YES(O(1), O(n^3)) 267.06/85.52 YES(O(1), O(n^3)) 267.06/85.55 267.06/85.55 267.06/85.55 267.06/85.55 267.06/85.55 267.06/85.55 Runtime Complexity (innermost) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml.xml 267.06/85.55 267.06/85.55 267.06/85.55
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The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(n^3)).

0 CpxTRS
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↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳2 CdtProblem
267.06/85.55 
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳4 CdtProblem
267.06/85.55 
↳5 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳6 CdtProblem
267.06/85.55 
↳7 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳8 CdtProblem
267.06/85.55 
↳9 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳10 CdtProblem
267.06/85.55 
↳11 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳12 CdtProblem
267.06/85.55 
↳13 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳14 CdtProblem
267.06/85.55 
↳15 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳16 CdtProblem
267.06/85.55 
↳17 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳18 CdtProblem
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↳19 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳20 CdtProblem
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↳21 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳22 CdtProblem
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↳23 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳24 CdtProblem
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↳25 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳26 CdtProblem
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↳27 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳28 CdtProblem
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↳29 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳30 CdtProblem
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↳31 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳32 CdtProblem
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↳33 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳34 CdtProblem
267.06/85.55 
↳35 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳36 CdtProblem
267.06/85.55 
↳37 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳38 CdtProblem
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↳39 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳40 CdtProblem
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↳41 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳42 CdtProblem
267.06/85.55 
↳43 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳44 CdtProblem
267.06/85.55 
↳45 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳46 CdtProblem
267.06/85.55 
↳47 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳48 CdtProblem
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↳49 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳50 CdtProblem
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↳51 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳52 CdtProblem
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↳53 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳54 CdtProblem
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↳55 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳56 CdtProblem
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↳57 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
267.06/85.55 
↳58 CdtProblem
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↳59 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
267.06/85.55 
↳60 CdtProblem
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↳61 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳62 CdtProblem
267.06/85.55 
↳63 CdtUnreachableProof (⇔)
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↳64 CdtProblem
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↳65 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
267.06/85.55 
↳66 CdtProblem
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↳67 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
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↳68 CdtProblem
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↳69 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))
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↳70 CdtProblem
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↳71 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
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↳72 CdtProblem
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↳73 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^3))))
267.79/85.71 
↳74 CdtProblem
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↳75 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
267.79/85.71 
↳76 CdtProblem
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↳77 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
267.79/85.71 
↳78 CdtProblem
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↳79 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
267.79/85.71 
↳80 CdtProblem
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↳81 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))
267.79/85.71 
↳82 CdtProblem
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↳83 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
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↳84 CdtProblem
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↳85 SIsEmptyProof (BOTH BOUNDS(ID, ID))
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↳86 BOUNDS(O(1), O(1))
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267.79/85.71

(0) Obligation:

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

active(dbl(0)) → mark(0) 267.79/85.71
active(dbl(s(X))) → mark(s(s(dbl(X)))) 267.79/85.71
active(dbls(nil)) → mark(nil) 267.79/85.71
active(dbls(cons(X, Y))) → mark(cons(dbl(X), dbls(Y))) 267.79/85.71
active(sel(0, cons(X, Y))) → mark(X) 267.79/85.71
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z)) 267.79/85.71
active(indx(nil, X)) → mark(nil) 267.79/85.71
active(indx(cons(X, Y), Z)) → mark(cons(sel(X, Z), indx(Y, Z))) 267.79/85.71
active(from(X)) → mark(cons(X, from(s(X)))) 267.79/85.71
active(dbl(X)) → dbl(active(X)) 267.79/85.71
active(dbls(X)) → dbls(active(X)) 267.79/85.71
active(sel(X1, X2)) → sel(active(X1), X2) 267.79/85.71
active(sel(X1, X2)) → sel(X1, active(X2)) 267.79/85.71
active(indx(X1, X2)) → indx(active(X1), X2) 267.79/85.71
dbl(mark(X)) → mark(dbl(X)) 267.79/85.71
dbls(mark(X)) → mark(dbls(X)) 267.79/85.71
sel(mark(X1), X2) → mark(sel(X1, X2)) 267.79/85.71
sel(X1, mark(X2)) → mark(sel(X1, X2)) 267.79/85.71
indx(mark(X1), X2) → mark(indx(X1, X2)) 267.79/85.71
proper(dbl(X)) → dbl(proper(X)) 267.79/85.71
proper(0) → ok(0) 267.79/85.71
proper(s(X)) → s(proper(X)) 267.79/85.71
proper(dbls(X)) → dbls(proper(X)) 267.79/85.71
proper(nil) → ok(nil) 267.79/85.71
proper(cons(X1, X2)) → cons(proper(X1), proper(X2)) 267.79/85.71
proper(sel(X1, X2)) → sel(proper(X1), proper(X2)) 267.79/85.71
proper(indx(X1, X2)) → indx(proper(X1), proper(X2)) 267.79/85.71
proper(from(X)) → from(proper(X)) 267.79/85.71
dbl(ok(X)) → ok(dbl(X)) 267.79/85.71
s(ok(X)) → ok(s(X)) 267.79/85.71
dbls(ok(X)) → ok(dbls(X)) 267.79/85.71
cons(ok(X1), ok(X2)) → ok(cons(X1, X2)) 267.79/85.71
sel(ok(X1), ok(X2)) → ok(sel(X1, X2)) 267.79/85.71
indx(ok(X1), ok(X2)) → ok(indx(X1, X2)) 267.79/85.71
from(ok(X)) → ok(from(X)) 267.79/85.71
top(mark(X)) → top(proper(X)) 267.79/85.71
top(ok(X)) → top(active(X))

Rewrite Strategy: INNERMOST
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267.79/85.71

