mark(z0)) → mark(from(z0)) 241.95/77.45
from(ok(z0)) → ok(from(z0)) 241.95/77.45
s(mark(z0)) → mark(s(z0)) 241.95/77.45
s(ok(z0)) → ok(s(z0)) 241.95/77.45
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.95/77.45
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.95/77.45
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.95/77.45
prefix(mark(z0)) → mark(prefix(z0)) 241.95/77.45
prefix(ok(z0)) → ok(prefix(z0)) 241.95/77.45
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.95/77.45
proper(nil) → ok(nil) 241.95/77.45
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.95/77.45
proper(from(z0)) → from(proper(z0)) 241.95/77.45
proper(s(z0)) → s(proper(z0)) 241.95/77.45
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.95/77.45
proper(prefix(z0)) → prefix(proper(z0)) 241.95/77.45
top(mark(z0)) → top(proper(z0)) 241.95/77.45
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.45
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.45
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.45
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.45
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.45
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.45
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.45
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.45
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.45
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.45
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.45
S(mark(z0)) → c22(S(z0)) 241.95/77.45
S(ok(z0)) → c23(S(z0)) 241.95/77.45
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.45
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.45
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.45
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.45
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.45
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.45
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.95/77.45
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.95/77.45
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.45
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.45
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.95/77.45
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.45
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.45
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.45
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.45
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.45
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.45
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.45
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.45
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.45
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.45
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.45
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.45
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.45
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.45
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.45
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.45
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.45
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.45
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.45
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.45
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.45
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.45
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.45
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.45
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.45
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.45
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.45
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.45
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.45
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.45
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.45
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.45
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.45
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.45
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.45
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.45
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.45
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.45
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.45
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.45
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.45
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.45
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.45
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.45
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.45
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.45
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.45
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.45
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.45
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.45
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.45
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.45
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.45
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.45
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.45
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.45
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.45
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.45
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.45
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.45
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.45
S(mark(z0)) → c22(S(z0)) 241.95/77.45
S(ok(z0)) → c23(S(z0)) 241.95/77.45
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.45
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.45
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.45
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.45
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.45
PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.45
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.95/77.45
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.95/77.45
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.45
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.45
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.45
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.45
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.45
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.45
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.45
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.45
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.45
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.45
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.45
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.45
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.45
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.45
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.45
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.45
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.45
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.45
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.45
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.45
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.45
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.45
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.45
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.45
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.45
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.45
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.45
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.45
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.45
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.45
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.45
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.45
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.45
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.45
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.45
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.45
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.45
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.45
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.45
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.45
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.45
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.45
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.45
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.45
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.45
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.45
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.45
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.45
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.45
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.45
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.45
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.45
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.45
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.45
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.45
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.45
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c7, c8, c12, c13, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c31, c32, c33, c34, c35, c36, c37, c2, c6, c, c9, c10, c11, c14, c29, c29

241.95/77.45
241.95/77.45

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

Use narrowing to replace PROPER(cons(z0, z1)) → c31(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.49
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 241.95/77.49
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.49
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.49
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.49
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 241.95/77.49
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1))
241.95/77.49
241.95/77.49

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 241.95/77.49
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.95/77.49
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.95/77.49
active(zWadr(nil, z0)) → mark(nil) 241.95/77.49
active(zWadr(z0, nil)) → mark(nil) 241.95/77.49
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.95/77.49
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.95/77.49
active(app(z0, z1)) → app(active(z0), z1) 241.95/77.49
active(app(z0, z1)) → app(z0, active(z1)) 241.95/77.49
active(cons(z0, z1)) → cons(active(z0), z1) 241.95/77.49
active(from(z0)) → from(active(z0)) 241.95/77.49
active(s(z0)) → s(active(z0)) 241.95/77.49
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.95/77.49
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.95/77.49
active(prefix(z0)) → prefix(active(z0)) 241.95/77.49
app(mark(z0), z1) → mark(app(z0, z1)) 241.95/77.49
app(z0, mark(z1)) → mark(app(z0, z1)) 241.95/77.49
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.95/77.49
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.95/77.49
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.95/77.49
from(mark(z0)) → mark(from(z0)) 241.95/77.49
from(ok(z0)) → ok(from(z0)) 241.95/77.49
s(mark(z0)) → mark(s(z0)) 241.95/77.49
s(ok(z0)) → ok(s(z0)) 241.95/77.49
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.95/77.49
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.95/77.49
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.95/77.49
prefix(mark(z0)) → mark(prefix(z0)) 241.95/77.49
prefix(ok(z0)) → ok(prefix(z0)) 241.95/77.49
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.95/77.49
proper(nil) → ok(nil) 241.95/77.49
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.95/77.49
proper(from(z0)) → from(proper(z0)) 241.95/77.49
proper(s(z0)) → s(proper(z0)) 241.95/77.49
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.95/77.49
proper(prefix(z0)) → prefix(proper(z0)) 241.95/77.49
top(mark(z0)) → top(proper(z0)) 241.95/77.49
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.49
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.49
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.49
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.49
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.49
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.49
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.49
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.49
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.49
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.49
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.49
S(mark(z0)) → c22(S(z0)) 241.95/77.49
S(ok(z0)) → c23(S(z0)) 241.95/77.49
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.49
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.49
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.49
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.49
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.49
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.95/77.49
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.95/77.49
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.49
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.49
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.95/77.49
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.49
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.49
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.49
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.49
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.49
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.49
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.49
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.49
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.49
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.49
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.49
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.49
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 241.95/77.49
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.49
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.49
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.49
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 241.95/77.49
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.49
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.49
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.49
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.49
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.49
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.49
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.49
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.49
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.49
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.49
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.49
S(mark(z0)) → c22(S(z0)) 241.95/77.49
S(ok(z0)) → c23(S(z0)) 241.95/77.49
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.49
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.49
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.49
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.49
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.49
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.95/77.49
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.95/77.49
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.49
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.49
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.49
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.49
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.49
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.49
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.49
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.49
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.49
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.49
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.49
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.49
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.49
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.49
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 241.95/77.49
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.49
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.49
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.49
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 241.95/77.49
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c7, c8, c12, c13, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c32, c33, c34, c35, c36, c37, c2, c6, c, c9, c10, c11, c14, c29, c29, c31

241.95/77.49
241.95/77.49

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

Removed 2 trailing tuple parts
241.95/77.49
241.95/77.49

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 241.95/77.49
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.95/77.49
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.95/77.49
active(zWadr(nil, z0)) → mark(nil) 241.95/77.49
active(zWadr(z0, nil)) → mark(nil) 241.95/77.49
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.95/77.49
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.95/77.49
active(app(z0, z1)) → app(active(z0), z1) 241.95/77.49
active(app(z0, z1)) → app(z0, active(z1)) 241.95/77.49
active(cons(z0, z1)) → cons(active(z0), z1) 241.95/77.49
active(from(z0)) → from(active(z0)) 241.95/77.49
active(s(z0)) → s(active(z0)) 241.95/77.49
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.95/77.49
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.95/77.49
active(prefix(z0)) → prefix(active(z0)) 241.95/77.49
app(mark(z0), z1) → mark(app(z0, z1)) 241.95/77.49
app(z0, mark(z1)) → mark(app(z0, z1)) 241.95/77.49
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.95/77.49
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.95/77.49
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.95/77.49
from(mark(z0)) → mark(from(z0)) 241.95/77.49
from(ok(z0)) → ok(from(z0)) 241.95/77.49
s(mark(z0)) → mark(s(z0)) 241.95/77.49
s(ok(z0)) → ok(s(z0)) 241.95/77.49
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.95/77.49
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.95/77.49
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.95/77.49
prefix(mark(z0)) → mark(prefix(z0)) 241.95/77.49
prefix(ok(z0)) → ok(prefix(z0)) 241.95/77.49
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.95/77.49
proper(nil) → ok(nil) 241.95/77.49
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.95/77.49
proper(from(z0)) → from(proper(z0)) 241.95/77.49
proper(s(z0)) → s(proper(z0)) 241.95/77.49
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.95/77.49
proper(prefix(z0)) → prefix(proper(z0)) 241.95/77.49
top(mark(z0)) → top(proper(z0)) 241.95/77.49
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.49
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.49
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.49
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.49
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.49
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.49
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.49
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.49
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.49
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.49
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.49
S(mark(z0)) → c22(S(z0)) 241.95/77.49
S(ok(z0)) → c23(S(z0)) 241.95/77.49
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.49
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.49
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.49
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.49
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.49
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.95/77.49
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.95/77.49
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.49
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.49
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.95/77.49
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.49
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.49
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.49
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.49
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.49
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.49
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.49
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.49
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.49
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.49
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.49
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.49
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.49
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.49
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.49
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.49
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.49
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.49
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.49
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.49
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.49
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.49
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.49
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.49
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.49
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.49
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.49
S(mark(z0)) → c22(S(z0)) 241.95/77.49
S(ok(z0)) → c23(S(z0)) 241.95/77.49
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.49
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.49
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.49
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.49
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.49
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 241.95/77.49
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.95/77.49
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.49
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.49
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.49
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.49
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.49
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.49
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.49
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.49
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.49
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.49
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.49
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.49
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.49
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.49
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.49
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.49
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.49
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.49
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c7, c8, c12, c13, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c32, c33, c34, c35, c36, c37, c2, c6, c, c9, c10, c11, c14, c29, c29, c31, c31

241.95/77.49
241.95/77.49

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

Use narrowing to replace PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) by

PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 241.95/77.49
PROPER(from(nil)) → c32(FROM(ok(nil)), PROPER(nil)) 241.95/77.49
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 241.95/77.49
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 241.95/77.49
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0)))
241.95/77.49
241.95/77.49

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 241.95/77.49
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.95/77.49
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.95/77.49
active(zWadr(nil, z0)) → mark(nil) 241.95/77.49
active(zWadr(z0, nil)) → mark(nil) 241.95/77.49
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.95/77.49
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.95/77.49
active(app(z0, z1)) → app(active(z0), z1) 241.95/77.49
active(app(z0, z1)) → app(z0, active(z1)) 241.95/77.49
active(cons(z0, z1)) → cons(active(z0), z1) 241.95/77.49
active(from(z0)) → from(active(z0)) 241.95/77.49
active(s(z0)) → s(active(z0)) 241.95/77.49
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.95/77.49
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.95/77.49
active(prefix(z0)) → prefix(active(z0)) 241.95/77.49
app(mark(z0), z1) → mark(app(z0, z1)) 241.95/77.49
app(z0, mark(z1)) → mark(app(z0, z1)) 241.95/77.49
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.95/77.49
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.95/77.49
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.95/77.49
from(mark(z0)) → mark(from(z0)) 241.95/77.49
from(ok(z0)) → ok(from(z0)) 241.95/77.49
s(mark(z0)) → mark(s(z0)) 241.95/77.49
s(ok(z0)) → ok(s(z0)) 241.95/77.49
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.95/77.49
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.95/77.49
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.95/77.49
prefix(mark(z0)) → mark(prefix(z0)) 241.95/77.49
prefix(ok(z0)) → ok(prefix(z0)) 241.95/77.49
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.95/77.49
proper(nil) → ok(nil) 241.95/77.49
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.95/77.49
proper(from(z0)) → from(proper(z0)) 241.95/77.49
proper(s(z0)) → s(proper(z0)) 241.95/77.49
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.95/77.49
proper(prefix(z0)) → prefix(proper(z0)) 241.95/77.49
top(mark(z0)) → top(proper(z0)) 241.95/77.49
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.49
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.49
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.49
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.49
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.49
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.49
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.49
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.49
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.49
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.49
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.49
S(mark(z0)) → c22(S(z0)) 241.95/77.49
S(ok(z0)) → c23(S(z0)) 241.95/77.49
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.49
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.49
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.49
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.49
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.49
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.95/77.49
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.49
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.49
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.95/77.49
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.49
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.49
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.49
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.49
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.49
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.49
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.49
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.49
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.49
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.49
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.49
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.49
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.49
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.49
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.49
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.49
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.49
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 241.95/77.49
PROPER(from(nil)) → c32(FROM(ok(nil)), PROPER(nil)) 241.95/77.49
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 241.95/77.49
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 241.95/77.49
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0)))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.49
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.49
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.49
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.49
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.49
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.49
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.49
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.49
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.49
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.49
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.49
S(mark(z0)) → c22(S(z0)) 241.95/77.49
S(ok(z0)) → c23(S(z0)) 241.95/77.49
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.49
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.49
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.49
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.49
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.49
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.95/77.49
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.49
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.49
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.49
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.49
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.49
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.49
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.49
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.49
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.49
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.49
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.49
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.49
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.49
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.49
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.49
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.49
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.49
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.49
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.49
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 241.95/77.49
PROPER(from(nil)) → c32(FROM(ok(nil)), PROPER(nil)) 241.95/77.49
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 241.95/77.49
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 241.95/77.49
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0)))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c7, c8, c12, c13, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c33, c34, c35, c36, c37, c2, c6, c, c9, c10, c11, c14, c29, c29, c31, c31, c32

241.95/77.49
241.95/77.49

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

Removed 1 trailing tuple parts
241.95/77.49
241.95/77.49

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 241.95/77.49
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.95/77.49
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.95/77.49
active(zWadr(nil, z0)) → mark(nil) 241.95/77.49
active(zWadr(z0, nil)) → mark(nil) 241.95/77.49
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.95/77.49
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.95/77.49
active(app(z0, z1)) → app(active(z0), z1) 241.95/77.49
active(app(z0, z1)) → app(z0, active(z1)) 241.95/77.49
active(cons(z0, z1)) → cons(active(z0), z1) 241.95/77.49
active(from(z0)) → from(active(z0)) 241.95/77.49
active(s(z0)) → s(active(z0)) 241.95/77.49
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.95/77.49
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.95/77.49
active(prefix(z0)) → prefix(active(z0)) 241.95/77.49
app(mark(z0), z1) → mark(app(z0, z1)) 241.95/77.49
app(z0, mark(z1)) → mark(app(z0, z1)) 241.95/77.49
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.95/77.49
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.95/77.49
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.95/77.49
from(mark(z0)) → mark(from(z0)) 241.95/77.49
from(ok(z0)) → ok(from(z0)) 241.95/77.49
s(mark(z0)) → mark(s(z0)) 241.95/77.49
s(ok(z0)) → ok(s(z0)) 241.95/77.49
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.95/77.49
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.95/77.49
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.95/77.49
prefix(mark(z0)) → mark(prefix(z0)) 241.95/77.49
prefix(ok(z0)) → ok(prefix(z0)) 241.95/77.49
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.95/77.49
proper(nil) → ok(nil) 241.95/77.49
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.95/77.49
proper(from(z0)) → from(proper(z0)) 241.95/77.49
proper(s(z0)) → s(proper(z0)) 241.95/77.49
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.95/77.49
proper(prefix(z0)) → prefix(proper(z0)) 241.95/77.49
top(mark(z0)) → top(proper(z0)) 241.95/77.49
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.49
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.49
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.49
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.49
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.49
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.49
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.49
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.49
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.49
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.49
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.49
S(mark(z0)) → c22(S(z0)) 241.95/77.49
S(ok(z0)) → c23(S(z0)) 241.95/77.49
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.49
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.49
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.49
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.49
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.49
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.95/77.49
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.49
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.49
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.95/77.49
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.49
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.49
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.49
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.49
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.49
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.49
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.49
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.49
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.49
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.49
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.49
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.49
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.49
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.49
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.49
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.49
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.49
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.49
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.49
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.49
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.49
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.49
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.49
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.49
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.49
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.49
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.49
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.49
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.49
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.49
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.49
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 241.95/77.49
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 241.95/77.49
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 241.95/77.49
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 241.95/77.49
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 241.95/77.49
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 241.95/77.50
PROPER(from(nil)) → c32(FROM(ok(nil)))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.50
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.50
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.50
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.50
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.50
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.50
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.50
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.50
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.50
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.50
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.50
S(mark(z0)) → c22(S(z0)) 241.95/77.50
S(ok(z0)) → c23(S(z0)) 241.95/77.50
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.50
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.50
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.50
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.50
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.50
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 241.95/77.50
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.50
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.50
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.50
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.50
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.50
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.50
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.50
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.50
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.50
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.50
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.50
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.50
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.50
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.50
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.50
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.50
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.50
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.50
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.50
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.50
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.50
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.50
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.50
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.50
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 241.95/77.50
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 241.95/77.50
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 241.95/77.50
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 241.95/77.50
PROPER(from(nil)) → c32(FROM(ok(nil)))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c7, c8, c12, c13, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c33, c34, c35, c36, c37, c2, c6, c, c9, c10, c11, c14, c29, c29, c31, c31, c32, c32

241.95/77.50
241.95/77.50

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

Use narrowing to replace PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) by

PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 241.95/77.50
PROPER(s(nil)) → c33(S(ok(nil)), PROPER(nil)) 241.95/77.50
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 241.95/77.50
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 241.95/77.50
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0)))
241.95/77.50
241.95/77.50

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 241.95/77.50
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.95/77.50
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.95/77.50
active(zWadr(nil, z0)) → mark(nil) 241.95/77.50
active(zWadr(z0, nil)) → mark(nil) 241.95/77.50
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.95/77.50
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.95/77.50
active(app(z0, z1)) → app(active(z0), z1) 241.95/77.50
active(app(z0, z1)) → app(z0, active(z1)) 241.95/77.50
active(cons(z0, z1)) → cons(active(z0), z1) 241.95/77.50
active(from(z0)) → from(active(z0)) 241.95/77.50
active(s(z0)) → s(active(z0)) 241.95/77.50
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.95/77.50
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.95/77.50
active(prefix(z0)) → prefix(active(z0)) 241.95/77.50
app(mark(z0), z1) → mark(app(z0, z1)) 241.95/77.50
app(z0, mark(z1)) → mark(app(z0, z1)) 241.95/77.50
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.95/77.50
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.95/77.50
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.95/77.50
from(mark(z0)) → mark(from(z0)) 241.95/77.50
from(ok(z0)) → ok(from(z0)) 241.95/77.50
s(mark(z0)) → mark(s(z0)) 241.95/77.50
s(ok(z0)) → ok(s(z0)) 241.95/77.50
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.95/77.50
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.95/77.50
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.95/77.50
prefix(mark(z0)) → mark(prefix(z0)) 241.95/77.50
prefix(ok(z0)) → ok(prefix(z0)) 241.95/77.50
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.95/77.50
proper(nil) → ok(nil) 241.95/77.50
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.95/77.50
proper(from(z0)) → from(proper(z0)) 241.95/77.50
proper(s(z0)) → s(proper(z0)) 241.95/77.50
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.95/77.50
proper(prefix(z0)) → prefix(proper(z0)) 241.95/77.50
top(mark(z0)) → top(proper(z0)) 241.95/77.50
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.50
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.50
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.50
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.50
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.50
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.50
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.50
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.50
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.50
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.50
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.50
S(mark(z0)) → c22(S(z0)) 241.95/77.50
S(ok(z0)) → c23(S(z0)) 241.95/77.50
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.50
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.50
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.50
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.50
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.50
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.50
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.50
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.95/77.50
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.50
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.50
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.50
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.50
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.50
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.50
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.50
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.50
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.50
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.50
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.50
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.50
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.50
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.50
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.50
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.50
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.50
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.50
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.50
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.50
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.50
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.50
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 241.95/77.50
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 241.95/77.50
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 241.95/77.50
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 241.95/77.50
PROPER(from(nil)) → c32(FROM(ok(nil))) 241.95/77.50
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 241.95/77.50
PROPER(s(nil)) → c33(S(ok(nil)), PROPER(nil)) 241.95/77.50
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 241.95/77.50
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 241.95/77.50
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0)))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.50
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.50
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.50
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.50
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.50
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.50
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.50
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.50
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.50
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.50
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.50
S(mark(z0)) → c22(S(z0)) 241.95/77.50
S(ok(z0)) → c23(S(z0)) 241.95/77.50
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.50
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.50
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.50
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.50
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.50
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.50
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.50
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.50
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.50
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.50
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.50
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.50
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.50
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.50
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.50
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.50
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.50
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.50
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.50
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.50
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.50
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.50
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.50
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.50
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.50
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.50
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.50
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.50
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.50
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 241.95/77.50
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 241.95/77.50
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 241.95/77.50
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 241.95/77.50
PROPER(from(nil)) → c32(FROM(ok(nil))) 241.95/77.50
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 241.95/77.50
PROPER(s(nil)) → c33(S(ok(nil)), PROPER(nil)) 241.95/77.50
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 241.95/77.50
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 241.95/77.50
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0)))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c7, c8, c12, c13, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c34, c35, c36, c37, c2, c6, c, c9, c10, c11, c14, c29, c29, c31, c31, c32, c32, c33

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241.95/77.50

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

Removed 1 trailing tuple parts
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241.95/77.50

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 241.95/77.50
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.95/77.50
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.95/77.50
active(zWadr(nil, z0)) → mark(nil) 241.95/77.50
active(zWadr(z0, nil)) → mark(nil) 241.95/77.50
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.95/77.50
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.95/77.50
active(app(z0, z1)) → app(active(z0), z1) 241.95/77.50
active(app(z0, z1)) → app(z0, active(z1)) 241.95/77.50
active(cons(z0, z1)) → cons(active(z0), z1) 241.95/77.50
active(from(z0)) → from(active(z0)) 241.95/77.50
active(s(z0)) → s(active(z0)) 241.95/77.50
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.95/77.50
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.95/77.50
active(prefix(z0)) → prefix(active(z0)) 241.95/77.50
app(mark(z0), z1) → mark(app(z0, z1)) 241.95/77.50
app(z0, mark(z1)) → mark(app(z0, z1)) 241.95/77.50
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.95/77.50
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.95/77.50
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.95/77.50
from(mark(z0)) → mark(from(z0)) 241.95/77.50
from(ok(z0)) → ok(from(z0)) 241.95/77.50
s(mark(z0)) → mark(s(z0)) 241.95/77.50
s(ok(z0)) → ok(s(z0)) 241.95/77.50
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.95/77.50
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.95/77.50
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.95/77.50
prefix(mark(z0)) → mark(prefix(z0)) 241.95/77.50
prefix(ok(z0)) → ok(prefix(z0)) 241.95/77.50
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.95/77.50
proper(nil) → ok(nil) 241.95/77.50
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.95/77.50
proper(from(z0)) → from(proper(z0)) 241.95/77.50
proper(s(z0)) → s(proper(z0)) 241.95/77.50
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.95/77.50
proper(prefix(z0)) → prefix(proper(z0)) 241.95/77.50
top(mark(z0)) → top(proper(z0)) 241.95/77.50
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.50
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.50
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.50
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.50
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.50
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.50
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.50
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.50
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.50
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.50
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.50
S(mark(z0)) → c22(S(z0)) 241.95/77.50
S(ok(z0)) → c23(S(z0)) 241.95/77.50
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.50
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.50
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.50
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.50
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.50
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.50
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.50
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.95/77.50
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.50
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.50
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.50
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.50
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.50
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.50
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.50
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.50
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.50
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.50
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.50
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.50
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.50
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.50
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.50
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.50
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.50
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.50
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.50
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.50
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.50
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.50
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 241.95/77.50
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 241.95/77.50
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 241.95/77.50
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 241.95/77.50
PROPER(from(nil)) → c32(FROM(ok(nil))) 241.95/77.50
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 241.95/77.50
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 241.95/77.50
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 241.95/77.50
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0))) 241.95/77.50
PROPER(s(nil)) → c33(S(ok(nil)))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.50
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.50
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.50
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.50
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.50
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.50
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.50
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.50
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.50
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.50
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.50
S(mark(z0)) → c22(S(z0)) 241.95/77.50
S(ok(z0)) → c23(S(z0)) 241.95/77.50
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.50
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.50
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.50
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.50
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.50
PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 241.95/77.50
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.50
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.50
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.50
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.50
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.50
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.50
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.50
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.50
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.50
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.50
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.50
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.50
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.50
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.50
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.50
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.50
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.50
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.50
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.50
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.50
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 241.95/77.50
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 241.95/77.50
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 241.95/77.50
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 241.95/77.50
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 241.95/77.50
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 241.95/77.50
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 241.95/77.50
PROPER(from(nil)) → c32(FROM(ok(nil))) 241.95/77.50
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 241.95/77.50
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 241.95/77.50
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 241.95/77.50
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0))) 241.95/77.50
PROPER(s(nil)) → c33(S(ok(nil)))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c7, c8, c12, c13, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c34, c35, c36, c37, c2, c6, c, c9, c10, c11, c14, c29, c29, c31, c31, c32, c32, c33, c33

241.95/77.50
241.95/77.50

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

Use narrowing to replace PROPER(zWadr(z0, z1)) → c34(ZWADR(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(zWadr(x0, app(z0, z1))) → c34(ZWADR(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 241.95/77.50
PROPER(zWadr(x0, nil)) → c34(ZWADR(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 241.95/77.50
PROPER(zWadr(x0, cons(z0, z1))) → c34(ZWADR(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 241.95/77.50
PROPER(zWadr(x0, from(z0))) → c34(ZWADR(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 241.95/77.50
PROPER(zWadr(x0, s(z0))) → c34(ZWADR(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 241.95/77.50
PROPER(zWadr(x0, zWadr(z0, z1))) → c34(ZWADR(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 241.95/77.50
PROPER(zWadr(x0, prefix(z0))) → c34(ZWADR(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 241.95/77.50
PROPER(zWadr(app(z0, z1), x1)) → c34(ZWADR(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(zWadr(nil, x1)) → c34(ZWADR(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 241.95/77.50
PROPER(zWadr(cons(z0, z1), x1)) → c34(ZWADR(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(zWadr(from(z0), x1)) → c34(ZWADR(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 241.95/77.50
PROPER(zWadr(s(z0), x1)) → c34(ZWADR(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 241.95/77.50
PROPER(zWadr(zWadr(z0, z1), x1)) → c34(ZWADR(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 241.95/77.50
PROPER(zWadr(prefix(z0), x1)) → c34(ZWADR(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1))
241.95/77.50
241.95/77.50

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 241.95/77.50
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 241.95/77.50
active(from(z0)) → mark(cons(z0, from(s(z0)))) 241.95/77.50
active(zWadr(nil, z0)) → mark(nil) 241.95/77.50
active(zWadr(z0, nil)) → mark(nil) 241.95/77.50
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 241.95/77.50
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 241.95/77.50
active(app(z0, z1)) → app(active(z0), z1) 241.95/77.50
active(app(z0, z1)) → app(z0, active(z1)) 241.95/77.50
active(cons(z0, z1)) → cons(active(z0), z1) 241.95/77.50
active(from(z0)) → from(active(z0)) 241.95/77.50
active(s(z0)) → s(active(z0)) 241.95/77.50
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 241.95/77.50
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 241.95/77.50
active(prefix(z0)) → prefix(active(z0)) 241.95/77.50
app(mark(z0), z1) → mark(app(z0, z1)) 241.95/77.50
app(z0, mark(z1)) → mark(app(z0, z1)) 241.95/77.50
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 241.95/77.50
cons(mark(z0), z1) → mark(cons(z0, z1)) 241.95/77.50
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 241.95/77.50
from(mark(z0)) → mark(from(z0)) 241.95/77.50
from(ok(z0)) → ok(from(z0)) 241.95/77.50
s(mark(z0)) → mark(s(z0)) 241.95/77.50
s(ok(z0)) → ok(s(z0)) 241.95/77.50
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 241.95/77.50
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 241.95/77.50
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 241.95/77.50
prefix(mark(z0)) → mark(prefix(z0)) 241.95/77.50
prefix(ok(z0)) → ok(prefix(z0)) 241.95/77.50
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 241.95/77.50
proper(nil) → ok(nil) 241.95/77.50
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 241.95/77.50
proper(from(z0)) → from(proper(z0)) 241.95/77.50
proper(s(z0)) → s(proper(z0)) 241.95/77.50
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 241.95/77.50
proper(prefix(z0)) → prefix(proper(z0)) 241.95/77.50
top(mark(z0)) → top(proper(z0)) 241.95/77.50
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 241.95/77.50
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 241.95/77.50
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 241.95/77.50
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 241.95/77.50
APP(mark(z0), z1) → c15(APP(z0, z1)) 241.95/77.50
APP(z0, mark(z1)) → c16(APP(z0, z1)) 241.95/77.50
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 241.95/77.50
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 241.95/77.50
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 241.95/77.50
FROM(mark(z0)) → c20(FROM(z0)) 241.95/77.50
FROM(ok(z0)) → c21(FROM(z0)) 241.95/77.50
S(mark(z0)) → c22(S(z0)) 241.95/77.50
S(ok(z0)) → c23(S(z0)) 241.95/77.50
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 241.95/77.50
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 241.95/77.50
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 241.95/77.50
PREFIX(mark(z0)) → c27(PREFIX(z0)) 241.95/77.50
PREFIX(ok(z0)) → c28(PREFIX(z0)) 241.95/77.50
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 241.95/77.50
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 241.95/77.50
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 241.95/77.50
ACTIVE(from(z0)) → c2(S(z0)) 241.95/77.50
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 241.95/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 241.95/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 241.95/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 241.95/77.50
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 241.95/77.50
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 241.95/77.50
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 241.95/77.50
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 241.95/77.50
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 241.95/77.50
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 241.95/77.50
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 241.95/77.50
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 241.95/77.50
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 241.95/77.50
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 241.95/77.50
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 241.95/77.50
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 242.33/77.50
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.50
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.50
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.50
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.50
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.50
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.50
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 242.33/77.50
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.50
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.50
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.50
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.50
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.50
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.50
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.50
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.50
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.50
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.50
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.50
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.50
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.50
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.50
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.50
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.50
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.50
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.50
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.50
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.50
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.50
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.50
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.50
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.50
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.50
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 242.33/77.50
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 242.33/77.50
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.50
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.50
PROPER(from(nil)) → c32(FROM(ok(nil))) 242.33/77.50
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.50
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.50
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 242.33/77.50
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 242.33/77.50
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.50
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.50
PROPER(s(nil)) → c33(S(ok(nil))) 242.33/77.50
PROPER(zWadr(x0, app(z0, z1))) → c34(ZWADR(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.50
PROPER(zWadr(x0, nil)) → c34(ZWADR(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 242.33/77.50
PROPER(zWadr(x0, cons(z0, z1))) → c34(ZWADR(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.50
PROPER(zWadr(x0, from(z0))) → c34(ZWADR(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.50
PROPER(zWadr(x0, s(z0))) → c34(ZWADR(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.50
PROPER(zWadr(x0, zWadr(z0, z1))) → c34(ZWADR(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.50
PROPER(zWadr(x0, prefix(z0))) → c34(ZWADR(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.50
PROPER(zWadr(app(z0, z1), x1)) → c34(ZWADR(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(zWadr(nil, x1)) → c34(ZWADR(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 242.33/77.50
PROPER(zWadr(cons(z0, z1), x1)) → c34(ZWADR(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(zWadr(from(z0), x1)) → c34(ZWADR(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.50
PROPER(zWadr(s(z0), x1)) → c34(ZWADR(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.50
PROPER(zWadr(zWadr(z0, z1), x1)) → c34(ZWADR(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(zWadr(prefix(z0), x1)) → c34(ZWADR(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 242.33/77.50
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 242.33/77.50
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 242.33/77.50
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 242.33/77.50
APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.50
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.50
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.50
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.50
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.50
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.50
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.50
S(mark(z0)) → c22(S(z0)) 242.33/77.50
S(ok(z0)) → c23(S(z0)) 242.33/77.50
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.50
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.50
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.50
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.50
PREFIX(ok(z0)) → c28(PREFIX(z0)) 242.33/77.50
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 242.33/77.50
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 242.33/77.50
ACTIVE(from(z0)) → c2(S(z0)) 242.33/77.50
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 242.33/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 242.33/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 242.33/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 242.33/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 242.33/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 242.33/77.50
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 242.33/77.50
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 242.33/77.50
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 242.33/77.50
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 242.33/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 242.33/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.50
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.50
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.50
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.50
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.50
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.50
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 242.33/77.50
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.50
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.50
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.50
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.50
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.50
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.50
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 242.33/77.50
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.50
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.50
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.50
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.50
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.50
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.50
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 242.33/77.50
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.50
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.50
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.50
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.50
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.50
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.50
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.50
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.50
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.50
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.50
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.50
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.50
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.50
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.50
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.50
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.50
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.50
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.50
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.50
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.50
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.50
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.50
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.50
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.50
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.50
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 242.33/77.50
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 242.33/77.50
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.50
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.50
PROPER(from(nil)) → c32(FROM(ok(nil))) 242.33/77.50
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.50
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.50
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 242.33/77.50
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 242.33/77.50
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.50
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.50
PROPER(s(nil)) → c33(S(ok(nil))) 242.33/77.50
PROPER(zWadr(x0, app(z0, z1))) → c34(ZWADR(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.50
PROPER(zWadr(x0, nil)) → c34(ZWADR(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 242.33/77.50
PROPER(zWadr(x0, cons(z0, z1))) → c34(ZWADR(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.50
PROPER(zWadr(x0, from(z0))) → c34(ZWADR(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.50
PROPER(zWadr(x0, s(z0))) → c34(ZWADR(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.50
PROPER(zWadr(x0, zWadr(z0, z1))) → c34(ZWADR(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.50
PROPER(zWadr(x0, prefix(z0))) → c34(ZWADR(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.50
PROPER(zWadr(app(z0, z1), x1)) → c34(ZWADR(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(zWadr(nil, x1)) → c34(ZWADR(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 242.33/77.50
PROPER(zWadr(cons(z0, z1), x1)) → c34(ZWADR(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(zWadr(from(z0), x1)) → c34(ZWADR(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.50
PROPER(zWadr(s(z0), x1)) → c34(ZWADR(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.50
PROPER(zWadr(zWadr(z0, z1), x1)) → c34(ZWADR(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(zWadr(prefix(z0), x1)) → c34(ZWADR(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c7, c8, c12, c13, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c35, c36, c37, c2, c6, c, c9, c10, c11, c14, c29, c29, c31, c31, c32, c32, c33, c33, c34