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

Converted CpxTRS to CDT
267.79/85.71
267.79/85.71

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 267.79/85.71
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 267.79/85.71
active(dbls(nil)) → mark(nil) 267.79/85.71
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 267.79/85.71
active(sel(0, cons(z0, z1))) → mark(z0) 267.79/85.71
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 267.79/85.71
active(indx(nil, z0)) → mark(nil) 267.79/85.71
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 267.79/85.71
active(from(z0)) → mark(cons(z0, from(s(z0)))) 267.79/85.71
active(dbl(z0)) → dbl(active(z0)) 267.79/85.71
active(dbls(z0)) → dbls(active(z0)) 267.79/85.71
active(sel(z0, z1)) → sel(active(z0), z1) 267.79/85.71
active(sel(z0, z1)) → sel(z0, active(z1)) 267.79/85.71
active(indx(z0, z1)) → indx(active(z0), z1) 267.79/85.71
dbl(mark(z0)) → mark(dbl(z0)) 267.79/85.71
dbl(ok(z0)) → ok(dbl(z0)) 267.79/85.71
dbls(mark(z0)) → mark(dbls(z0)) 267.79/85.71
dbls(ok(z0)) → ok(dbls(z0)) 267.79/85.71
sel(mark(z0), z1) → mark(sel(z0, z1)) 267.79/85.71
sel(z0, mark(z1)) → mark(sel(z0, z1)) 267.79/85.71
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 267.79/85.71
indx(mark(z0), z1) → mark(indx(z0, z1)) 267.79/85.71
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 267.79/85.71
proper(dbl(z0)) → dbl(proper(z0)) 267.79/85.71
proper(0) → ok(0) 267.79/85.71
proper(s(z0)) → s(proper(z0)) 267.79/85.71
proper(dbls(z0)) → dbls(proper(z0)) 267.79/85.71
proper(nil) → ok(nil) 267.79/85.71
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 267.79/85.71
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 267.79/85.71
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 267.79/85.71
proper(from(z0)) → from(proper(z0)) 267.79/85.71
s(ok(z0)) → ok(s(z0)) 267.79/85.71
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 267.79/85.71
from(ok(z0)) → ok(from(z0)) 267.79/85.71
top(mark(z0)) → top(proper(z0)) 267.79/85.71
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0))), S(dbl(z0)), DBL(z0)) 267.79/85.71
ACTIVE(dbls(cons(z0, z1))) → c3(CONS(dbl(z0), dbls(z1)), DBL(z0), DBLS(z1)) 267.79/85.71
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 267.79/85.71
ACTIVE(indx(cons(z0, z1), z2)) → c7(CONS(sel(z0, z2), indx(z1, z2)), SEL(z0, z2), INDX(z1, z2)) 267.79/85.71
ACTIVE(from(z0)) → c8(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0)) 267.79/85.71
ACTIVE(dbl(z0)) → c9(DBL(active(z0)), ACTIVE(z0)) 267.79/85.71
ACTIVE(dbls(z0)) → c10(DBLS(active(z0)), ACTIVE(z0)) 267.79/85.71
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 267.79/85.71
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 267.79/85.71
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 267.79/85.71
DBL(mark(z0)) → c14(DBL(z0)) 267.79/85.71
DBL(ok(z0)) → c15(DBL(z0)) 267.79/85.71
DBLS(mark(z0)) → c16(DBLS(z0)) 267.79/85.71
DBLS(ok(z0)) → c17(DBLS(z0)) 267.79/85.71
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 267.79/85.71
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 267.79/85.71
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 267.79/85.71
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 267.79/85.71
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 267.79/85.71
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 267.79/85.71
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 267.79/85.71
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 267.79/85.71
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 267.79/85.71
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 267.79/85.71
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 267.79/85.71
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 267.79/85.71
S(ok(z0)) → c32(S(z0)) 267.79/85.71
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 267.79/85.71
FROM(ok(z0)) → c34(FROM(z0)) 267.79/85.71
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 267.79/85.71
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0))
S tuples:

ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0))), S(dbl(z0)), DBL(z0)) 267.79/85.71
ACTIVE(dbls(cons(z0, z1))) → c3(CONS(dbl(z0), dbls(z1)), DBL(z0), DBLS(z1)) 267.79/85.71
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 267.79/85.71
ACTIVE(indx(cons(z0, z1), z2)) → c7(CONS(sel(z0, z2), indx(z1, z2)), SEL(z0, z2), INDX(z1, z2)) 267.79/85.71
ACTIVE(from(z0)) → c8(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0)) 267.79/85.71
ACTIVE(dbl(z0)) → c9(DBL(active(z0)), ACTIVE(z0)) 267.79/85.71
ACTIVE(dbls(z0)) → c10(DBLS(active(z0)), ACTIVE(z0)) 267.79/85.71
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 267.79/85.71
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 267.79/85.71
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 267.79/85.71
DBL(mark(z0)) → c14(DBL(z0)) 267.79/85.71
DBL(ok(z0)) → c15(DBL(z0)) 267.79/85.71
DBLS(mark(z0)) → c16(DBLS(z0)) 267.79/85.71
DBLS(ok(z0)) → c17(DBLS(z0)) 267.79/85.71
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 267.79/85.71
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 267.79/85.71
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 267.79/85.71
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 267.79/85.71
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 267.79/85.71
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 267.79/85.71
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 267.79/85.71
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 267.79/85.71
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 267.79/85.71
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 267.79/85.71
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 267.79/85.71
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 267.79/85.71
S(ok(z0)) → c32(S(z0)) 267.79/85.71
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 267.79/85.71
FROM(ok(z0)) → c34(FROM(z0)) 267.79/85.71
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 267.79/85.71
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c1, c3, c5, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36