242.33/77.50
242.33/77.50

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

Removed 2 trailing tuple parts
242.33/77.50
242.33/77.50

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 242.33/77.50
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 242.33/77.50
active(from(z0)) → mark(cons(z0, from(s(z0)))) 242.33/77.50
active(zWadr(nil, z0)) → mark(nil) 242.33/77.50
active(zWadr(z0, nil)) → mark(nil) 242.33/77.50
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 242.33/77.50
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 242.33/77.50
active(app(z0, z1)) → app(active(z0), z1) 242.33/77.50
active(app(z0, z1)) → app(z0, active(z1)) 242.33/77.50
active(cons(z0, z1)) → cons(active(z0), z1) 242.33/77.50
active(from(z0)) → from(active(z0)) 242.33/77.50
active(s(z0)) → s(active(z0)) 242.33/77.50
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 242.33/77.50
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 242.33/77.50
active(prefix(z0)) → prefix(active(z0)) 242.33/77.50
app(mark(z0), z1) → mark(app(z0, z1)) 242.33/77.50
app(z0, mark(z1)) → mark(app(z0, z1)) 242.33/77.50
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 242.33/77.50
cons(mark(z0), z1) → mark(cons(z0, z1)) 242.33/77.50
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 242.33/77.50
from(mark(z0)) → mark(from(z0)) 242.33/77.50
from(ok(z0)) → ok(from(z0)) 242.33/77.50
s(mark(z0)) → mark(s(z0)) 242.33/77.50
s(ok(z0)) → ok(s(z0)) 242.33/77.50
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 242.33/77.50
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 242.33/77.50
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 242.33/77.50
prefix(mark(z0)) → mark(prefix(z0)) 242.33/77.50
prefix(ok(z0)) → ok(prefix(z0)) 242.33/77.50
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 242.33/77.50
proper(nil) → ok(nil) 242.33/77.50
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 242.33/77.50
proper(from(z0)) → from(proper(z0)) 242.33/77.50
proper(s(z0)) → s(proper(z0)) 242.33/77.50
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 242.33/77.50
proper(prefix(z0)) → prefix(proper(z0)) 242.33/77.50
top(mark(z0)) → top(proper(z0)) 242.33/77.50
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 242.33/77.50
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 242.33/77.50
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 242.33/77.50
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 242.33/77.50
APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.50
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.50
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.50
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.50
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.50
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.50
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.50
S(mark(z0)) → c22(S(z0)) 242.33/77.50
S(ok(z0)) → c23(S(z0)) 242.33/77.50
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.50
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.50
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.50
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.50
PREFIX(ok(z0)) → c28(PREFIX(z0)) 242.33/77.50
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 242.33/77.50
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 242.33/77.50
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 242.33/77.50
ACTIVE(from(z0)) → c2(S(z0)) 242.33/77.50
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 242.33/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 242.33/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 242.33/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 242.33/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 242.33/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 242.33/77.50
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 242.33/77.50
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 242.33/77.50
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 242.33/77.50
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 242.33/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 242.33/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.50
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.50
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.50
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.50
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.50
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.50
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 242.33/77.50
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.50
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.50
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.50
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.50
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.50
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.50
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 242.33/77.50
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.50
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.50
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.50
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.50
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.50
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.50
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 242.33/77.50
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.50
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.50
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.50
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.50
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.50
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.50
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.50
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.50
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.50
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.50
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.50
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.50
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.50
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.50
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.50
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.50
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.50
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.50
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.50
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.50
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.50
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.50
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.50
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.50
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.50
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 242.33/77.50
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 242.33/77.50
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.50
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.50
PROPER(from(nil)) → c32(FROM(ok(nil))) 242.33/77.50
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.50
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.50
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 242.33/77.50
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 242.33/77.50
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.50
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.50
PROPER(s(nil)) → c33(S(ok(nil))) 242.33/77.50
PROPER(zWadr(x0, app(z0, z1))) → c34(ZWADR(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.50
PROPER(zWadr(x0, cons(z0, z1))) → c34(ZWADR(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.50
PROPER(zWadr(x0, from(z0))) → c34(ZWADR(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.50
PROPER(zWadr(x0, s(z0))) → c34(ZWADR(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.50
PROPER(zWadr(x0, zWadr(z0, z1))) → c34(ZWADR(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.50
PROPER(zWadr(x0, prefix(z0))) → c34(ZWADR(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.50
PROPER(zWadr(app(z0, z1), x1)) → c34(ZWADR(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(zWadr(cons(z0, z1), x1)) → c34(ZWADR(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(zWadr(from(z0), x1)) → c34(ZWADR(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.50
PROPER(zWadr(s(z0), x1)) → c34(ZWADR(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.50
PROPER(zWadr(zWadr(z0, z1), x1)) → c34(ZWADR(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.50
PROPER(zWadr(prefix(z0), x1)) → c34(ZWADR(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.50
PROPER(zWadr(x0, nil)) → c34(ZWADR(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.50
PROPER(zWadr(nil, x1)) → c34(ZWADR(ok(nil), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 242.33/77.50
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 242.33/77.50
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 242.33/77.50
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 242.33/77.50
APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.50
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.50
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.50
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.50
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.50
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.50
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.50
S(mark(z0)) → c22(S(z0)) 242.33/77.50
S(ok(z0)) → c23(S(z0)) 242.33/77.50
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.50
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.50
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.50
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.50
PREFIX(ok(z0)) → c28(PREFIX(z0)) 242.33/77.50
PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) 242.33/77.50
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 242.33/77.50
ACTIVE(from(z0)) → c2(S(z0)) 242.33/77.50
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 242.33/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 242.33/77.50
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 242.33/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 242.33/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 242.33/77.50
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 242.33/77.50
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 242.33/77.50
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 242.33/77.50
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 242.33/77.50
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 242.33/77.50
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 242.33/77.50
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 242.33/77.50
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 242.33/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.50
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 242.33/77.50
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.50
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.50
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(from(nil)) → c32(FROM(ok(nil))) 242.33/77.51
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(s(nil)) → c33(S(ok(nil))) 242.33/77.51
PROPER(zWadr(x0, app(z0, z1))) → c34(ZWADR(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, cons(z0, z1))) → c34(ZWADR(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, from(z0))) → c34(ZWADR(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(zWadr(x0, s(z0))) → c34(ZWADR(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(zWadr(x0, zWadr(z0, z1))) → c34(ZWADR(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, prefix(z0))) → c34(ZWADR(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(zWadr(app(z0, z1), x1)) → c34(ZWADR(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(cons(z0, z1), x1)) → c34(ZWADR(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(from(z0), x1)) → c34(ZWADR(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(s(z0), x1)) → c34(ZWADR(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(zWadr(z0, z1), x1)) → c34(ZWADR(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(prefix(z0), x1)) → c34(ZWADR(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(x0, nil)) → c34(ZWADR(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(zWadr(nil, x1)) → c34(ZWADR(ok(nil), proper(x1)), PROPER(x1))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c7, c8, c12, c13, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c35, c36, c37, c2, c6, c, c9, c10, c11, c14, c29, c29, c31, c31, c32, c32, c33, c33, c34, c34

242.33/77.51
242.33/77.51

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

Use narrowing to replace PROPER(prefix(z0)) → c35(PREFIX(proper(z0)), PROPER(z0)) by

PROPER(prefix(app(z0, z1))) → c35(PREFIX(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(prefix(nil)) → c35(PREFIX(ok(nil)), PROPER(nil)) 242.33/77.51
PROPER(prefix(cons(z0, z1))) → c35(PREFIX(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(prefix(from(z0))) → c35(PREFIX(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(prefix(s(z0))) → c35(PREFIX(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(prefix(zWadr(z0, z1))) → c35(PREFIX(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(prefix(prefix(z0))) → c35(PREFIX(prefix(proper(z0))), PROPER(prefix(z0)))
242.33/77.51
242.33/77.51

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 242.33/77.51
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 242.33/77.51
active(from(z0)) → mark(cons(z0, from(s(z0)))) 242.33/77.51
active(zWadr(nil, z0)) → mark(nil) 242.33/77.51
active(zWadr(z0, nil)) → mark(nil) 242.33/77.51
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 242.33/77.51
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 242.33/77.51
active(app(z0, z1)) → app(active(z0), z1) 242.33/77.51
active(app(z0, z1)) → app(z0, active(z1)) 242.33/77.51
active(cons(z0, z1)) → cons(active(z0), z1) 242.33/77.51
active(from(z0)) → from(active(z0)) 242.33/77.51
active(s(z0)) → s(active(z0)) 242.33/77.51
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 242.33/77.51
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 242.33/77.51
active(prefix(z0)) → prefix(active(z0)) 242.33/77.51
app(mark(z0), z1) → mark(app(z0, z1)) 242.33/77.51
app(z0, mark(z1)) → mark(app(z0, z1)) 242.33/77.51
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 242.33/77.51
cons(mark(z0), z1) → mark(cons(z0, z1)) 242.33/77.51
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 242.33/77.51
from(mark(z0)) → mark(from(z0)) 242.33/77.51
from(ok(z0)) → ok(from(z0)) 242.33/77.51
s(mark(z0)) → mark(s(z0)) 242.33/77.51
s(ok(z0)) → ok(s(z0)) 242.33/77.51
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 242.33/77.51
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 242.33/77.51
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 242.33/77.51
prefix(mark(z0)) → mark(prefix(z0)) 242.33/77.51
prefix(ok(z0)) → ok(prefix(z0)) 242.33/77.51
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 242.33/77.51
proper(nil) → ok(nil) 242.33/77.51
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 242.33/77.51
proper(from(z0)) → from(proper(z0)) 242.33/77.51
proper(s(z0)) → s(proper(z0)) 242.33/77.51
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 242.33/77.51
proper(prefix(z0)) → prefix(proper(z0)) 242.33/77.51
top(mark(z0)) → top(proper(z0)) 242.33/77.51
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 242.33/77.51
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 242.33/77.51
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 242.33/77.51
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 242.33/77.51
APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.51
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.51
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.51
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.51
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.51
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.51
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.51
S(mark(z0)) → c22(S(z0)) 242.33/77.51
S(ok(z0)) → c23(S(z0)) 242.33/77.51
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.51
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.51
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.51
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.51
PREFIX(ok(z0)) → c28(PREFIX(z0)) 242.33/77.51
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 242.33/77.51
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 242.33/77.51
ACTIVE(from(z0)) → c2(S(z0)) 242.33/77.51
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 242.33/77.51
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 242.33/77.51
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 242.33/77.51
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(from(nil)) → c32(FROM(ok(nil))) 242.33/77.51
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(s(nil)) → c33(S(ok(nil))) 242.33/77.51
PROPER(zWadr(x0, app(z0, z1))) → c34(ZWADR(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, cons(z0, z1))) → c34(ZWADR(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, from(z0))) → c34(ZWADR(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(zWadr(x0, s(z0))) → c34(ZWADR(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(zWadr(x0, zWadr(z0, z1))) → c34(ZWADR(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, prefix(z0))) → c34(ZWADR(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(zWadr(app(z0, z1), x1)) → c34(ZWADR(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(cons(z0, z1), x1)) → c34(ZWADR(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(from(z0), x1)) → c34(ZWADR(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(s(z0), x1)) → c34(ZWADR(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(zWadr(z0, z1), x1)) → c34(ZWADR(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(prefix(z0), x1)) → c34(ZWADR(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(x0, nil)) → c34(ZWADR(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(zWadr(nil, x1)) → c34(ZWADR(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(prefix(app(z0, z1))) → c35(PREFIX(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(prefix(nil)) → c35(PREFIX(ok(nil)), PROPER(nil)) 242.33/77.51
PROPER(prefix(cons(z0, z1))) → c35(PREFIX(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(prefix(from(z0))) → c35(PREFIX(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(prefix(s(z0))) → c35(PREFIX(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(prefix(zWadr(z0, z1))) → c35(PREFIX(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(prefix(prefix(z0))) → c35(PREFIX(prefix(proper(z0))), PROPER(prefix(z0)))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 242.33/77.51
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 242.33/77.51
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 242.33/77.51
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 242.33/77.51
APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.51
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.51
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.51
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.51
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.51
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.51
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.51
S(mark(z0)) → c22(S(z0)) 242.33/77.51
S(ok(z0)) → c23(S(z0)) 242.33/77.51
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.51
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.51
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.51
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.51
PREFIX(ok(z0)) → c28(PREFIX(z0)) 242.33/77.51
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 242.33/77.51
ACTIVE(from(z0)) → c2(S(z0)) 242.33/77.51
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 242.33/77.51
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 242.33/77.51
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 242.33/77.51
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(from(nil)) → c32(FROM(ok(nil))) 242.33/77.51
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(s(nil)) → c33(S(ok(nil))) 242.33/77.51
PROPER(zWadr(x0, app(z0, z1))) → c34(ZWADR(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, cons(z0, z1))) → c34(ZWADR(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, from(z0))) → c34(ZWADR(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(zWadr(x0, s(z0))) → c34(ZWADR(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(zWadr(x0, zWadr(z0, z1))) → c34(ZWADR(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, prefix(z0))) → c34(ZWADR(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(zWadr(app(z0, z1), x1)) → c34(ZWADR(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(cons(z0, z1), x1)) → c34(ZWADR(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(from(z0), x1)) → c34(ZWADR(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(s(z0), x1)) → c34(ZWADR(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(zWadr(z0, z1), x1)) → c34(ZWADR(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(prefix(z0), x1)) → c34(ZWADR(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(x0, nil)) → c34(ZWADR(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(zWadr(nil, x1)) → c34(ZWADR(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(prefix(app(z0, z1))) → c35(PREFIX(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(prefix(nil)) → c35(PREFIX(ok(nil)), PROPER(nil)) 242.33/77.51
PROPER(prefix(cons(z0, z1))) → c35(PREFIX(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(prefix(from(z0))) → c35(PREFIX(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(prefix(s(z0))) → c35(PREFIX(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(prefix(zWadr(z0, z1))) → c35(PREFIX(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(prefix(prefix(z0))) → c35(PREFIX(prefix(proper(z0))), PROPER(prefix(z0)))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, TOP, PROPER

Compound Symbols:

c7, c8, c12, c13, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c36, c37, c2, c6, c, c9, c10, c11, c14, c29, c29, c31, c31, c32, c32, c33, c33, c34, c34, c35