267.79/85.71
267.79/85.71

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

Removed 2 trailing tuple parts
267.79/85.71
267.79/85.71

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 267.79/85.71
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 267.79/85.71
active(dbls(nil)) → mark(nil) 267.79/85.71
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 267.79/85.71
active(sel(0, cons(z0, z1))) → mark(z0) 267.79/85.71
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 267.79/85.71
active(indx(nil, z0)) → mark(nil) 267.79/85.71
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 267.79/85.71
active(from(z0)) → mark(cons(z0, from(s(z0)))) 267.79/85.71
active(dbl(z0)) → dbl(active(z0)) 267.79/85.71
active(dbls(z0)) → dbls(active(z0)) 267.79/85.71
active(sel(z0, z1)) → sel(active(z0), z1) 267.79/85.71
active(sel(z0, z1)) → sel(z0, active(z1)) 267.79/85.71
active(indx(z0, z1)) → indx(active(z0), z1) 267.79/85.71
dbl(mark(z0)) → mark(dbl(z0)) 267.79/85.71
dbl(ok(z0)) → ok(dbl(z0)) 267.79/85.71
dbls(mark(z0)) → mark(dbls(z0)) 267.79/85.71
dbls(ok(z0)) → ok(dbls(z0)) 267.79/85.71
sel(mark(z0), z1) → mark(sel(z0, z1)) 267.79/85.71
sel(z0, mark(z1)) → mark(sel(z0, z1)) 267.79/85.71
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 267.79/85.71
indx(mark(z0), z1) → mark(indx(z0, z1)) 267.79/85.71
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 267.79/85.71
proper(dbl(z0)) → dbl(proper(z0)) 267.79/85.71
proper(0) → ok(0) 267.79/85.71
proper(s(z0)) → s(proper(z0)) 267.79/85.71
proper(dbls(z0)) → dbls(proper(z0)) 267.79/85.71
proper(nil) → ok(nil) 267.79/85.71
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 267.79/85.71
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 267.79/85.71
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 267.79/85.71
proper(from(z0)) → from(proper(z0)) 267.79/85.71
s(ok(z0)) → ok(s(z0)) 267.79/85.71
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 267.79/85.71
from(ok(z0)) → ok(from(z0)) 267.79/85.71
top(mark(z0)) → top(proper(z0)) 267.79/85.71
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0))), S(dbl(z0)), DBL(z0)) 267.79/85.71
ACTIVE(dbls(cons(z0, z1))) → c3(CONS(dbl(z0), dbls(z1)), DBL(z0), DBLS(z1)) 267.79/85.71
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 267.79/85.71
ACTIVE(indx(cons(z0, z1), z2)) → c7(CONS(sel(z0, z2), indx(z1, z2)), SEL(z0, z2), INDX(z1, z2)) 267.79/85.71
ACTIVE(dbl(z0)) → c9(DBL(active(z0)), ACTIVE(z0)) 267.79/85.71
ACTIVE(dbls(z0)) → c10(DBLS(active(z0)), ACTIVE(z0)) 267.79/85.71
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 267.79/85.71
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 267.79/85.71
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 267.79/85.71
DBL(mark(z0)) → c14(DBL(z0)) 267.79/85.71
DBL(ok(z0)) → c15(DBL(z0)) 267.79/85.71
DBLS(mark(z0)) → c16(DBLS(z0)) 267.79/85.71
DBLS(ok(z0)) → c17(DBLS(z0)) 267.79/85.71
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 267.79/85.71
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 267.79/85.71
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 267.79/85.71
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 267.79/85.71
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 267.79/85.71
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 267.79/85.71
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 267.79/85.71
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 267.79/85.71
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 267.79/85.71
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 267.79/85.71
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 267.79/85.71
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 267.79/85.71
S(ok(z0)) → c32(S(z0)) 267.79/85.71
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 267.79/85.71
FROM(ok(z0)) → c34(FROM(z0)) 267.79/85.71
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 267.79/85.71
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 267.79/85.71
ACTIVE(from(z0)) → c8(S(z0))
S tuples:

ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0))), S(dbl(z0)), DBL(z0)) 268.22/85.85
ACTIVE(dbls(cons(z0, z1))) → c3(CONS(dbl(z0), dbls(z1)), DBL(z0), DBLS(z1)) 268.22/85.85
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.85
ACTIVE(indx(cons(z0, z1), z2)) → c7(CONS(sel(z0, z2), indx(z1, z2)), SEL(z0, z2), INDX(z1, z2)) 268.22/85.85
ACTIVE(dbl(z0)) → c9(DBL(active(z0)), ACTIVE(z0)) 268.22/85.85
ACTIVE(dbls(z0)) → c10(DBLS(active(z0)), ACTIVE(z0)) 268.22/85.85
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.85
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.85
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 268.22/85.85
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.85
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.85
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.85
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.85
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.85
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.85
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.85
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.85
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.85
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.85
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.85
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.85
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.85
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.85
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.85
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.85
S(ok(z0)) → c32(S(z0)) 268.22/85.85
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.85
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.85
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.85
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.85
ACTIVE(from(z0)) → c8(S(z0))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c1, c3, c5, c7, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c8

268.22/85.85
268.22/85.85

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

Split RHS of tuples not part of any SCC
268.22/85.85
268.22/85.85

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.85
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.85
active(dbls(nil)) → mark(nil) 268.22/85.85
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.85
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.85
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.85
active(indx(nil, z0)) → mark(nil) 268.22/85.85
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.85
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.85
active(dbl(z0)) → dbl(active(z0)) 268.22/85.85
active(dbls(z0)) → dbls(active(z0)) 268.22/85.85
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.85
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.85
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.85
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.85
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.85
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.85
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.85
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.85
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.85
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.85
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.85
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.85
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.85
proper(0) → ok(0) 268.22/85.85
proper(s(z0)) → s(proper(z0)) 268.22/85.85
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.85
proper(nil) → ok(nil) 268.22/85.85
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.85
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.85
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.85
proper(from(z0)) → from(proper(z0)) 268.22/85.85
s(ok(z0)) → ok(s(z0)) 268.22/85.85
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.85
from(ok(z0)) → ok(from(z0)) 268.22/85.85
top(mark(z0)) → top(proper(z0)) 268.22/85.85
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.85
ACTIVE(dbl(z0)) → c9(DBL(active(z0)), ACTIVE(z0)) 268.22/85.85
ACTIVE(dbls(z0)) → c10(DBLS(active(z0)), ACTIVE(z0)) 268.22/85.85
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.85
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.85
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 268.22/85.85
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.85
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.85
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.85
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.85
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.85
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.85
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.85
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.85
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.85
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.85
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.85
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.85
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.85
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.85
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.85
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.85
S(ok(z0)) → c32(S(z0)) 268.22/85.85
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.85
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.85
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.85
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.85
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.85
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.85
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.85
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.85
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.85
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.85
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.85
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.85
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.85
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.85
ACTIVE(dbl(z0)) → c9(DBL(active(z0)), ACTIVE(z0)) 268.22/85.85
ACTIVE(dbls(z0)) → c10(DBLS(active(z0)), ACTIVE(z0)) 268.22/85.85
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.85
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.85
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 268.22/85.85
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.85
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.85
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.85
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.85
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.85
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.85
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.85
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.85
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.85
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.85
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.85
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.85
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.85
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.85
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.85
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.85
S(ok(z0)) → c32(S(z0)) 268.22/85.85
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.85
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.85
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.85
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.85
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.85
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.85
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.85
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.85
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.85
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.85
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.85
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.85
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.85
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c8, c

268.22/85.85
268.22/85.85

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

Use narrowing to replace ACTIVE(dbl(z0)) → c9(DBL(active(z0)), ACTIVE(z0)) by

ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0)), ACTIVE(dbl(0))) 268.22/85.85
ACTIVE(dbl(dbl(s(z0)))) → c9(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 268.22/85.85
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil)), ACTIVE(dbls(nil))) 268.22/85.85
ACTIVE(dbl(dbls(cons(z0, z1)))) → c9(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.85
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.85
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.85
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.85
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c9(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.85
ACTIVE(dbl(from(z0))) → c9(DBL(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 268.22/85.85
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.85
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.85
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.85
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.85
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
268.22/85.85
268.22/85.85

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.85
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.85
active(dbls(nil)) → mark(nil) 268.22/85.85
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.85
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.85
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.85
active(indx(nil, z0)) → mark(nil) 268.22/85.85
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.85
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.85
active(dbl(z0)) → dbl(active(z0)) 268.22/85.85
active(dbls(z0)) → dbls(active(z0)) 268.22/85.85
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.85
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.85
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.85
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.85
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.85
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.85
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.85
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.85
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.85
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.85
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.85
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.85
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.85
proper(0) → ok(0) 268.22/85.85
proper(s(z0)) → s(proper(z0)) 268.22/85.85
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.85
proper(nil) → ok(nil) 268.22/85.85
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.85
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.85
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.85
proper(from(z0)) → from(proper(z0)) 268.22/85.85
s(ok(z0)) → ok(s(z0)) 268.22/85.85
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.85
from(ok(z0)) → ok(from(z0)) 268.22/85.85
top(mark(z0)) → top(proper(z0)) 268.22/85.85
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.85
ACTIVE(dbls(z0)) → c10(DBLS(active(z0)), ACTIVE(z0)) 268.22/85.85
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.85
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.85
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 268.22/85.85
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.85
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.85
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.85
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.85
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.85
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.85
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.85
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.85
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.85
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.85
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.85
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.85
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.85
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.85
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.85
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.85
S(ok(z0)) → c32(S(z0)) 268.22/85.85
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.85
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.85
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.86
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.86
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0)), ACTIVE(dbl(0))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c9(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil)), ACTIVE(dbls(nil))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c9(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c9(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c9(DBL(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.86
ACTIVE(dbls(z0)) → c10(DBLS(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.86
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 268.22/85.86
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.86
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.86
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.86
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.86
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.86
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.86
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.86
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.86
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.86
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.86
S(ok(z0)) → c32(S(z0)) 268.22/85.86
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.86
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.86
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.86
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.86
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0)), ACTIVE(dbl(0))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c9(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil)), ACTIVE(dbls(nil))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c9(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c9(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c9(DBL(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c8, c, c9

268.22/85.86
268.22/85.86

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

Removed 1 trailing tuple parts
268.22/85.86
268.22/85.86

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.86
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.86
active(dbls(nil)) → mark(nil) 268.22/85.86
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.86
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.86
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.86
active(indx(nil, z0)) → mark(nil) 268.22/85.86
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.86
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.86
active(dbl(z0)) → dbl(active(z0)) 268.22/85.86
active(dbls(z0)) → dbls(active(z0)) 268.22/85.86
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.86
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.86
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.86
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.86
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.86
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.86
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.86
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.86
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.86
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.86
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.86
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.86
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.86
proper(0) → ok(0) 268.22/85.86
proper(s(z0)) → s(proper(z0)) 268.22/85.86
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.86
proper(nil) → ok(nil) 268.22/85.86
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.86
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.86
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.86
proper(from(z0)) → from(proper(z0)) 268.22/85.86
s(ok(z0)) → ok(s(z0)) 268.22/85.86
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.86
from(ok(z0)) → ok(from(z0)) 268.22/85.86
top(mark(z0)) → top(proper(z0)) 268.22/85.86
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.86
ACTIVE(dbls(z0)) → c10(DBLS(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.86
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 268.22/85.86
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.86
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.86
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.86
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.86
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.86
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.86
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.86
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.86
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.86
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.86
S(ok(z0)) → c32(S(z0)) 268.22/85.86
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.86
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.86
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.86
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c9(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil)), ACTIVE(dbls(nil))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c9(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c9(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c9(DBL(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.86
ACTIVE(dbls(z0)) → c10(DBLS(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.86
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 268.22/85.86
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.86
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.86
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.86
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.86
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.86
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.86
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.86
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.86
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.86
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.86
S(ok(z0)) → c32(S(z0)) 268.22/85.86
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.86
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.86
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.86
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c9(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil)), ACTIVE(dbls(nil))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c9(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c9(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c9(DBL(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9

268.22/85.86
268.22/85.86

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

Split RHS of tuples not part of any SCC
268.22/85.86
268.22/85.86

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.86
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.86
active(dbls(nil)) → mark(nil) 268.22/85.86
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.86
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.86
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.86
active(indx(nil, z0)) → mark(nil) 268.22/85.86
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.86
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.86
active(dbl(z0)) → dbl(active(z0)) 268.22/85.86
active(dbls(z0)) → dbls(active(z0)) 268.22/85.86
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.86
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.86
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.86
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.86
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.86
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.86
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.86
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.86
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.86
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.86
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.86
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.86
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.86
proper(0) → ok(0) 268.22/85.86
proper(s(z0)) → s(proper(z0)) 268.22/85.86
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.86
proper(nil) → ok(nil) 268.22/85.86
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.86
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.86
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.86
proper(from(z0)) → from(proper(z0)) 268.22/85.86
s(ok(z0)) → ok(s(z0)) 268.22/85.86
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.86
from(ok(z0)) → ok(from(z0)) 268.22/85.86
top(mark(z0)) → top(proper(z0)) 268.22/85.86
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.86
ACTIVE(dbls(z0)) → c10(DBLS(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.86
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 268.22/85.86
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.86
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.86
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.86
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.86
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.86
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.86
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.86
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.86
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.86
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.86
S(ok(z0)) → c32(S(z0)) 268.22/85.86
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.86
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.86
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.86
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.86
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil)), ACTIVE(dbls(nil))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c9(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c9(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.86
ACTIVE(dbls(z0)) → c10(DBLS(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.86
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 268.22/85.86
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.86
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.86
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.86
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.86
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.86
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.86
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.86
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.86
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.86
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.86
S(ok(z0)) → c32(S(z0)) 268.22/85.86
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.86
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.86
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.86
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.86
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil)), ACTIVE(dbls(nil))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c9(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c9(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1

268.22/85.86
268.22/85.86

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

Use narrowing to replace ACTIVE(dbls(z0)) → c10(DBLS(active(z0)), ACTIVE(z0)) by

ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0)), ACTIVE(dbl(0))) 268.22/85.86
ACTIVE(dbls(dbl(s(z0)))) → c10(DBLS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil)), ACTIVE(dbls(nil))) 268.22/85.86
ACTIVE(dbls(dbls(cons(z0, z1)))) → c10(DBLS(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c10(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbls(from(z0))) → c10(DBLS(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
268.22/85.86
268.22/85.86