242.33/77.51
242.33/77.51

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

Removed 1 trailing tuple parts
242.33/77.51
242.33/77.51

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 242.33/77.51
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 242.33/77.51
active(from(z0)) → mark(cons(z0, from(s(z0)))) 242.33/77.51
active(zWadr(nil, z0)) → mark(nil) 242.33/77.51
active(zWadr(z0, nil)) → mark(nil) 242.33/77.51
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 242.33/77.51
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 242.33/77.51
active(app(z0, z1)) → app(active(z0), z1) 242.33/77.51
active(app(z0, z1)) → app(z0, active(z1)) 242.33/77.51
active(cons(z0, z1)) → cons(active(z0), z1) 242.33/77.51
active(from(z0)) → from(active(z0)) 242.33/77.51
active(s(z0)) → s(active(z0)) 242.33/77.51
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 242.33/77.51
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 242.33/77.51
active(prefix(z0)) → prefix(active(z0)) 242.33/77.51
app(mark(z0), z1) → mark(app(z0, z1)) 242.33/77.51
app(z0, mark(z1)) → mark(app(z0, z1)) 242.33/77.51
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 242.33/77.51
cons(mark(z0), z1) → mark(cons(z0, z1)) 242.33/77.51
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 242.33/77.51
from(mark(z0)) → mark(from(z0)) 242.33/77.51
from(ok(z0)) → ok(from(z0)) 242.33/77.51
s(mark(z0)) → mark(s(z0)) 242.33/77.51
s(ok(z0)) → ok(s(z0)) 242.33/77.51
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 242.33/77.51
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 242.33/77.51
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 242.33/77.51
prefix(mark(z0)) → mark(prefix(z0)) 242.33/77.51
prefix(ok(z0)) → ok(prefix(z0)) 242.33/77.51
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 242.33/77.51
proper(nil) → ok(nil) 242.33/77.51
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 242.33/77.51
proper(from(z0)) → from(proper(z0)) 242.33/77.51
proper(s(z0)) → s(proper(z0)) 242.33/77.51
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 242.33/77.51
proper(prefix(z0)) → prefix(proper(z0)) 242.33/77.51
top(mark(z0)) → top(proper(z0)) 242.33/77.51
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 242.33/77.51
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 242.33/77.51
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 242.33/77.51
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 242.33/77.51
APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.51
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.51
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.51
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.51
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.51
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.51
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.51
S(mark(z0)) → c22(S(z0)) 242.33/77.51
S(ok(z0)) → c23(S(z0)) 242.33/77.51
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.51
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.51
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.51
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.51
PREFIX(ok(z0)) → c28(PREFIX(z0)) 242.33/77.51
TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) 242.33/77.51
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 242.33/77.51
ACTIVE(from(z0)) → c2(S(z0)) 242.33/77.51
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 242.33/77.51
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 242.33/77.51
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 242.33/77.51
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(from(nil)) → c32(FROM(ok(nil))) 242.33/77.51
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(s(nil)) → c33(S(ok(nil))) 242.33/77.51
PROPER(zWadr(x0, app(z0, z1))) → c34(ZWADR(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, cons(z0, z1))) → c34(ZWADR(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, from(z0))) → c34(ZWADR(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(zWadr(x0, s(z0))) → c34(ZWADR(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(zWadr(x0, zWadr(z0, z1))) → c34(ZWADR(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, prefix(z0))) → c34(ZWADR(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(zWadr(app(z0, z1), x1)) → c34(ZWADR(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(cons(z0, z1), x1)) → c34(ZWADR(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(from(z0), x1)) → c34(ZWADR(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(s(z0), x1)) → c34(ZWADR(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(zWadr(z0, z1), x1)) → c34(ZWADR(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(prefix(z0), x1)) → c34(ZWADR(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(x0, nil)) → c34(ZWADR(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(zWadr(nil, x1)) → c34(ZWADR(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(prefix(app(z0, z1))) → c35(PREFIX(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(prefix(cons(z0, z1))) → c35(PREFIX(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(prefix(from(z0))) → c35(PREFIX(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(prefix(s(z0))) → c35(PREFIX(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(prefix(zWadr(z0, z1))) → c35(PREFIX(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(prefix(prefix(z0))) → c35(PREFIX(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(prefix(nil)) → c35(PREFIX(ok(nil)))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 242.33/77.51
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 242.33/77.51
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 242.33/77.51
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 242.33/77.51
APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.51
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.51
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.51
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.51
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.51
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.51
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.51
S(mark(z0)) → c22(S(z0)) 242.33/77.51
S(ok(z0)) → c23(S(z0)) 242.33/77.51
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.51
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.51
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.51
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.51
PREFIX(ok(z0)) → c28(PREFIX(z0)) 242.33/77.51
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 242.33/77.51
ACTIVE(from(z0)) → c2(S(z0)) 242.33/77.51
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 242.33/77.51
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 242.33/77.51
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 242.33/77.51
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(from(nil)) → c32(FROM(ok(nil))) 242.33/77.51
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(s(nil)) → c33(S(ok(nil))) 242.33/77.51
PROPER(zWadr(x0, app(z0, z1))) → c34(ZWADR(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, cons(z0, z1))) → c34(ZWADR(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, from(z0))) → c34(ZWADR(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(zWadr(x0, s(z0))) → c34(ZWADR(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(zWadr(x0, zWadr(z0, z1))) → c34(ZWADR(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, prefix(z0))) → c34(ZWADR(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(zWadr(app(z0, z1), x1)) → c34(ZWADR(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(cons(z0, z1), x1)) → c34(ZWADR(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(from(z0), x1)) → c34(ZWADR(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(s(z0), x1)) → c34(ZWADR(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(zWadr(z0, z1), x1)) → c34(ZWADR(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(prefix(z0), x1)) → c34(ZWADR(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(x0, nil)) → c34(ZWADR(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(zWadr(nil, x1)) → c34(ZWADR(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(prefix(app(z0, z1))) → c35(PREFIX(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(prefix(cons(z0, z1))) → c35(PREFIX(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(prefix(from(z0))) → c35(PREFIX(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(prefix(s(z0))) → c35(PREFIX(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(prefix(zWadr(z0, z1))) → c35(PREFIX(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(prefix(prefix(z0))) → c35(PREFIX(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(prefix(nil)) → c35(PREFIX(ok(nil)))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, TOP, PROPER

Compound Symbols:

c7, c8, c12, c13, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c36, c37, c2, c6, c, c9, c10, c11, c14, c29, c29, c31, c31, c32, c32, c33, c33, c34, c34, c35, c35

242.33/77.51
242.33/77.51

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

Use narrowing to replace TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0)) by

TOP(mark(app(z0, z1))) → c36(TOP(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
TOP(mark(nil)) → c36(TOP(ok(nil)), PROPER(nil)) 242.33/77.51
TOP(mark(cons(z0, z1))) → c36(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
TOP(mark(from(z0))) → c36(TOP(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
TOP(mark(s(z0))) → c36(TOP(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
TOP(mark(zWadr(z0, z1))) → c36(TOP(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
TOP(mark(prefix(z0))) → c36(TOP(prefix(proper(z0))), PROPER(prefix(z0)))
242.33/77.51
242.33/77.51

(42) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 242.33/77.51
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 242.33/77.51
active(from(z0)) → mark(cons(z0, from(s(z0)))) 242.33/77.51
active(zWadr(nil, z0)) → mark(nil) 242.33/77.51
active(zWadr(z0, nil)) → mark(nil) 242.33/77.51
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 242.33/77.51
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 242.33/77.51
active(app(z0, z1)) → app(active(z0), z1) 242.33/77.51
active(app(z0, z1)) → app(z0, active(z1)) 242.33/77.51
active(cons(z0, z1)) → cons(active(z0), z1) 242.33/77.51
active(from(z0)) → from(active(z0)) 242.33/77.51
active(s(z0)) → s(active(z0)) 242.33/77.51
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 242.33/77.51
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 242.33/77.51
active(prefix(z0)) → prefix(active(z0)) 242.33/77.51
app(mark(z0), z1) → mark(app(z0, z1)) 242.33/77.51
app(z0, mark(z1)) → mark(app(z0, z1)) 242.33/77.51
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 242.33/77.51
cons(mark(z0), z1) → mark(cons(z0, z1)) 242.33/77.51
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 242.33/77.51
from(mark(z0)) → mark(from(z0)) 242.33/77.51
from(ok(z0)) → ok(from(z0)) 242.33/77.51
s(mark(z0)) → mark(s(z0)) 242.33/77.51
s(ok(z0)) → ok(s(z0)) 242.33/77.51
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 242.33/77.51
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 242.33/77.51
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 242.33/77.51
prefix(mark(z0)) → mark(prefix(z0)) 242.33/77.51
prefix(ok(z0)) → ok(prefix(z0)) 242.33/77.51
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 242.33/77.51
proper(nil) → ok(nil) 242.33/77.51
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 242.33/77.51
proper(from(z0)) → from(proper(z0)) 242.33/77.51
proper(s(z0)) → s(proper(z0)) 242.33/77.51
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 242.33/77.51
proper(prefix(z0)) → prefix(proper(z0)) 242.33/77.51
top(mark(z0)) → top(proper(z0)) 242.33/77.51
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 242.33/77.51
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 242.33/77.51
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 242.33/77.51
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 242.33/77.51
APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.51
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.51
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.51
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.51
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.51
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.51
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.51
S(mark(z0)) → c22(S(z0)) 242.33/77.51
S(ok(z0)) → c23(S(z0)) 242.33/77.51
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.51
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.51
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.51
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.51
PREFIX(ok(z0)) → c28(PREFIX(z0)) 242.33/77.51
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 242.33/77.51
ACTIVE(from(z0)) → c2(S(z0)) 242.33/77.51
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 242.33/77.51
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 242.33/77.51
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 242.33/77.51
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(from(nil)) → c32(FROM(ok(nil))) 242.33/77.51
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(s(nil)) → c33(S(ok(nil))) 242.33/77.51
PROPER(zWadr(x0, app(z0, z1))) → c34(ZWADR(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, cons(z0, z1))) → c34(ZWADR(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, from(z0))) → c34(ZWADR(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(zWadr(x0, s(z0))) → c34(ZWADR(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(zWadr(x0, zWadr(z0, z1))) → c34(ZWADR(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, prefix(z0))) → c34(ZWADR(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(zWadr(app(z0, z1), x1)) → c34(ZWADR(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(cons(z0, z1), x1)) → c34(ZWADR(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(from(z0), x1)) → c34(ZWADR(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(s(z0), x1)) → c34(ZWADR(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(zWadr(z0, z1), x1)) → c34(ZWADR(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(prefix(z0), x1)) → c34(ZWADR(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(x0, nil)) → c34(ZWADR(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(zWadr(nil, x1)) → c34(ZWADR(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(prefix(app(z0, z1))) → c35(PREFIX(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(prefix(cons(z0, z1))) → c35(PREFIX(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(prefix(from(z0))) → c35(PREFIX(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(prefix(s(z0))) → c35(PREFIX(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(prefix(zWadr(z0, z1))) → c35(PREFIX(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(prefix(prefix(z0))) → c35(PREFIX(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(prefix(nil)) → c35(PREFIX(ok(nil))) 242.33/77.51
TOP(mark(app(z0, z1))) → c36(TOP(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
TOP(mark(nil)) → c36(TOP(ok(nil)), PROPER(nil)) 242.33/77.51
TOP(mark(cons(z0, z1))) → c36(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
TOP(mark(from(z0))) → c36(TOP(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
TOP(mark(s(z0))) → c36(TOP(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
TOP(mark(zWadr(z0, z1))) → c36(TOP(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
TOP(mark(prefix(z0))) → c36(TOP(prefix(proper(z0))), PROPER(prefix(z0)))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 242.33/77.51
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 242.33/77.51
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 242.33/77.51
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 242.33/77.51
APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.51
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.51
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.51
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.51
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.51
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.51
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.51
S(mark(z0)) → c22(S(z0)) 242.33/77.51
S(ok(z0)) → c23(S(z0)) 242.33/77.51
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.51
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.51
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.51
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.51
PREFIX(ok(z0)) → c28(PREFIX(z0)) 242.33/77.51
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 242.33/77.51
ACTIVE(from(z0)) → c2(S(z0)) 242.33/77.51
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 242.33/77.51
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 242.33/77.51
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 242.33/77.51
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(from(nil)) → c32(FROM(ok(nil))) 242.33/77.51
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(s(nil)) → c33(S(ok(nil))) 242.33/77.51
PROPER(zWadr(x0, app(z0, z1))) → c34(ZWADR(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, cons(z0, z1))) → c34(ZWADR(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, from(z0))) → c34(ZWADR(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(zWadr(x0, s(z0))) → c34(ZWADR(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(zWadr(x0, zWadr(z0, z1))) → c34(ZWADR(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, prefix(z0))) → c34(ZWADR(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(zWadr(app(z0, z1), x1)) → c34(ZWADR(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(cons(z0, z1), x1)) → c34(ZWADR(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(from(z0), x1)) → c34(ZWADR(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(s(z0), x1)) → c34(ZWADR(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(zWadr(z0, z1), x1)) → c34(ZWADR(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(prefix(z0), x1)) → c34(ZWADR(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(x0, nil)) → c34(ZWADR(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(zWadr(nil, x1)) → c34(ZWADR(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(prefix(app(z0, z1))) → c35(PREFIX(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(prefix(cons(z0, z1))) → c35(PREFIX(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(prefix(from(z0))) → c35(PREFIX(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(prefix(s(z0))) → c35(PREFIX(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(prefix(zWadr(z0, z1))) → c35(PREFIX(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(prefix(prefix(z0))) → c35(PREFIX(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(prefix(nil)) → c35(PREFIX(ok(nil)))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, TOP, PROPER

Compound Symbols:

c7, c8, c12, c13, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c37, c2, c6, c, c9, c10, c11, c14, c29, c29, c31, c31, c32, c32, c33, c33, c34, c34, c35, c35, c36