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.86
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.86
active(dbls(nil)) → mark(nil) 268.22/85.86
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.86
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.86
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.86
active(indx(nil, z0)) → mark(nil) 268.22/85.86
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.86
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.86
active(dbl(z0)) → dbl(active(z0)) 268.22/85.86
active(dbls(z0)) → dbls(active(z0)) 268.22/85.86
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.86
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.86
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.86
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.86
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.86
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.86
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.86
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.86
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.86
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.86
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.86
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.86
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.86
proper(0) → ok(0) 268.22/85.86
proper(s(z0)) → s(proper(z0)) 268.22/85.86
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.86
proper(nil) → ok(nil) 268.22/85.86
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.86
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.86
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.86
proper(from(z0)) → from(proper(z0)) 268.22/85.86
s(ok(z0)) → ok(s(z0)) 268.22/85.86
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.86
from(ok(z0)) → ok(from(z0)) 268.22/85.86
top(mark(z0)) → top(proper(z0)) 268.22/85.86
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.86
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 268.22/85.86
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.86
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.86
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.86
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.86
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.86
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.86
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.86
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.86
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.86
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.86
S(ok(z0)) → c32(S(z0)) 268.22/85.86
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.86
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.86
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.86
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.86
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil)), ACTIVE(dbls(nil))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c9(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c9(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0)), ACTIVE(dbl(0))) 268.22/85.86
ACTIVE(dbls(dbl(s(z0)))) → c10(DBLS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil)), ACTIVE(dbls(nil))) 268.22/85.86
ACTIVE(dbls(dbls(cons(z0, z1)))) → c10(DBLS(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c10(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbls(from(z0))) → c10(DBLS(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.86
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 268.22/85.86
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.86
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.86
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.86
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.86
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.86
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.86
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.86
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.86
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.86
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.86
S(ok(z0)) → c32(S(z0)) 268.22/85.86
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.86
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.86
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.86
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.86
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil)), ACTIVE(dbls(nil))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c9(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c9(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0)), ACTIVE(dbl(0))) 268.22/85.86
ACTIVE(dbls(dbl(s(z0)))) → c10(DBLS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil)), ACTIVE(dbls(nil))) 268.22/85.86
ACTIVE(dbls(dbls(cons(z0, z1)))) → c10(DBLS(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c10(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbls(from(z0))) → c10(DBLS(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10

268.22/85.86
268.22/85.86

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

Removed 3 trailing tuple parts
268.22/85.86
268.22/85.86

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.86
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.86
active(dbls(nil)) → mark(nil) 268.22/85.86
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.86
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.86
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.86
active(indx(nil, z0)) → mark(nil) 268.22/85.86
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.86
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.86
active(dbl(z0)) → dbl(active(z0)) 268.22/85.86
active(dbls(z0)) → dbls(active(z0)) 268.22/85.86
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.86
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.86
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.86
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.86
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.86
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.86
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.86
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.86
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.86
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.86
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.86
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.86
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.86
proper(0) → ok(0) 268.22/85.86
proper(s(z0)) → s(proper(z0)) 268.22/85.86
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.86
proper(nil) → ok(nil) 268.22/85.86
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.86
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.86
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.86
proper(from(z0)) → from(proper(z0)) 268.22/85.86
s(ok(z0)) → ok(s(z0)) 268.22/85.86
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.86
from(ok(z0)) → ok(from(z0)) 268.22/85.86
top(mark(z0)) → top(proper(z0)) 268.22/85.86
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.86
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 268.22/85.86
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.86
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.86
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.86
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.86
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.86
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.86
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.86
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.86
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.86
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.86
S(ok(z0)) → c32(S(z0)) 268.22/85.86
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.86
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.86
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.86
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c9(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c9(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbls(dbl(s(z0)))) → c10(DBLS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbls(dbls(cons(z0, z1)))) → c10(DBLS(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c10(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbls(from(z0))) → c10(DBLS(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.86
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.86
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.86
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 268.22/85.86
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.86
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.86
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.86
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.86
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.86
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.86
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.86
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.86
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.86
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.86
S(ok(z0)) → c32(S(z0)) 268.22/85.86
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.86
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.86
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.86
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c9(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c9(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbls(dbl(s(z0)))) → c10(DBLS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbls(dbls(cons(z0, z1)))) → c10(DBLS(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c10(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbls(from(z0))) → c10(DBLS(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.86
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.86
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10

268.22/85.86
268.22/85.86

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

Split RHS of tuples not part of any SCC
268.22/85.86
268.22/85.86

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.86
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.86
active(dbls(nil)) → mark(nil) 268.22/85.86
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.86
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.86
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.86
active(indx(nil, z0)) → mark(nil) 268.22/85.86
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.86
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.86
active(dbl(z0)) → dbl(active(z0)) 268.22/85.86
active(dbls(z0)) → dbls(active(z0)) 268.22/85.86
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.86
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.86
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.86
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.86
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.86
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.86
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.86
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.86
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.86
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.86
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.86
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.86
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.86
proper(0) → ok(0) 268.22/85.86
proper(s(z0)) → s(proper(z0)) 268.22/85.86
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.86
proper(nil) → ok(nil) 268.22/85.86
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.86
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.86
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.86
proper(from(z0)) → from(proper(z0)) 268.22/85.86
s(ok(z0)) → ok(s(z0)) 268.22/85.86
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.86
from(ok(z0)) → ok(from(z0)) 268.22/85.86
top(mark(z0)) → top(proper(z0)) 268.22/85.86
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.86
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 268.22/85.86
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.86
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.86
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.86
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.86
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.86
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.86
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.86
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.86
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.86
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.86
S(ok(z0)) → c32(S(z0)) 268.22/85.86
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.86
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.86
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.86
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.86
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c9(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c10(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.86
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.86
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.86
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.86
ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) 268.22/85.86
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.86
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.86
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.86
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.86
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.86
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.86
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.86
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.86
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.86
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.86
S(ok(z0)) → c32(S(z0)) 268.22/85.86
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.86
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.86
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.86
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.86
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c9(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c10(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.86
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.86
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.86
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2

268.22/85.86
268.22/85.86

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

Use narrowing to replace ACTIVE(indx(z0, z1)) → c13(INDX(active(z0), z1), ACTIVE(z0)) by

ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1), ACTIVE(dbl(0))) 268.22/85.86
ACTIVE(indx(dbl(s(z0)), x1)) → c13(INDX(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1), ACTIVE(dbls(nil))) 268.22/85.86
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c13(INDX(mark(cons(dbl(z0), dbls(z1))), x1), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c13(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(indx(from(z0), x1)) → c13(INDX(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 268.22/85.86
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
268.22/85.86
268.22/85.86

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.86
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.86
active(dbls(nil)) → mark(nil) 268.22/85.86
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.86
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.86
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.86
active(indx(nil, z0)) → mark(nil) 268.22/85.86
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.86
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.86
active(dbl(z0)) → dbl(active(z0)) 268.22/85.86
active(dbls(z0)) → dbls(active(z0)) 268.22/85.86
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.86
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.86
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.86
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.86
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.86
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.86
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.86
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.86
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.86
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.86
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.86
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.86
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.86
proper(0) → ok(0) 268.22/85.86
proper(s(z0)) → s(proper(z0)) 268.22/85.86
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.86
proper(nil) → ok(nil) 268.22/85.86
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.86
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.86
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.86
proper(from(z0)) → from(proper(z0)) 268.22/85.86
s(ok(z0)) → ok(s(z0)) 268.22/85.86
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.86
from(ok(z0)) → ok(from(z0)) 268.22/85.86
top(mark(z0)) → top(proper(z0)) 268.22/85.86
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.86
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.86
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.86
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.86
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.86
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.86
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.86
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.86
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.86
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.86
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.86
S(ok(z0)) → c32(S(z0)) 268.22/85.86
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.86
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.86
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.86
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.86
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c9(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c10(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.86
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.86
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.86
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.86
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1), ACTIVE(dbl(0))) 268.22/85.86
ACTIVE(indx(dbl(s(z0)), x1)) → c13(INDX(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1), ACTIVE(dbls(nil))) 268.22/85.86
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c13(INDX(mark(cons(dbl(z0), dbls(z1))), x1), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c13(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(indx(from(z0), x1)) → c13(INDX(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 268.22/85.86
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.86
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.86
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.86
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.86
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.86
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.86
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.86
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.86
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.86
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.86
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.86
S(ok(z0)) → c32(S(z0)) 268.22/85.86
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.86
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.86
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.86
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.86
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c9(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil)), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c10(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.86
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.86
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.86
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.86
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1), ACTIVE(dbl(0))) 268.22/85.86
ACTIVE(indx(dbl(s(z0)), x1)) → c13(INDX(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1), ACTIVE(dbls(nil))) 268.22/85.86
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c13(INDX(mark(cons(dbl(z0), dbls(z1))), x1), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1), ACTIVE(indx(nil, z0))) 268.22/85.86
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c13(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(indx(from(z0), x1)) → c13(INDX(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 268.22/85.86
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2, c13

268.22/85.86
268.22/85.86

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

Removed 5 trailing tuple parts
268.22/85.86
268.22/85.86

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.86
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.86
active(dbls(nil)) → mark(nil) 268.22/85.86
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.86
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.86
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.86
active(indx(nil, z0)) → mark(nil) 268.22/85.86
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.86
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.86
active(dbl(z0)) → dbl(active(z0)) 268.22/85.86
active(dbls(z0)) → dbls(active(z0)) 268.22/85.86
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.86
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.86
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.86
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.86
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.86
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.86
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.86
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.86
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.86
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.86
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.86
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.86
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.86
proper(0) → ok(0) 268.22/85.86
proper(s(z0)) → s(proper(z0)) 268.22/85.86
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.86
proper(nil) → ok(nil) 268.22/85.86
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.86
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.86
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.86
proper(from(z0)) → from(proper(z0)) 268.22/85.86
s(ok(z0)) → ok(s(z0)) 268.22/85.86
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.86
from(ok(z0)) → ok(from(z0)) 268.22/85.86
top(mark(z0)) → top(proper(z0)) 268.22/85.86
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.86
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.86
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.86
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.86
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.86
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.86
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.86
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.86
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.86
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.86
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.86
S(ok(z0)) → c32(S(z0)) 268.22/85.86
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.86
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.86
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.86
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.86
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c9(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c10(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.86
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.86
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.86
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.86
ACTIVE(indx(dbl(s(z0)), x1)) → c13(INDX(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c13(INDX(mark(cons(dbl(z0), dbls(z1))), x1), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c13(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(indx(from(z0), x1)) → c13(INDX(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 268.22/85.86
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.86
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.86
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.86
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.86
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.86
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.86
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.86
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.86
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.86
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.86
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.86
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.86
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.86
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.86
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.86
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.86
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.86
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.86
S(ok(z0)) → c32(S(z0)) 268.22/85.86
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.86
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.86
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.86
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.86
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.86
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.86
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.86
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.86
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c9(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.86
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c10(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.86
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.86
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.86
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.86
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.86
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.86
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.86
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.86
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.86
ACTIVE(indx(dbl(s(z0)), x1)) → c13(INDX(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 268.22/85.86
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c13(INDX(mark(cons(dbl(z0), dbls(z1))), x1), ACTIVE(dbls(cons(z0, z1)))) 268.22/85.86
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.86
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.86
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c13(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1), ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.86
ACTIVE(indx(from(z0), x1)) → c13(INDX(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 268.22/85.86
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.86
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.87
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13

268.22/85.87
268.22/85.87

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

Split RHS of tuples not part of any SCC
268.22/85.87
268.22/85.87

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.87
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.87
active(dbls(nil)) → mark(nil) 268.22/85.87
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.87
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.87
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.87
active(indx(nil, z0)) → mark(nil) 268.22/85.87
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.87
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.87
active(dbl(z0)) → dbl(active(z0)) 268.22/85.87
active(dbls(z0)) → dbls(active(z0)) 268.22/85.87
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.87
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.87
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.87
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.87
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.87
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.87
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.87
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.87
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.87
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.87
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.87
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.87
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.87
proper(0) → ok(0) 268.22/85.87
proper(s(z0)) → s(proper(z0)) 268.22/85.87
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.87
proper(nil) → ok(nil) 268.22/85.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.87
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.87
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.87
proper(from(z0)) → from(proper(z0)) 268.22/85.87
s(ok(z0)) → ok(s(z0)) 268.22/85.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.87
from(ok(z0)) → ok(from(z0)) 268.22/85.87
top(mark(z0)) → top(proper(z0)) 268.22/85.87
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.87
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.87
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.87
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.87
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.87
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.87
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.87
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.87
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.87
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.87
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.87
S(ok(z0)) → c32(S(z0)) 268.22/85.87
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.87
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.87
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.87
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.87
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.87
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.87
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.87
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.87
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.87
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.87
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.87
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.87
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.87
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.87
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.87
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.87
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.87
PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.87
S(ok(z0)) → c32(S(z0)) 268.22/85.87
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.87
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.87
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.87
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.87
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.87
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.87
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.87
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3