242.33/77.51
242.33/77.51

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

Removed 1 trailing tuple parts
242.33/77.51
242.33/77.51

(44) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 242.33/77.51
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 242.33/77.51
active(from(z0)) → mark(cons(z0, from(s(z0)))) 242.33/77.51
active(zWadr(nil, z0)) → mark(nil) 242.33/77.51
active(zWadr(z0, nil)) → mark(nil) 242.33/77.51
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 242.33/77.51
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 242.33/77.51
active(app(z0, z1)) → app(active(z0), z1) 242.33/77.51
active(app(z0, z1)) → app(z0, active(z1)) 242.33/77.51
active(cons(z0, z1)) → cons(active(z0), z1) 242.33/77.51
active(from(z0)) → from(active(z0)) 242.33/77.51
active(s(z0)) → s(active(z0)) 242.33/77.51
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 242.33/77.51
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 242.33/77.51
active(prefix(z0)) → prefix(active(z0)) 242.33/77.51
app(mark(z0), z1) → mark(app(z0, z1)) 242.33/77.51
app(z0, mark(z1)) → mark(app(z0, z1)) 242.33/77.51
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 242.33/77.51
cons(mark(z0), z1) → mark(cons(z0, z1)) 242.33/77.51
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 242.33/77.51
from(mark(z0)) → mark(from(z0)) 242.33/77.51
from(ok(z0)) → ok(from(z0)) 242.33/77.51
s(mark(z0)) → mark(s(z0)) 242.33/77.51
s(ok(z0)) → ok(s(z0)) 242.33/77.51
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 242.33/77.51
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 242.33/77.51
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 242.33/77.51
prefix(mark(z0)) → mark(prefix(z0)) 242.33/77.51
prefix(ok(z0)) → ok(prefix(z0)) 242.33/77.51
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 242.33/77.51
proper(nil) → ok(nil) 242.33/77.51
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 242.33/77.51
proper(from(z0)) → from(proper(z0)) 242.33/77.51
proper(s(z0)) → s(proper(z0)) 242.33/77.51
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 242.33/77.51
proper(prefix(z0)) → prefix(proper(z0)) 242.33/77.51
top(mark(z0)) → top(proper(z0)) 242.33/77.51
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 242.33/77.51
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 242.33/77.51
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 242.33/77.51
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 242.33/77.51
APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.51
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.51
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.51
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.51
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.51
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.51
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.51
S(mark(z0)) → c22(S(z0)) 242.33/77.51
S(ok(z0)) → c23(S(z0)) 242.33/77.51
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.51
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.51
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.51
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.51
PREFIX(ok(z0)) → c28(PREFIX(z0)) 242.33/77.51
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 242.33/77.51
ACTIVE(from(z0)) → c2(S(z0)) 242.33/77.51
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 242.33/77.51
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 242.33/77.51
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 242.33/77.51
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(from(nil)) → c32(FROM(ok(nil))) 242.33/77.51
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(s(nil)) → c33(S(ok(nil))) 242.33/77.51
PROPER(zWadr(x0, app(z0, z1))) → c34(ZWADR(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, cons(z0, z1))) → c34(ZWADR(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, from(z0))) → c34(ZWADR(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(zWadr(x0, s(z0))) → c34(ZWADR(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(zWadr(x0, zWadr(z0, z1))) → c34(ZWADR(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, prefix(z0))) → c34(ZWADR(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(zWadr(app(z0, z1), x1)) → c34(ZWADR(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(cons(z0, z1), x1)) → c34(ZWADR(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(from(z0), x1)) → c34(ZWADR(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(s(z0), x1)) → c34(ZWADR(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(zWadr(z0, z1), x1)) → c34(ZWADR(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(prefix(z0), x1)) → c34(ZWADR(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(x0, nil)) → c34(ZWADR(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(zWadr(nil, x1)) → c34(ZWADR(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(prefix(app(z0, z1))) → c35(PREFIX(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(prefix(cons(z0, z1))) → c35(PREFIX(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(prefix(from(z0))) → c35(PREFIX(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(prefix(s(z0))) → c35(PREFIX(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(prefix(zWadr(z0, z1))) → c35(PREFIX(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(prefix(prefix(z0))) → c35(PREFIX(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(prefix(nil)) → c35(PREFIX(ok(nil))) 242.33/77.51
TOP(mark(app(z0, z1))) → c36(TOP(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
TOP(mark(cons(z0, z1))) → c36(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
TOP(mark(from(z0))) → c36(TOP(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
TOP(mark(s(z0))) → c36(TOP(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
TOP(mark(zWadr(z0, z1))) → c36(TOP(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
TOP(mark(prefix(z0))) → c36(TOP(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
TOP(mark(nil)) → c36(TOP(ok(nil)))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 242.33/77.51
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 242.33/77.51
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 242.33/77.51
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 242.33/77.51
APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.51
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.51
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.51
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.51
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.51
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.51
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.51
S(mark(z0)) → c22(S(z0)) 242.33/77.51
S(ok(z0)) → c23(S(z0)) 242.33/77.51
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.51
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.51
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.51
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.51
PREFIX(ok(z0)) → c28(PREFIX(z0)) 242.33/77.51
TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) 242.33/77.51
ACTIVE(from(z0)) → c2(S(z0)) 242.33/77.51
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 242.33/77.51
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 242.33/77.51
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 242.33/77.51
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 242.33/77.51
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.51
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.51
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.51
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.51
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 242.33/77.51
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.51
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.51
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.51
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.51
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.51
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(from(nil)) → c32(FROM(ok(nil))) 242.33/77.51
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.51
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 242.33/77.51
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 242.33/77.51
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.51
PROPER(s(nil)) → c33(S(ok(nil))) 242.33/77.51
PROPER(zWadr(x0, app(z0, z1))) → c34(ZWADR(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, cons(z0, z1))) → c34(ZWADR(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, from(z0))) → c34(ZWADR(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.51
PROPER(zWadr(x0, s(z0))) → c34(ZWADR(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.51
PROPER(zWadr(x0, zWadr(z0, z1))) → c34(ZWADR(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.51
PROPER(zWadr(x0, prefix(z0))) → c34(ZWADR(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.51
PROPER(zWadr(app(z0, z1), x1)) → c34(ZWADR(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(cons(z0, z1), x1)) → c34(ZWADR(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.51
PROPER(zWadr(from(z0), x1)) → c34(ZWADR(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(s(z0), x1)) → c34(ZWADR(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(zWadr(z0, z1), x1)) → c34(ZWADR(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(prefix(z0), x1)) → c34(ZWADR(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(x0, nil)) → c34(ZWADR(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.52
PROPER(zWadr(nil, x1)) → c34(ZWADR(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.52
PROPER(prefix(app(z0, z1))) → c35(PREFIX(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.52
PROPER(prefix(cons(z0, z1))) → c35(PREFIX(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(prefix(from(z0))) → c35(PREFIX(from(proper(z0))), PROPER(from(z0))) 242.33/77.52
PROPER(prefix(s(z0))) → c35(PREFIX(s(proper(z0))), PROPER(s(z0))) 242.33/77.52
PROPER(prefix(zWadr(z0, z1))) → c35(PREFIX(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(prefix(prefix(z0))) → c35(PREFIX(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.52
PROPER(prefix(nil)) → c35(PREFIX(ok(nil)))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, TOP, PROPER

Compound Symbols:

c7, c8, c12, c13, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c37, c2, c6, c, c9, c10, c11, c14, c29, c29, c31, c31, c32, c32, c33, c33, c34, c34, c35, c35, c36, c36

242.33/77.52
242.33/77.52

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

Use narrowing to replace TOP(ok(z0)) → c37(TOP(active(z0)), ACTIVE(z0)) by

TOP(ok(app(nil, z0))) → c37(TOP(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.52
TOP(ok(app(cons(z0, z1), z2))) → c37(TOP(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.52
TOP(ok(from(z0))) → c37(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.52
TOP(ok(zWadr(nil, z0))) → c37(TOP(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.52
TOP(ok(zWadr(z0, nil))) → c37(TOP(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.52
TOP(ok(zWadr(cons(z0, z1), cons(z2, z3)))) → c37(TOP(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.52
TOP(ok(prefix(z0))) → c37(TOP(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.52
TOP(ok(app(z0, z1))) → c37(TOP(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.52
TOP(ok(app(z0, z1))) → c37(TOP(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.52
TOP(ok(cons(z0, z1))) → c37(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.52
TOP(ok(from(z0))) → c37(TOP(from(active(z0))), ACTIVE(from(z0))) 242.33/77.52
TOP(ok(s(z0))) → c37(TOP(s(active(z0))), ACTIVE(s(z0))) 242.33/77.52
TOP(ok(zWadr(z0, z1))) → c37(TOP(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.52
TOP(ok(zWadr(z0, z1))) → c37(TOP(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.52
TOP(ok(prefix(z0))) → c37(TOP(prefix(active(z0))), ACTIVE(prefix(z0)))
242.33/77.52
242.33/77.52

(46) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 242.33/77.52
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 242.33/77.52
active(from(z0)) → mark(cons(z0, from(s(z0)))) 242.33/77.52
active(zWadr(nil, z0)) → mark(nil) 242.33/77.52
active(zWadr(z0, nil)) → mark(nil) 242.33/77.52
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 242.33/77.52
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 242.33/77.52
active(app(z0, z1)) → app(active(z0), z1) 242.33/77.52
active(app(z0, z1)) → app(z0, active(z1)) 242.33/77.52
active(cons(z0, z1)) → cons(active(z0), z1) 242.33/77.52
active(from(z0)) → from(active(z0)) 242.33/77.52
active(s(z0)) → s(active(z0)) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 242.33/77.52
active(prefix(z0)) → prefix(active(z0)) 242.33/77.52
app(mark(z0), z1) → mark(app(z0, z1)) 242.33/77.52
app(z0, mark(z1)) → mark(app(z0, z1)) 242.33/77.52
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 242.33/77.52
cons(mark(z0), z1) → mark(cons(z0, z1)) 242.33/77.52
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 242.33/77.52
from(mark(z0)) → mark(from(z0)) 242.33/77.52
from(ok(z0)) → ok(from(z0)) 242.33/77.52
s(mark(z0)) → mark(s(z0)) 242.33/77.52
s(ok(z0)) → ok(s(z0)) 242.33/77.52
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 242.33/77.52
prefix(mark(z0)) → mark(prefix(z0)) 242.33/77.52
prefix(ok(z0)) → ok(prefix(z0)) 242.33/77.52
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 242.33/77.52
proper(nil) → ok(nil) 242.33/77.52
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 242.33/77.52
proper(from(z0)) → from(proper(z0)) 242.33/77.52
proper(s(z0)) → s(proper(z0)) 242.33/77.52
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 242.33/77.52
proper(prefix(z0)) → prefix(proper(z0)) 242.33/77.52
top(mark(z0)) → top(proper(z0)) 242.33/77.52
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 242.33/77.52
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 242.33/77.52
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 242.33/77.52
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 242.33/77.52
APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0)) 242.33/77.52
ACTIVE(from(z0)) → c2(S(z0)) 242.33/77.52
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 242.33/77.52
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 242.33/77.52
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 242.33/77.52
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 242.33/77.52
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 242.33/77.52
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 242.33/77.52
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 242.33/77.52
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.52
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 242.33/77.52
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 242.33/77.52
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.52
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 242.33/77.52
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 242.33/77.52
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.52
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.52
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.52
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.52
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.52
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.52
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 242.33/77.52
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.52
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.52
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.52
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.52
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.52
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.52
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 242.33/77.52
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.52
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.52
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.52
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.52
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.52
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.52
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 242.33/77.52
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.52
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.52
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.52
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.52
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.52
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.52
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.52
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.52
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.52
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.52
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.52
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.52
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.52
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.52
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.52
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.52
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.52
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.52
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.52
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.52
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 242.33/77.52
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 242.33/77.52
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.52
PROPER(from(nil)) → c32(FROM(ok(nil))) 242.33/77.52
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.52
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 242.33/77.52
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 242.33/77.52
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.52
PROPER(s(nil)) → c33(S(ok(nil))) 242.33/77.52
PROPER(zWadr(x0, app(z0, z1))) → c34(ZWADR(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.52
PROPER(zWadr(x0, cons(z0, z1))) → c34(ZWADR(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(zWadr(x0, from(z0))) → c34(ZWADR(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.52
PROPER(zWadr(x0, s(z0))) → c34(ZWADR(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.52
PROPER(zWadr(x0, zWadr(z0, z1))) → c34(ZWADR(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(zWadr(x0, prefix(z0))) → c34(ZWADR(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.52
PROPER(zWadr(app(z0, z1), x1)) → c34(ZWADR(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(cons(z0, z1), x1)) → c34(ZWADR(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(from(z0), x1)) → c34(ZWADR(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(s(z0), x1)) → c34(ZWADR(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(zWadr(z0, z1), x1)) → c34(ZWADR(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(prefix(z0), x1)) → c34(ZWADR(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(x0, nil)) → c34(ZWADR(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.52
PROPER(zWadr(nil, x1)) → c34(ZWADR(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.52
PROPER(prefix(app(z0, z1))) → c35(PREFIX(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.52
PROPER(prefix(cons(z0, z1))) → c35(PREFIX(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(prefix(from(z0))) → c35(PREFIX(from(proper(z0))), PROPER(from(z0))) 242.33/77.52
PROPER(prefix(s(z0))) → c35(PREFIX(s(proper(z0))), PROPER(s(z0))) 242.33/77.52
PROPER(prefix(zWadr(z0, z1))) → c35(PREFIX(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(prefix(prefix(z0))) → c35(PREFIX(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.52
PROPER(prefix(nil)) → c35(PREFIX(ok(nil))) 242.33/77.52
TOP(mark(app(z0, z1))) → c36(TOP(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.52
TOP(mark(cons(z0, z1))) → c36(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.52
TOP(mark(from(z0))) → c36(TOP(from(proper(z0))), PROPER(from(z0))) 242.33/77.52
TOP(mark(s(z0))) → c36(TOP(s(proper(z0))), PROPER(s(z0))) 242.33/77.52
TOP(mark(zWadr(z0, z1))) → c36(TOP(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.52
TOP(mark(prefix(z0))) → c36(TOP(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.52
TOP(mark(nil)) → c36(TOP(ok(nil))) 242.33/77.52
TOP(ok(app(nil, z0))) → c37(TOP(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.52
TOP(ok(app(cons(z0, z1), z2))) → c37(TOP(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.52
TOP(ok(from(z0))) → c37(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.52
TOP(ok(zWadr(nil, z0))) → c37(TOP(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.52
TOP(ok(zWadr(z0, nil))) → c37(TOP(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.52
TOP(ok(zWadr(cons(z0, z1), cons(z2, z3)))) → c37(TOP(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.52
TOP(ok(prefix(z0))) → c37(TOP(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.52
TOP(ok(app(z0, z1))) → c37(TOP(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.52
TOP(ok(app(z0, z1))) → c37(TOP(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.52
TOP(ok(cons(z0, z1))) → c37(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.52
TOP(ok(from(z0))) → c37(TOP(from(active(z0))), ACTIVE(from(z0))) 242.33/77.52
TOP(ok(s(z0))) → c37(TOP(s(active(z0))), ACTIVE(s(z0))) 242.33/77.52
TOP(ok(zWadr(z0, z1))) → c37(TOP(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.52
TOP(ok(zWadr(z0, z1))) → c37(TOP(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.52
TOP(ok(prefix(z0))) → c37(TOP(prefix(active(z0))), ACTIVE(prefix(z0)))
S tuples:

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 242.33/77.52
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 242.33/77.52
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 242.33/77.52
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 242.33/77.52
APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0)) 242.33/77.52
ACTIVE(from(z0)) → c2(S(z0)) 242.33/77.52
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 242.33/77.52
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 242.33/77.52
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 242.33/77.52
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 242.33/77.52
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 242.33/77.52
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 242.33/77.52
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 242.33/77.52
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.52
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 242.33/77.52
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 242.33/77.52
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.52
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 242.33/77.52
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 242.33/77.52
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.52
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.52
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.52
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.52
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.52
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.52
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 242.33/77.52
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.52
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.52
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.52
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.52
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.52
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.52
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 242.33/77.52
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.52
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.52
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.52
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.52
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.52
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.52
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 242.33/77.52
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.52
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.52
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.52
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.52
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.52
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.52
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.52
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.52
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.52
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.52
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.52
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.52
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.52
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.52
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.52
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.52
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.52
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.52
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.52
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.52
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 242.33/77.52
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 242.33/77.52
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.52
PROPER(from(nil)) → c32(FROM(ok(nil))) 242.33/77.52
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.52
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 242.33/77.52
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 242.33/77.52
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.52
PROPER(s(nil)) → c33(S(ok(nil))) 242.33/77.52
PROPER(zWadr(x0, app(z0, z1))) → c34(ZWADR(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.52
PROPER(zWadr(x0, cons(z0, z1))) → c34(ZWADR(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(zWadr(x0, from(z0))) → c34(ZWADR(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.52
PROPER(zWadr(x0, s(z0))) → c34(ZWADR(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.52
PROPER(zWadr(x0, zWadr(z0, z1))) → c34(ZWADR(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(zWadr(x0, prefix(z0))) → c34(ZWADR(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.52
PROPER(zWadr(app(z0, z1), x1)) → c34(ZWADR(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(cons(z0, z1), x1)) → c34(ZWADR(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(from(z0), x1)) → c34(ZWADR(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(s(z0), x1)) → c34(ZWADR(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(zWadr(z0, z1), x1)) → c34(ZWADR(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(prefix(z0), x1)) → c34(ZWADR(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(x0, nil)) → c34(ZWADR(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.52
PROPER(zWadr(nil, x1)) → c34(ZWADR(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.52
PROPER(prefix(app(z0, z1))) → c35(PREFIX(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.52
PROPER(prefix(cons(z0, z1))) → c35(PREFIX(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(prefix(from(z0))) → c35(PREFIX(from(proper(z0))), PROPER(from(z0))) 242.33/77.52
PROPER(prefix(s(z0))) → c35(PREFIX(s(proper(z0))), PROPER(s(z0))) 242.33/77.52
PROPER(prefix(zWadr(z0, z1))) → c35(PREFIX(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(prefix(prefix(z0))) → c35(PREFIX(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.52
PROPER(prefix(nil)) → c35(PREFIX(ok(nil))) 242.33/77.52
TOP(ok(app(nil, z0))) → c37(TOP(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.52
TOP(ok(app(cons(z0, z1), z2))) → c37(TOP(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.52
TOP(ok(from(z0))) → c37(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.52
TOP(ok(zWadr(nil, z0))) → c37(TOP(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.52
TOP(ok(zWadr(z0, nil))) → c37(TOP(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.52
TOP(ok(zWadr(cons(z0, z1), cons(z2, z3)))) → c37(TOP(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.52
TOP(ok(prefix(z0))) → c37(TOP(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.52
TOP(ok(app(z0, z1))) → c37(TOP(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.52
TOP(ok(app(z0, z1))) → c37(TOP(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.52
TOP(ok(cons(z0, z1))) → c37(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.52
TOP(ok(from(z0))) → c37(TOP(from(active(z0))), ACTIVE(from(z0))) 242.33/77.52
TOP(ok(s(z0))) → c37(TOP(s(active(z0))), ACTIVE(s(z0))) 242.33/77.52
TOP(ok(zWadr(z0, z1))) → c37(TOP(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.52
TOP(ok(zWadr(z0, z1))) → c37(TOP(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.52
TOP(ok(prefix(z0))) → c37(TOP(prefix(active(z0))), ACTIVE(prefix(z0)))
K tuples:

TOP(mark(z0)) → c36(TOP(proper(z0)), PROPER(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

ACTIVE, APP, CONS, FROM, S, ZWADR, PREFIX, PROPER, TOP

Compound Symbols:

c7, c8, c12, c13, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c2, c6, c, c9, c10, c11, c14, c29, c29, c31, c31, c32, c32, c33, c33, c34, c34, c35, c35, c36, c36, c37

242.33/77.52
242.33/77.52

(47) CdtUnreachableProof (EQUIVALENT transformation)

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

ACTIVE(app(z0, z1)) → c7(APP(active(z0), z1), ACTIVE(z0)) 242.33/77.52
ACTIVE(app(z0, z1)) → c8(APP(z0, active(z1)), ACTIVE(z1)) 242.33/77.52
ACTIVE(zWadr(z0, z1)) → c12(ZWADR(active(z0), z1), ACTIVE(z0)) 242.33/77.52
ACTIVE(zWadr(z0, z1)) → c13(ZWADR(z0, active(z1)), ACTIVE(z1)) 242.33/77.52
ACTIVE(from(z0)) → c2(S(z0)) 242.33/77.52
ACTIVE(prefix(z0)) → c6(PREFIX(z0)) 242.33/77.52
ACTIVE(app(cons(z0, z1), z2)) → c(CONS(z0, app(z1, z2))) 242.33/77.52
ACTIVE(app(cons(z0, z1), z2)) → c(APP(z1, z2)) 242.33/77.52
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(APP(z2, cons(z0, nil))) 242.33/77.52
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(CONS(z0, nil)) 242.33/77.52
ACTIVE(zWadr(cons(z0, z1), cons(z2, z3))) → c(ZWADR(z1, z3)) 242.33/77.52
ACTIVE(cons(app(nil, z0), x1)) → c9(CONS(mark(z0), x1), ACTIVE(app(nil, z0))) 242.33/77.52
ACTIVE(cons(app(cons(z0, z1), z2), x1)) → c9(CONS(mark(cons(z0, app(z1, z2))), x1), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.52
ACTIVE(cons(from(z0), x1)) → c9(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(cons(zWadr(nil, z0), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(nil, z0))) 242.33/77.52
ACTIVE(cons(zWadr(z0, nil), x1)) → c9(CONS(mark(nil), x1), ACTIVE(zWadr(z0, nil))) 242.33/77.52
ACTIVE(cons(zWadr(cons(z0, z1), cons(z2, z3)), x1)) → c9(CONS(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))), x1), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.52
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(mark(cons(nil, zWadr(z0, prefix(z0)))), x1), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(active(z0), z1), x1), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(cons(app(z0, z1), x1)) → c9(CONS(app(z0, active(z1)), x1), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(cons(cons(z0, z1), x1)) → c9(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 242.33/77.52
ACTIVE(cons(from(z0), x1)) → c9(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(cons(s(z0), x1)) → c9(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 242.33/77.52
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(active(z0), z1), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(cons(zWadr(z0, z1), x1)) → c9(CONS(zWadr(z0, active(z1)), x1), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(cons(prefix(z0), x1)) → c9(CONS(prefix(active(z0)), x1), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(from(app(nil, z0))) → c10(FROM(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.52
ACTIVE(from(app(cons(z0, z1), z2))) → c10(FROM(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.52
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(from(zWadr(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.52
ACTIVE(from(zWadr(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.52
ACTIVE(from(zWadr(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.52
ACTIVE(from(prefix(z0))) → c10(FROM(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(from(app(z0, z1))) → c10(FROM(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(from(app(z0, z1))) → c10(FROM(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.52
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0))) 242.33/77.52
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(from(zWadr(z0, z1))) → c10(FROM(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(from(prefix(z0))) → c10(FROM(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(s(app(nil, z0))) → c11(S(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.52
ACTIVE(s(app(cons(z0, z1), z2))) → c11(S(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.52
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(s(zWadr(nil, z0))) → c11(S(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.52
ACTIVE(s(zWadr(z0, nil))) → c11(S(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.52
ACTIVE(s(zWadr(cons(z0, z1), cons(z2, z3)))) → c11(S(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.52
ACTIVE(s(prefix(z0))) → c11(S(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(s(app(z0, z1))) → c11(S(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(s(app(z0, z1))) → c11(S(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.52
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 242.33/77.52
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(s(zWadr(z0, z1))) → c11(S(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(s(prefix(z0))) → c11(S(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(prefix(app(nil, z0))) → c14(PREFIX(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.52
ACTIVE(prefix(app(cons(z0, z1), z2))) → c14(PREFIX(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.52
ACTIVE(prefix(from(z0))) → c14(PREFIX(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(prefix(zWadr(nil, z0))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.52
ACTIVE(prefix(zWadr(z0, nil))) → c14(PREFIX(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.52
ACTIVE(prefix(zWadr(cons(z0, z1), cons(z2, z3)))) → c14(PREFIX(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.52
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.52
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(prefix(app(z0, z1))) → c14(PREFIX(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.52
ACTIVE(prefix(cons(z0, z1))) → c14(PREFIX(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.52
ACTIVE(prefix(from(z0))) → c14(PREFIX(from(active(z0))), ACTIVE(from(z0))) 242.33/77.52
ACTIVE(prefix(s(z0))) → c14(PREFIX(s(active(z0))), ACTIVE(s(z0))) 242.33/77.52
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(prefix(zWadr(z0, z1))) → c14(PREFIX(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.52
ACTIVE(prefix(prefix(z0))) → c14(PREFIX(prefix(active(z0))), ACTIVE(prefix(z0))) 242.33/77.52
PROPER(app(x0, app(z0, z1))) → c29(APP(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.52
PROPER(app(x0, cons(z0, z1))) → c29(APP(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(app(x0, from(z0))) → c29(APP(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.52
PROPER(app(x0, s(z0))) → c29(APP(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.52
PROPER(app(x0, zWadr(z0, z1))) → c29(APP(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(app(x0, prefix(z0))) → c29(APP(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.52
PROPER(app(app(z0, z1), x1)) → c29(APP(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(app(cons(z0, z1), x1)) → c29(APP(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(app(from(z0), x1)) → c29(APP(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.52
PROPER(app(s(z0), x1)) → c29(APP(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.52
PROPER(app(zWadr(z0, z1), x1)) → c29(APP(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(app(prefix(z0), x1)) → c29(APP(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.52
PROPER(app(x0, nil)) → c29(APP(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.52
PROPER(app(nil, x1)) → c29(APP(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.52
PROPER(cons(x0, app(z0, z1))) → c31(CONS(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.52
PROPER(cons(x0, cons(z0, z1))) → c31(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(cons(x0, from(z0))) → c31(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.52
PROPER(cons(x0, s(z0))) → c31(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.52
PROPER(cons(x0, zWadr(z0, z1))) → c31(CONS(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(cons(x0, prefix(z0))) → c31(CONS(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.52
PROPER(cons(app(z0, z1), x1)) → c31(CONS(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(cons(cons(z0, z1), x1)) → c31(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(cons(from(z0), x1)) → c31(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.52
PROPER(cons(s(z0), x1)) → c31(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.52
PROPER(cons(zWadr(z0, z1), x1)) → c31(CONS(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(cons(prefix(z0), x1)) → c31(CONS(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.52
PROPER(cons(x0, nil)) → c31(CONS(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.52
PROPER(cons(nil, x1)) → c31(CONS(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.52
PROPER(from(app(z0, z1))) → c32(FROM(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.52
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 242.33/77.52
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 242.33/77.52
PROPER(from(zWadr(z0, z1))) → c32(FROM(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(from(prefix(z0))) → c32(FROM(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.52
PROPER(from(nil)) → c32(FROM(ok(nil))) 242.33/77.52
PROPER(s(app(z0, z1))) → c33(S(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.52
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(s(from(z0))) → c33(S(from(proper(z0))), PROPER(from(z0))) 242.33/77.52
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 242.33/77.52
PROPER(s(zWadr(z0, z1))) → c33(S(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(s(prefix(z0))) → c33(S(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.52
PROPER(s(nil)) → c33(S(ok(nil))) 242.33/77.52
PROPER(zWadr(x0, app(z0, z1))) → c34(ZWADR(proper(x0), app(proper(z0), proper(z1))), PROPER(x0), PROPER(app(z0, z1))) 242.33/77.52
PROPER(zWadr(x0, cons(z0, z1))) → c34(ZWADR(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(zWadr(x0, from(z0))) → c34(ZWADR(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 242.33/77.52
PROPER(zWadr(x0, s(z0))) → c34(ZWADR(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 242.33/77.52
PROPER(zWadr(x0, zWadr(z0, z1))) → c34(ZWADR(proper(x0), zWadr(proper(z0), proper(z1))), PROPER(x0), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(zWadr(x0, prefix(z0))) → c34(ZWADR(proper(x0), prefix(proper(z0))), PROPER(x0), PROPER(prefix(z0))) 242.33/77.52
PROPER(zWadr(app(z0, z1), x1)) → c34(ZWADR(app(proper(z0), proper(z1)), proper(x1)), PROPER(app(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(cons(z0, z1), x1)) → c34(ZWADR(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(from(z0), x1)) → c34(ZWADR(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(s(z0), x1)) → c34(ZWADR(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(zWadr(z0, z1), x1)) → c34(ZWADR(zWadr(proper(z0), proper(z1)), proper(x1)), PROPER(zWadr(z0, z1)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(prefix(z0), x1)) → c34(ZWADR(prefix(proper(z0)), proper(x1)), PROPER(prefix(z0)), PROPER(x1)) 242.33/77.52
PROPER(zWadr(x0, nil)) → c34(ZWADR(proper(x0), ok(nil)), PROPER(x0)) 242.33/77.52
PROPER(zWadr(nil, x1)) → c34(ZWADR(ok(nil), proper(x1)), PROPER(x1)) 242.33/77.52
PROPER(prefix(app(z0, z1))) → c35(PREFIX(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.52
PROPER(prefix(cons(z0, z1))) → c35(PREFIX(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.52
PROPER(prefix(from(z0))) → c35(PREFIX(from(proper(z0))), PROPER(from(z0))) 242.33/77.52
PROPER(prefix(s(z0))) → c35(PREFIX(s(proper(z0))), PROPER(s(z0))) 242.33/77.52
PROPER(prefix(zWadr(z0, z1))) → c35(PREFIX(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.52
PROPER(prefix(prefix(z0))) → c35(PREFIX(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.52
PROPER(prefix(nil)) → c35(PREFIX(ok(nil))) 242.33/77.52
TOP(mark(app(z0, z1))) → c36(TOP(app(proper(z0), proper(z1))), PROPER(app(z0, z1))) 242.33/77.52
TOP(mark(cons(z0, z1))) → c36(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 242.33/77.52
TOP(mark(from(z0))) → c36(TOP(from(proper(z0))), PROPER(from(z0))) 242.33/77.52
TOP(mark(s(z0))) → c36(TOP(s(proper(z0))), PROPER(s(z0))) 242.33/77.52
TOP(mark(zWadr(z0, z1))) → c36(TOP(zWadr(proper(z0), proper(z1))), PROPER(zWadr(z0, z1))) 242.33/77.52
TOP(mark(prefix(z0))) → c36(TOP(prefix(proper(z0))), PROPER(prefix(z0))) 242.33/77.52
TOP(ok(app(nil, z0))) → c37(TOP(mark(z0)), ACTIVE(app(nil, z0))) 242.33/77.52
TOP(ok(app(cons(z0, z1), z2))) → c37(TOP(mark(cons(z0, app(z1, z2)))), ACTIVE(app(cons(z0, z1), z2))) 242.33/77.52
TOP(ok(from(z0))) → c37(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 242.33/77.52
TOP(ok(zWadr(nil, z0))) → c37(TOP(mark(nil)), ACTIVE(zWadr(nil, z0))) 242.33/77.52
TOP(ok(zWadr(z0, nil))) → c37(TOP(mark(nil)), ACTIVE(zWadr(z0, nil))) 242.33/77.52
TOP(ok(zWadr(cons(z0, z1), cons(z2, z3)))) → c37(TOP(mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3)))), ACTIVE(zWadr(cons(z0, z1), cons(z2, z3)))) 242.33/77.52
TOP(ok(prefix(z0))) → c37(TOP(mark(cons(nil, zWadr(z0, prefix(z0))))), ACTIVE(prefix(z0))) 242.33/77.52
TOP(ok(app(z0, z1))) → c37(TOP(app(active(z0), z1)), ACTIVE(app(z0, z1))) 242.33/77.52
TOP(ok(app(z0, z1))) → c37(TOP(app(z0, active(z1))), ACTIVE(app(z0, z1))) 242.33/77.52
TOP(ok(cons(z0, z1))) → c37(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 242.33/77.52
TOP(ok(from(z0))) → c37(TOP(from(active(z0))), ACTIVE(from(z0))) 242.33/77.52
TOP(ok(s(z0))) → c37(TOP(s(active(z0))), ACTIVE(s(z0))) 242.33/77.52
TOP(ok(zWadr(z0, z1))) → c37(TOP(zWadr(active(z0), z1)), ACTIVE(zWadr(z0, z1))) 242.33/77.52
TOP(ok(zWadr(z0, z1))) → c37(TOP(zWadr(z0, active(z1))), ACTIVE(zWadr(z0, z1))) 242.33/77.52
TOP(ok(prefix(z0))) → c37(TOP(prefix(active(z0))), ACTIVE(prefix(z0)))
242.33/77.52
242.33/77.52

(48) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 242.33/77.52
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 242.33/77.52
active(from(z0)) → mark(cons(z0, from(s(z0)))) 242.33/77.52
active(zWadr(nil, z0)) → mark(nil) 242.33/77.52
active(zWadr(z0, nil)) → mark(nil) 242.33/77.52
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 242.33/77.52
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 242.33/77.52
active(app(z0, z1)) → app(active(z0), z1) 242.33/77.52
active(app(z0, z1)) → app(z0, active(z1)) 242.33/77.52
active(cons(z0, z1)) → cons(active(z0), z1) 242.33/77.52
active(from(z0)) → from(active(z0)) 242.33/77.52
active(s(z0)) → s(active(z0)) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 242.33/77.52
active(prefix(z0)) → prefix(active(z0)) 242.33/77.52
app(mark(z0), z1) → mark(app(z0, z1)) 242.33/77.52
app(z0, mark(z1)) → mark(app(z0, z1)) 242.33/77.52
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 242.33/77.52
cons(mark(z0), z1) → mark(cons(z0, z1)) 242.33/77.52
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 242.33/77.52
from(mark(z0)) → mark(from(z0)) 242.33/77.52
from(ok(z0)) → ok(from(z0)) 242.33/77.52
s(mark(z0)) → mark(s(z0)) 242.33/77.52
s(ok(z0)) → ok(s(z0)) 242.33/77.52
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 242.33/77.52
prefix(mark(z0)) → mark(prefix(z0)) 242.33/77.52
prefix(ok(z0)) → ok(prefix(z0)) 242.33/77.52
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 242.33/77.52
proper(nil) → ok(nil) 242.33/77.52
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 242.33/77.52
proper(from(z0)) → from(proper(z0)) 242.33/77.52
proper(s(z0)) → s(proper(z0)) 242.33/77.52
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 242.33/77.52
proper(prefix(z0)) → prefix(proper(z0)) 242.33/77.52
top(mark(z0)) → top(proper(z0)) 242.33/77.52
top(ok(z0)) → top(active(z0))
Tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0)) 242.33/77.52
TOP(mark(nil)) → c36(TOP(ok(nil)))
S tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
K tuples:none
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