268.22/85.87
268.22/85.87

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

Use narrowing to replace PROPER(dbl(z0)) → c23(DBL(proper(z0)), PROPER(z0)) by

PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(dbl(0)) → c23(DBL(ok(0)), PROPER(0)) 268.22/85.87
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(dbl(nil)) → c23(DBL(ok(nil)), PROPER(nil)) 268.22/85.87
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0)))
268.22/85.87
268.22/85.87

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.87
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.87
active(dbls(nil)) → mark(nil) 268.22/85.87
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.87
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.87
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.87
active(indx(nil, z0)) → mark(nil) 268.22/85.87
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.87
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.87
active(dbl(z0)) → dbl(active(z0)) 268.22/85.87
active(dbls(z0)) → dbls(active(z0)) 268.22/85.87
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.87
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.87
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.87
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.87
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.87
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.87
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.87
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.87
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.87
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.87
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.87
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.87
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.87
proper(0) → ok(0) 268.22/85.87
proper(s(z0)) → s(proper(z0)) 268.22/85.87
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.87
proper(nil) → ok(nil) 268.22/85.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.87
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.87
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.87
proper(from(z0)) → from(proper(z0)) 268.22/85.87
s(ok(z0)) → ok(s(z0)) 268.22/85.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.87
from(ok(z0)) → ok(from(z0)) 268.22/85.87
top(mark(z0)) → top(proper(z0)) 268.22/85.87
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.87
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.87
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.87
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.87
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.87
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.87
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.87
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.87
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.87
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.87
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.87
S(ok(z0)) → c32(S(z0)) 268.22/85.87
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.87
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.87
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.87
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.87
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.87
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.87
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.87
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.87
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(dbl(0)) → c23(DBL(ok(0)), PROPER(0)) 268.22/85.87
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(dbl(nil)) → c23(DBL(ok(nil)), PROPER(nil)) 268.22/85.87
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.87
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.87
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.87
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.87
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.87
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.87
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.87
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.87
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.87
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.87
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.87
S(ok(z0)) → c32(S(z0)) 268.22/85.87
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.87
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.87
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.87
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.87
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.87
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.87
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.87
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.87
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(dbl(0)) → c23(DBL(ok(0)), PROPER(0)) 268.22/85.87
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(dbl(nil)) → c23(DBL(ok(nil)), PROPER(nil)) 268.22/85.87
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23

268.22/85.87
268.22/85.87

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

Removed 2 trailing tuple parts
268.22/85.87
268.22/85.87

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.87
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.87
active(dbls(nil)) → mark(nil) 268.22/85.87
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.87
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.87
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.87
active(indx(nil, z0)) → mark(nil) 268.22/85.87
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.87
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.87
active(dbl(z0)) → dbl(active(z0)) 268.22/85.87
active(dbls(z0)) → dbls(active(z0)) 268.22/85.87
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.87
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.87
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.87
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.87
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.87
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.87
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.87
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.87
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.87
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.87
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.87
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.87
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.87
proper(0) → ok(0) 268.22/85.87
proper(s(z0)) → s(proper(z0)) 268.22/85.87
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.87
proper(nil) → ok(nil) 268.22/85.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.87
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.87
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.87
proper(from(z0)) → from(proper(z0)) 268.22/85.87
s(ok(z0)) → ok(s(z0)) 268.22/85.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.87
from(ok(z0)) → ok(from(z0)) 268.22/85.87
top(mark(z0)) → top(proper(z0)) 268.22/85.87
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.87
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.87
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.87
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.87
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.87
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.87
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.87
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.87
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.87
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.87
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.87
S(ok(z0)) → c32(S(z0)) 268.22/85.87
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.87
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.87
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.87
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.87
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.87
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.87
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.87
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.87
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.87
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.87
PROPER(dbl(nil)) → c23(DBL(ok(nil)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.87
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.87
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.87
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.87
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.87
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.87
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.87
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.87
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.87
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.87
PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.87
S(ok(z0)) → c32(S(z0)) 268.22/85.87
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.87
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.87
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.87
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.87
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.87
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.87
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.87
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.87
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.87
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.87
PROPER(dbl(nil)) → c23(DBL(ok(nil)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23

268.22/85.87
268.22/85.87

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

Use narrowing to replace PROPER(s(z0)) → c25(S(proper(z0)), PROPER(z0)) by

PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(s(0)) → c25(S(ok(0)), PROPER(0)) 268.22/85.87
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(s(nil)) → c25(S(ok(nil)), PROPER(nil)) 268.22/85.87
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0)))
268.22/85.87
268.22/85.87

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.87
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.87
active(dbls(nil)) → mark(nil) 268.22/85.87
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.87
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.87
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.87
active(indx(nil, z0)) → mark(nil) 268.22/85.87
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.87
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.87
active(dbl(z0)) → dbl(active(z0)) 268.22/85.87
active(dbls(z0)) → dbls(active(z0)) 268.22/85.87
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.87
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.87
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.87
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.87
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.87
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.87
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.87
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.87
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.87
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.87
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.87
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.87
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.87
proper(0) → ok(0) 268.22/85.87
proper(s(z0)) → s(proper(z0)) 268.22/85.87
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.87
proper(nil) → ok(nil) 268.22/85.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.87
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.87
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.87
proper(from(z0)) → from(proper(z0)) 268.22/85.87
s(ok(z0)) → ok(s(z0)) 268.22/85.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.87
from(ok(z0)) → ok(from(z0)) 268.22/85.87
top(mark(z0)) → top(proper(z0)) 268.22/85.87
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.87
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.87
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.87
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.87
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.87
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.87
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.87
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.87
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.87
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.87
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.87
S(ok(z0)) → c32(S(z0)) 268.22/85.87
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.87
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.87
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.87
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.87
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.87
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.87
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.87
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.87
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.87
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.87
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.87
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(s(0)) → c25(S(ok(0)), PROPER(0)) 268.22/85.87
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(s(nil)) → c25(S(ok(nil)), PROPER(nil)) 268.22/85.87
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.87
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.87
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.87
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.87
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.87
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.87
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.87
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.87
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.87
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.87
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.87
S(ok(z0)) → c32(S(z0)) 268.22/85.87
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.87
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.87
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.87
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.87
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.87
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.87
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.87
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.87
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.87
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.87
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.87
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(s(0)) → c25(S(ok(0)), PROPER(0)) 268.22/85.87
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(s(nil)) → c25(S(ok(nil)), PROPER(nil)) 268.22/85.87
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23, c25