APP, CONS, FROM, S, ZWADR, PREFIX, TOP

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c36

242.33/77.52
242.33/77.52

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

Removed 1 trailing tuple parts
242.33/77.52
242.33/77.52

(50) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 242.33/77.52
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 242.33/77.52
active(from(z0)) → mark(cons(z0, from(s(z0)))) 242.33/77.52
active(zWadr(nil, z0)) → mark(nil) 242.33/77.52
active(zWadr(z0, nil)) → mark(nil) 242.33/77.52
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 242.33/77.52
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 242.33/77.52
active(app(z0, z1)) → app(active(z0), z1) 242.33/77.52
active(app(z0, z1)) → app(z0, active(z1)) 242.33/77.52
active(cons(z0, z1)) → cons(active(z0), z1) 242.33/77.52
active(from(z0)) → from(active(z0)) 242.33/77.52
active(s(z0)) → s(active(z0)) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 242.33/77.52
active(prefix(z0)) → prefix(active(z0)) 242.33/77.52
app(mark(z0), z1) → mark(app(z0, z1)) 242.33/77.52
app(z0, mark(z1)) → mark(app(z0, z1)) 242.33/77.52
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 242.33/77.52
cons(mark(z0), z1) → mark(cons(z0, z1)) 242.33/77.52
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 242.33/77.52
from(mark(z0)) → mark(from(z0)) 242.33/77.52
from(ok(z0)) → ok(from(z0)) 242.33/77.52
s(mark(z0)) → mark(s(z0)) 242.33/77.52
s(ok(z0)) → ok(s(z0)) 242.33/77.52
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 242.33/77.52
prefix(mark(z0)) → mark(prefix(z0)) 242.33/77.52
prefix(ok(z0)) → ok(prefix(z0)) 242.33/77.52
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 242.33/77.52
proper(nil) → ok(nil) 242.33/77.52
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 242.33/77.52
proper(from(z0)) → from(proper(z0)) 242.33/77.52
proper(s(z0)) → s(proper(z0)) 242.33/77.52
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 242.33/77.52
proper(prefix(z0)) → prefix(proper(z0)) 242.33/77.52
top(mark(z0)) → top(proper(z0)) 242.33/77.52
top(ok(z0)) → top(active(z0))
Tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0)) 242.33/77.52
TOP(mark(nil)) → c36
S tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
K tuples:none
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

APP, CONS, FROM, S, ZWADR, PREFIX, TOP

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c36

242.33/77.52
242.33/77.52

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

Removed 1 trailing nodes:

TOP(mark(nil)) → c36
242.33/77.52
242.33/77.52

(52) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 242.33/77.52
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 242.33/77.52
active(from(z0)) → mark(cons(z0, from(s(z0)))) 242.33/77.52
active(zWadr(nil, z0)) → mark(nil) 242.33/77.52
active(zWadr(z0, nil)) → mark(nil) 242.33/77.52
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 242.33/77.52
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 242.33/77.52
active(app(z0, z1)) → app(active(z0), z1) 242.33/77.52
active(app(z0, z1)) → app(z0, active(z1)) 242.33/77.52
active(cons(z0, z1)) → cons(active(z0), z1) 242.33/77.52
active(from(z0)) → from(active(z0)) 242.33/77.52
active(s(z0)) → s(active(z0)) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 242.33/77.52
active(prefix(z0)) → prefix(active(z0)) 242.33/77.52
app(mark(z0), z1) → mark(app(z0, z1)) 242.33/77.52
app(z0, mark(z1)) → mark(app(z0, z1)) 242.33/77.52
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 242.33/77.52
cons(mark(z0), z1) → mark(cons(z0, z1)) 242.33/77.52
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 242.33/77.52
from(mark(z0)) → mark(from(z0)) 242.33/77.52
from(ok(z0)) → ok(from(z0)) 242.33/77.52
s(mark(z0)) → mark(s(z0)) 242.33/77.52
s(ok(z0)) → ok(s(z0)) 242.33/77.52
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 242.33/77.52
prefix(mark(z0)) → mark(prefix(z0)) 242.33/77.52
prefix(ok(z0)) → ok(prefix(z0)) 242.33/77.52
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 242.33/77.52
proper(nil) → ok(nil) 242.33/77.52
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 242.33/77.52
proper(from(z0)) → from(proper(z0)) 242.33/77.52
proper(s(z0)) → s(proper(z0)) 242.33/77.52
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 242.33/77.52
proper(prefix(z0)) → prefix(proper(z0)) 242.33/77.52
top(mark(z0)) → top(proper(z0)) 242.33/77.52
top(ok(z0)) → top(active(z0))
Tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
S tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
K tuples:none
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

APP, CONS, FROM, S, ZWADR, PREFIX

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28

242.33/77.52
242.33/77.52

(53) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

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

APP(ok(z0), ok(z1)) → c17(APP(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 242.33/77.52

POL(APP(x1, x2)) = [2]x1    242.33/77.52
POL(CONS(x1, x2)) = 0    242.33/77.52
POL(FROM(x1)) = 0    242.33/77.52
POL(PREFIX(x1)) = 0    242.33/77.52
POL(S(x1)) = 0    242.33/77.52
POL(ZWADR(x1, x2)) = 0    242.33/77.52
POL(c15(x1)) = x1    242.33/77.52
POL(c16(x1)) = x1    242.33/77.52
POL(c17(x1)) = x1    242.33/77.52
POL(c18(x1)) = x1    242.33/77.52
POL(c19(x1)) = x1    242.33/77.52
POL(c20(x1)) = x1    242.33/77.52
POL(c21(x1)) = x1    242.33/77.52
POL(c22(x1)) = x1    242.33/77.52
POL(c23(x1)) = x1    242.33/77.52
POL(c24(x1)) = x1    242.33/77.52
POL(c25(x1)) = x1    242.33/77.52
POL(c26(x1)) = x1    242.33/77.52
POL(c27(x1)) = x1    242.33/77.52
POL(c28(x1)) = x1    242.33/77.52
POL(mark(x1)) = x1    242.33/77.52
POL(ok(x1)) = [1] + x1   
242.33/77.52
242.33/77.52

(54) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 242.33/77.52
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 242.33/77.52
active(from(z0)) → mark(cons(z0, from(s(z0)))) 242.33/77.52
active(zWadr(nil, z0)) → mark(nil) 242.33/77.52
active(zWadr(z0, nil)) → mark(nil) 242.33/77.52
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 242.33/77.52
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 242.33/77.52
active(app(z0, z1)) → app(active(z0), z1) 242.33/77.52
active(app(z0, z1)) → app(z0, active(z1)) 242.33/77.52
active(cons(z0, z1)) → cons(active(z0), z1) 242.33/77.52
active(from(z0)) → from(active(z0)) 242.33/77.52
active(s(z0)) → s(active(z0)) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 242.33/77.52
active(prefix(z0)) → prefix(active(z0)) 242.33/77.52
app(mark(z0), z1) → mark(app(z0, z1)) 242.33/77.52
app(z0, mark(z1)) → mark(app(z0, z1)) 242.33/77.52
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 242.33/77.52
cons(mark(z0), z1) → mark(cons(z0, z1)) 242.33/77.52
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 242.33/77.52
from(mark(z0)) → mark(from(z0)) 242.33/77.52
from(ok(z0)) → ok(from(z0)) 242.33/77.52
s(mark(z0)) → mark(s(z0)) 242.33/77.52
s(ok(z0)) → ok(s(z0)) 242.33/77.52
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 242.33/77.52
prefix(mark(z0)) → mark(prefix(z0)) 242.33/77.52
prefix(ok(z0)) → ok(prefix(z0)) 242.33/77.52
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 242.33/77.52
proper(nil) → ok(nil) 242.33/77.52
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 242.33/77.52
proper(from(z0)) → from(proper(z0)) 242.33/77.52
proper(s(z0)) → s(proper(z0)) 242.33/77.52
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 242.33/77.52
proper(prefix(z0)) → prefix(proper(z0)) 242.33/77.52
top(mark(z0)) → top(proper(z0)) 242.33/77.52
top(ok(z0)) → top(active(z0))
Tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
S tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
K tuples:

APP(ok(z0), ok(z1)) → c17(APP(z0, z1))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

APP, CONS, FROM, S, ZWADR, PREFIX

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28

242.33/77.52
242.33/77.52

(55) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

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

CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 242.33/77.52

POL(APP(x1, x2)) = 0    242.33/77.52
POL(CONS(x1, x2)) = x1    242.33/77.52
POL(FROM(x1)) = 0    242.33/77.52
POL(PREFIX(x1)) = 0    242.33/77.52
POL(S(x1)) = 0    242.33/77.52
POL(ZWADR(x1, x2)) = 0    242.33/77.52
POL(c15(x1)) = x1    242.33/77.52
POL(c16(x1)) = x1    242.33/77.52
POL(c17(x1)) = x1    242.33/77.52
POL(c18(x1)) = x1    242.33/77.52
POL(c19(x1)) = x1    242.33/77.52
POL(c20(x1)) = x1    242.33/77.52
POL(c21(x1)) = x1    242.33/77.52
POL(c22(x1)) = x1    242.33/77.52
POL(c23(x1)) = x1    242.33/77.52
POL(c24(x1)) = x1    242.33/77.52
POL(c25(x1)) = x1    242.33/77.52
POL(c26(x1)) = x1    242.33/77.52
POL(c27(x1)) = x1    242.33/77.52
POL(c28(x1)) = x1    242.33/77.52
POL(mark(x1)) = [1] + x1    242.33/77.52
POL(ok(x1)) = [1] + x1   
242.33/77.52
242.33/77.52

(56) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 242.33/77.52
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 242.33/77.52
active(from(z0)) → mark(cons(z0, from(s(z0)))) 242.33/77.52
active(zWadr(nil, z0)) → mark(nil) 242.33/77.52
active(zWadr(z0, nil)) → mark(nil) 242.33/77.52
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 242.33/77.52
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 242.33/77.52
active(app(z0, z1)) → app(active(z0), z1) 242.33/77.52
active(app(z0, z1)) → app(z0, active(z1)) 242.33/77.52
active(cons(z0, z1)) → cons(active(z0), z1) 242.33/77.52
active(from(z0)) → from(active(z0)) 242.33/77.52
active(s(z0)) → s(active(z0)) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 242.33/77.52
active(prefix(z0)) → prefix(active(z0)) 242.33/77.52
app(mark(z0), z1) → mark(app(z0, z1)) 242.33/77.52
app(z0, mark(z1)) → mark(app(z0, z1)) 242.33/77.52
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 242.33/77.52
cons(mark(z0), z1) → mark(cons(z0, z1)) 242.33/77.52
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 242.33/77.52
from(mark(z0)) → mark(from(z0)) 242.33/77.52
from(ok(z0)) → ok(from(z0)) 242.33/77.52
s(mark(z0)) → mark(s(z0)) 242.33/77.52
s(ok(z0)) → ok(s(z0)) 242.33/77.52
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 242.33/77.52
prefix(mark(z0)) → mark(prefix(z0)) 242.33/77.52
prefix(ok(z0)) → ok(prefix(z0)) 242.33/77.52
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 242.33/77.52
proper(nil) → ok(nil) 242.33/77.52
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 242.33/77.52
proper(from(z0)) → from(proper(z0)) 242.33/77.52
proper(s(z0)) → s(proper(z0)) 242.33/77.52
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 242.33/77.52
proper(prefix(z0)) → prefix(proper(z0)) 242.33/77.52
top(mark(z0)) → top(proper(z0)) 242.33/77.52
top(ok(z0)) → top(active(z0))
Tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
S tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
K tuples:

APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

APP, CONS, FROM, S, ZWADR, PREFIX

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28

242.33/77.52
242.33/77.52

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

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

S(mark(z0)) → c22(S(z0))
We considered the (Usable) Rules:none
And the Tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 242.33/77.52

POL(APP(x1, x2)) = 0    242.33/77.52
POL(CONS(x1, x2)) = [5]x1 + [3]x2    242.33/77.52
POL(FROM(x1)) = 0    242.33/77.52
POL(PREFIX(x1)) = 0    242.33/77.52
POL(S(x1)) = x1    242.33/77.52
POL(ZWADR(x1, x2)) = 0    242.33/77.52
POL(c15(x1)) = x1    242.33/77.52
POL(c16(x1)) = x1    242.33/77.52
POL(c17(x1)) = x1    242.33/77.52
POL(c18(x1)) = x1    242.33/77.52
POL(c19(x1)) = x1    242.33/77.52
POL(c20(x1)) = x1    242.33/77.52
POL(c21(x1)) = x1    242.33/77.52
POL(c22(x1)) = x1    242.33/77.52
POL(c23(x1)) = x1    242.33/77.52
POL(c24(x1)) = x1    242.33/77.52
POL(c25(x1)) = x1    242.33/77.52
POL(c26(x1)) = x1    242.33/77.52
POL(c27(x1)) = x1    242.33/77.52
POL(c28(x1)) = x1    242.33/77.52
POL(mark(x1)) = [1] + x1    242.33/77.52
POL(ok(x1)) = x1   
242.33/77.52
242.33/77.52

(58) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 242.33/77.52
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 242.33/77.52
active(from(z0)) → mark(cons(z0, from(s(z0)))) 242.33/77.52
active(zWadr(nil, z0)) → mark(nil) 242.33/77.52
active(zWadr(z0, nil)) → mark(nil) 242.33/77.52
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 242.33/77.52
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 242.33/77.52
active(app(z0, z1)) → app(active(z0), z1) 242.33/77.52
active(app(z0, z1)) → app(z0, active(z1)) 242.33/77.52
active(cons(z0, z1)) → cons(active(z0), z1) 242.33/77.52
active(from(z0)) → from(active(z0)) 242.33/77.52
active(s(z0)) → s(active(z0)) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 242.33/77.52
active(prefix(z0)) → prefix(active(z0)) 242.33/77.52
app(mark(z0), z1) → mark(app(z0, z1)) 242.33/77.52
app(z0, mark(z1)) → mark(app(z0, z1)) 242.33/77.52
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 242.33/77.52
cons(mark(z0), z1) → mark(cons(z0, z1)) 242.33/77.52
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 242.33/77.52
from(mark(z0)) → mark(from(z0)) 242.33/77.52
from(ok(z0)) → ok(from(z0)) 242.33/77.52
s(mark(z0)) → mark(s(z0)) 242.33/77.52
s(ok(z0)) → ok(s(z0)) 242.33/77.52
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 242.33/77.52
prefix(mark(z0)) → mark(prefix(z0)) 242.33/77.52
prefix(ok(z0)) → ok(prefix(z0)) 242.33/77.52
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 242.33/77.52
proper(nil) → ok(nil) 242.33/77.52
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 242.33/77.52
proper(from(z0)) → from(proper(z0)) 242.33/77.52
proper(s(z0)) → s(proper(z0)) 242.33/77.52
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 242.33/77.52
proper(prefix(z0)) → prefix(proper(z0)) 242.33/77.52
top(mark(z0)) → top(proper(z0)) 242.33/77.52
top(ok(z0)) → top(active(z0))
Tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
S tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
K tuples:

APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
S(mark(z0)) → c22(S(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

APP, CONS, FROM, S, ZWADR, PREFIX

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28

242.33/77.52
242.33/77.52

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

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

ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 242.33/77.52

POL(APP(x1, x2)) = 0    242.33/77.52
POL(CONS(x1, x2)) = [3]x1 + [5]x2    242.33/77.52
POL(FROM(x1)) = 0    242.33/77.52
POL(PREFIX(x1)) = 0    242.33/77.52
POL(S(x1)) = 0    242.33/77.52
POL(ZWADR(x1, x2)) = x2    242.33/77.52
POL(c15(x1)) = x1    242.33/77.52
POL(c16(x1)) = x1    242.33/77.52
POL(c17(x1)) = x1    242.33/77.52
POL(c18(x1)) = x1    242.33/77.52
POL(c19(x1)) = x1    242.33/77.52
POL(c20(x1)) = x1    242.33/77.52
POL(c21(x1)) = x1    242.33/77.52
POL(c22(x1)) = x1    242.33/77.52
POL(c23(x1)) = x1    242.33/77.52
POL(c24(x1)) = x1    242.33/77.52
POL(c25(x1)) = x1    242.33/77.52
POL(c26(x1)) = x1    242.33/77.52
POL(c27(x1)) = x1    242.33/77.52
POL(c28(x1)) = x1    242.33/77.52
POL(mark(x1)) = [1] + x1    242.33/77.52
POL(ok(x1)) = x1   
242.33/77.52
242.33/77.52

(60) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 242.33/77.52
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 242.33/77.52
active(from(z0)) → mark(cons(z0, from(s(z0)))) 242.33/77.52
active(zWadr(nil, z0)) → mark(nil) 242.33/77.52
active(zWadr(z0, nil)) → mark(nil) 242.33/77.52
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 242.33/77.52
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 242.33/77.52
active(app(z0, z1)) → app(active(z0), z1) 242.33/77.52
active(app(z0, z1)) → app(z0, active(z1)) 242.33/77.52
active(cons(z0, z1)) → cons(active(z0), z1) 242.33/77.52
active(from(z0)) → from(active(z0)) 242.33/77.52
active(s(z0)) → s(active(z0)) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 242.33/77.52
active(prefix(z0)) → prefix(active(z0)) 242.33/77.52
app(mark(z0), z1) → mark(app(z0, z1)) 242.33/77.52
app(z0, mark(z1)) → mark(app(z0, z1)) 242.33/77.52
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 242.33/77.52
cons(mark(z0), z1) → mark(cons(z0, z1)) 242.33/77.52
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 242.33/77.52
from(mark(z0)) → mark(from(z0)) 242.33/77.52
from(ok(z0)) → ok(from(z0)) 242.33/77.52
s(mark(z0)) → mark(s(z0)) 242.33/77.52
s(ok(z0)) → ok(s(z0)) 242.33/77.52
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 242.33/77.52
prefix(mark(z0)) → mark(prefix(z0)) 242.33/77.52
prefix(ok(z0)) → ok(prefix(z0)) 242.33/77.52
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 242.33/77.52
proper(nil) → ok(nil) 242.33/77.52
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 242.33/77.52
proper(from(z0)) → from(proper(z0)) 242.33/77.52
proper(s(z0)) → s(proper(z0)) 242.33/77.52
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 242.33/77.52
proper(prefix(z0)) → prefix(proper(z0)) 242.33/77.52
top(mark(z0)) → top(proper(z0)) 242.33/77.52
top(ok(z0)) → top(active(z0))
Tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
S tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
K tuples:

APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

APP, CONS, FROM, S, ZWADR, PREFIX

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28

242.33/77.52
242.33/77.52

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

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

FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
We considered the (Usable) Rules:none
And the Tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 242.33/77.52

POL(APP(x1, x2)) = 0    242.33/77.52
POL(CONS(x1, x2)) = [3]x1 + [3]x2    242.33/77.52
POL(FROM(x1)) = x1    242.33/77.52
POL(PREFIX(x1)) = x1    242.33/77.52
POL(S(x1)) = x1    242.33/77.52
POL(ZWADR(x1, x2)) = [4]x1    242.33/77.52
POL(c15(x1)) = x1    242.33/77.52
POL(c16(x1)) = x1    242.33/77.52
POL(c17(x1)) = x1    242.33/77.52
POL(c18(x1)) = x1    242.33/77.52
POL(c19(x1)) = x1    242.33/77.52
POL(c20(x1)) = x1    242.33/77.52
POL(c21(x1)) = x1    242.33/77.52
POL(c22(x1)) = x1    242.33/77.52
POL(c23(x1)) = x1    242.33/77.52
POL(c24(x1)) = x1    242.33/77.52
POL(c25(x1)) = x1    242.33/77.52
POL(c26(x1)) = x1    242.33/77.52
POL(c27(x1)) = x1    242.33/77.52
POL(c28(x1)) = x1    242.33/77.52
POL(mark(x1)) = [1] + x1    242.33/77.52
POL(ok(x1)) = [2] + x1   
242.33/77.52
242.33/77.52

(62) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 242.33/77.52
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 242.33/77.52
active(from(z0)) → mark(cons(z0, from(s(z0)))) 242.33/77.52
active(zWadr(nil, z0)) → mark(nil) 242.33/77.52
active(zWadr(z0, nil)) → mark(nil) 242.33/77.52
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 242.33/77.52
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 242.33/77.52
active(app(z0, z1)) → app(active(z0), z1) 242.33/77.52
active(app(z0, z1)) → app(z0, active(z1)) 242.33/77.52
active(cons(z0, z1)) → cons(active(z0), z1) 242.33/77.52
active(from(z0)) → from(active(z0)) 242.33/77.52
active(s(z0)) → s(active(z0)) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 242.33/77.52
active(prefix(z0)) → prefix(active(z0)) 242.33/77.52
app(mark(z0), z1) → mark(app(z0, z1)) 242.33/77.52
app(z0, mark(z1)) → mark(app(z0, z1)) 242.33/77.52
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 242.33/77.52
cons(mark(z0), z1) → mark(cons(z0, z1)) 242.33/77.52
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 242.33/77.52
from(mark(z0)) → mark(from(z0)) 242.33/77.52
from(ok(z0)) → ok(from(z0)) 242.33/77.52
s(mark(z0)) → mark(s(z0)) 242.33/77.52
s(ok(z0)) → ok(s(z0)) 242.33/77.52
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 242.33/77.52
prefix(mark(z0)) → mark(prefix(z0)) 242.33/77.52
prefix(ok(z0)) → ok(prefix(z0)) 242.33/77.52
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 242.33/77.52
proper(nil) → ok(nil) 242.33/77.52
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 242.33/77.52
proper(from(z0)) → from(proper(z0)) 242.33/77.52
proper(s(z0)) → s(proper(z0)) 242.33/77.52
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 242.33/77.52
proper(prefix(z0)) → prefix(proper(z0)) 242.33/77.52
top(mark(z0)) → top(proper(z0)) 242.33/77.52
top(ok(z0)) → top(active(z0))
Tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
S tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1))
K tuples:

APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

APP, CONS, FROM, S, ZWADR, PREFIX

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28

242.33/77.52
242.33/77.52

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

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

APP(mark(z0), z1) → c15(APP(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 242.33/77.52

POL(APP(x1, x2)) = x1    242.33/77.52
POL(CONS(x1, x2)) = [3]x1 + [5]x2    242.33/77.52
POL(FROM(x1)) = [5]x1    242.33/77.52
POL(PREFIX(x1)) = [5]x1    242.33/77.52
POL(S(x1)) = [5]x1    242.33/77.52
POL(ZWADR(x1, x2)) = [5]x1 + [5]x2    242.33/77.52
POL(c15(x1)) = x1    242.33/77.52
POL(c16(x1)) = x1    242.33/77.52
POL(c17(x1)) = x1    242.33/77.52
POL(c18(x1)) = x1    242.33/77.52
POL(c19(x1)) = x1    242.33/77.52
POL(c20(x1)) = x1    242.33/77.52
POL(c21(x1)) = x1    242.33/77.52
POL(c22(x1)) = x1    242.33/77.52
POL(c23(x1)) = x1    242.33/77.52
POL(c24(x1)) = x1    242.33/77.52
POL(c25(x1)) = x1    242.33/77.52
POL(c26(x1)) = x1    242.33/77.52
POL(c27(x1)) = x1    242.33/77.52
POL(c28(x1)) = x1    242.33/77.52
POL(mark(x1)) = [1] + x1    242.33/77.52
POL(ok(x1)) = x1   
242.33/77.52
242.33/77.52

(64) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 242.33/77.52
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 242.33/77.52
active(from(z0)) → mark(cons(z0, from(s(z0)))) 242.33/77.52
active(zWadr(nil, z0)) → mark(nil) 242.33/77.52
active(zWadr(z0, nil)) → mark(nil) 242.33/77.52
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 242.33/77.52
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 242.33/77.52
active(app(z0, z1)) → app(active(z0), z1) 242.33/77.52
active(app(z0, z1)) → app(z0, active(z1)) 242.33/77.52
active(cons(z0, z1)) → cons(active(z0), z1) 242.33/77.52
active(from(z0)) → from(active(z0)) 242.33/77.52
active(s(z0)) → s(active(z0)) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 242.33/77.52
active(prefix(z0)) → prefix(active(z0)) 242.33/77.52
app(mark(z0), z1) → mark(app(z0, z1)) 242.33/77.52
app(z0, mark(z1)) → mark(app(z0, z1)) 242.33/77.52
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 242.33/77.52
cons(mark(z0), z1) → mark(cons(z0, z1)) 242.33/77.52
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 242.33/77.52
from(mark(z0)) → mark(from(z0)) 242.33/77.52
from(ok(z0)) → ok(from(z0)) 242.33/77.52
s(mark(z0)) → mark(s(z0)) 242.33/77.52
s(ok(z0)) → ok(s(z0)) 242.33/77.52
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 242.33/77.52
prefix(mark(z0)) → mark(prefix(z0)) 242.33/77.52
prefix(ok(z0)) → ok(prefix(z0)) 242.33/77.52
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 242.33/77.52
proper(nil) → ok(nil) 242.33/77.52
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 242.33/77.52
proper(from(z0)) → from(proper(z0)) 242.33/77.52
proper(s(z0)) → s(proper(z0)) 242.33/77.52
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 242.33/77.52
proper(prefix(z0)) → prefix(proper(z0)) 242.33/77.52
top(mark(z0)) → top(proper(z0)) 242.33/77.52
top(ok(z0)) → top(active(z0))
Tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
S tuples:

APP(z0, mark(z1)) → c16(APP(z0, z1))
K tuples:

APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0)) 242.33/77.52
APP(mark(z0), z1) → c15(APP(z0, z1))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

APP, CONS, FROM, S, ZWADR, PREFIX

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28

242.33/77.52
242.33/77.52

(65) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))) transformation)

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

APP(z0, mark(z1)) → c16(APP(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 242.33/77.52

POL(APP(x1, x2)) = x1 + x2 + [3]x1·x2    242.33/77.52
POL(CONS(x1, x2)) = x1 + x2 + [3]x22 + [3]x1·x2 + [3]x12    242.33/77.52
POL(FROM(x1)) = [3]x1 + [3]x12    242.33/77.52
POL(PREFIX(x1)) = [3]x1 + [3]x12    242.33/77.52
POL(S(x1)) = [3]x1 + [3]x12    242.33/77.52
POL(ZWADR(x1, x2)) = x1 + x2 + [3]x22 + [3]x1·x2 + [3]x12    242.33/77.52
POL(c15(x1)) = x1    242.33/77.52
POL(c16(x1)) = x1    242.33/77.52
POL(c17(x1)) = x1    242.33/77.52
POL(c18(x1)) = x1    242.33/77.52
POL(c19(x1)) = x1    242.33/77.52
POL(c20(x1)) = x1    242.33/77.52
POL(c21(x1)) = x1    242.33/77.52
POL(c22(x1)) = x1    242.33/77.52
POL(c23(x1)) = x1    242.33/77.52
POL(c24(x1)) = x1    242.33/77.52
POL(c25(x1)) = x1    242.33/77.52
POL(c26(x1)) = x1    242.33/77.52
POL(c27(x1)) = x1    242.33/77.52
POL(c28(x1)) = x1    242.33/77.52
POL(mark(x1)) = [1] + x1    242.33/77.52
POL(ok(x1)) = x1   
242.33/77.52
242.33/77.52

(66) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(app(nil, z0)) → mark(z0) 242.33/77.52
active(app(cons(z0, z1), z2)) → mark(cons(z0, app(z1, z2))) 242.33/77.52
active(from(z0)) → mark(cons(z0, from(s(z0)))) 242.33/77.52
active(zWadr(nil, z0)) → mark(nil) 242.33/77.52
active(zWadr(z0, nil)) → mark(nil) 242.33/77.52
active(zWadr(cons(z0, z1), cons(z2, z3))) → mark(cons(app(z2, cons(z0, nil)), zWadr(z1, z3))) 242.33/77.52
active(prefix(z0)) → mark(cons(nil, zWadr(z0, prefix(z0)))) 242.33/77.52
active(app(z0, z1)) → app(active(z0), z1) 242.33/77.52
active(app(z0, z1)) → app(z0, active(z1)) 242.33/77.52
active(cons(z0, z1)) → cons(active(z0), z1) 242.33/77.52
active(from(z0)) → from(active(z0)) 242.33/77.52
active(s(z0)) → s(active(z0)) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(active(z0), z1) 242.33/77.52
active(zWadr(z0, z1)) → zWadr(z0, active(z1)) 242.33/77.52
active(prefix(z0)) → prefix(active(z0)) 242.33/77.52
app(mark(z0), z1) → mark(app(z0, z1)) 242.33/77.52
app(z0, mark(z1)) → mark(app(z0, z1)) 242.33/77.52
app(ok(z0), ok(z1)) → ok(app(z0, z1)) 242.33/77.52
cons(mark(z0), z1) → mark(cons(z0, z1)) 242.33/77.52
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 242.33/77.52
from(mark(z0)) → mark(from(z0)) 242.33/77.52
from(ok(z0)) → ok(from(z0)) 242.33/77.52
s(mark(z0)) → mark(s(z0)) 242.33/77.52
s(ok(z0)) → ok(s(z0)) 242.33/77.52
zWadr(mark(z0), z1) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(z0, mark(z1)) → mark(zWadr(z0, z1)) 242.33/77.52
zWadr(ok(z0), ok(z1)) → ok(zWadr(z0, z1)) 242.33/77.52
prefix(mark(z0)) → mark(prefix(z0)) 242.33/77.52
prefix(ok(z0)) → ok(prefix(z0)) 242.33/77.52
proper(app(z0, z1)) → app(proper(z0), proper(z1)) 242.33/77.52
proper(nil) → ok(nil) 242.33/77.52
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 242.33/77.52
proper(from(z0)) → from(proper(z0)) 242.33/77.52
proper(s(z0)) → s(proper(z0)) 242.33/77.52
proper(zWadr(z0, z1)) → zWadr(proper(z0), proper(z1)) 242.33/77.52
proper(prefix(z0)) → prefix(proper(z0)) 242.33/77.52
top(mark(z0)) → top(proper(z0)) 242.33/77.52
top(ok(z0)) → top(active(z0))
Tuples:

APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1)) 242.33/77.52
APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0))
S tuples:none
K tuples:

APP(ok(z0), ok(z1)) → c17(APP(z0, z1)) 242.33/77.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 242.33/77.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 242.33/77.52
S(mark(z0)) → c22(S(z0)) 242.33/77.52
ZWADR(z0, mark(z1)) → c25(ZWADR(z0, z1)) 242.33/77.52
FROM(mark(z0)) → c20(FROM(z0)) 242.33/77.52
FROM(ok(z0)) → c21(FROM(z0)) 242.33/77.52
S(ok(z0)) → c23(S(z0)) 242.33/77.52
ZWADR(mark(z0), z1) → c24(ZWADR(z0, z1)) 242.33/77.52
ZWADR(ok(z0), ok(z1)) → c26(ZWADR(z0, z1)) 242.33/77.52
PREFIX(mark(z0)) → c27(PREFIX(z0)) 242.33/77.52
PREFIX(ok(z0)) → c28(PREFIX(z0)) 242.33/77.52
APP(mark(z0), z1) → c15(APP(z0, z1)) 242.33/77.52
APP(z0, mark(z1)) → c16(APP(z0, z1))
Defined Rule Symbols:

active, app, cons, from, s, zWadr, prefix, proper, top

Defined Pair Symbols:

APP, CONS, FROM, S, ZWADR, PREFIX

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28

242.33/77.52
242.33/77.52

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

The set S is empty
242.33/77.52
242.33/77.52

(68) BOUNDS(O(1), O(1))

242.33/77.52
242.33/77.52
242.53/77.69 EOF