268.22/85.87
268.22/85.87

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

Removed 2 trailing tuple parts
268.22/85.87
268.22/85.87

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.87
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.87
active(dbls(nil)) → mark(nil) 268.22/85.87
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.87
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.87
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.87
active(indx(nil, z0)) → mark(nil) 268.22/85.87
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.87
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.87
active(dbl(z0)) → dbl(active(z0)) 268.22/85.87
active(dbls(z0)) → dbls(active(z0)) 268.22/85.87
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.87
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.87
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.87
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.87
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.87
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.87
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.87
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.87
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.87
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.87
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.87
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.87
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.87
proper(0) → ok(0) 268.22/85.87
proper(s(z0)) → s(proper(z0)) 268.22/85.87
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.87
proper(nil) → ok(nil) 268.22/85.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.87
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.87
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.87
proper(from(z0)) → from(proper(z0)) 268.22/85.87
s(ok(z0)) → ok(s(z0)) 268.22/85.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.87
from(ok(z0)) → ok(from(z0)) 268.22/85.87
top(mark(z0)) → top(proper(z0)) 268.22/85.87
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.87
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.87
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.87
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.87
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.87
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.87
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.87
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.87
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.87
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.87
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.87
S(ok(z0)) → c32(S(z0)) 268.22/85.87
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.87
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.87
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.87
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.87
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.87
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.87
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.87
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.87
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.87
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.87
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.87
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.87
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.87
PROPER(s(nil)) → c25(S(ok(nil)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.87
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.87
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.87
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.87
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.87
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.87
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.87
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.87
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.87
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.87
PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) 268.22/85.87
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.87
S(ok(z0)) → c32(S(z0)) 268.22/85.87
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.87
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.87
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.87
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.87
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.87
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.87
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.87
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.87
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.87
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.87
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.87
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.87
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.87
PROPER(s(nil)) → c25(S(ok(nil)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23, c25, c25

268.22/85.87
268.22/85.87

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

Use narrowing to replace PROPER(dbls(z0)) → c26(DBLS(proper(z0)), PROPER(z0)) by

PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(dbls(0)) → c26(DBLS(ok(0)), PROPER(0)) 268.22/85.87
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(dbls(nil)) → c26(DBLS(ok(nil)), PROPER(nil)) 268.22/85.87
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0)))
268.22/85.87
268.22/85.87

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.87
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.87
active(dbls(nil)) → mark(nil) 268.22/85.87
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.87
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.87
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.87
active(indx(nil, z0)) → mark(nil) 268.22/85.87
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.87
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.87
active(dbl(z0)) → dbl(active(z0)) 268.22/85.87
active(dbls(z0)) → dbls(active(z0)) 268.22/85.87
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.87
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.87
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.87
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.87
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.87
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.87
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.87
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.87
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.87
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.87
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.87
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.87
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.87
proper(0) → ok(0) 268.22/85.87
proper(s(z0)) → s(proper(z0)) 268.22/85.87
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.87
proper(nil) → ok(nil) 268.22/85.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.87
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.87
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.87
proper(from(z0)) → from(proper(z0)) 268.22/85.87
s(ok(z0)) → ok(s(z0)) 268.22/85.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.87
from(ok(z0)) → ok(from(z0)) 268.22/85.87
top(mark(z0)) → top(proper(z0)) 268.22/85.87
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.87
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.87
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.87
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.87
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.87
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.87
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.87
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.87
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.87
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.87
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.87
S(ok(z0)) → c32(S(z0)) 268.22/85.87
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.87
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.87
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.87
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.87
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.87
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.87
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.87
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.87
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.87
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.87
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.87
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.87
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.87
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.87
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(dbls(0)) → c26(DBLS(ok(0)), PROPER(0)) 268.22/85.87
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(dbls(nil)) → c26(DBLS(ok(nil)), PROPER(nil)) 268.22/85.87
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.87
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.87
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.87
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.87
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.87
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.87
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.87
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.87
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.87
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.87
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.87
S(ok(z0)) → c32(S(z0)) 268.22/85.87
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.87
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.87
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.87
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.87
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.87
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.87
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.87
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.87
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.87
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.87
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.87
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.87
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.87
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.87
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(dbls(0)) → c26(DBLS(ok(0)), PROPER(0)) 268.22/85.87
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(dbls(nil)) → c26(DBLS(ok(nil)), PROPER(nil)) 268.22/85.87
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c28, c29, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23, c25, c25, c26

268.22/85.87
268.22/85.87

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

Removed 2 trailing tuple parts
268.22/85.87
268.22/85.87

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.87
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.87
active(dbls(nil)) → mark(nil) 268.22/85.87
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.87
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.87
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.87
active(indx(nil, z0)) → mark(nil) 268.22/85.87
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.87
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.87
active(dbl(z0)) → dbl(active(z0)) 268.22/85.87
active(dbls(z0)) → dbls(active(z0)) 268.22/85.87
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.87
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.87
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.87
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.87
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.87
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.87
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.87
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.87
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.87
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.87
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.87
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.87
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.87
proper(0) → ok(0) 268.22/85.87
proper(s(z0)) → s(proper(z0)) 268.22/85.87
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.87
proper(nil) → ok(nil) 268.22/85.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.87
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.87
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.87
proper(from(z0)) → from(proper(z0)) 268.22/85.87
s(ok(z0)) → ok(s(z0)) 268.22/85.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.87
from(ok(z0)) → ok(from(z0)) 268.22/85.87
top(mark(z0)) → top(proper(z0)) 268.22/85.87
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.87
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.87
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.87
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.87
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.87
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.87
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.87
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.87
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.87
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.87
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.87
S(ok(z0)) → c32(S(z0)) 268.22/85.87
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.87
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.87
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.87
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.87
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.87
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.87
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.87
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.87
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.87
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.87
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.87
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.87
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.87
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.87
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.87
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.87
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.87
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.87
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.87
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.87
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.87
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.87
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.87
PROPER(dbls(nil)) → c26(DBLS(ok(nil)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.87
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.87
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.87
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.87
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.87
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.87
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.87
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.87
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.87
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.87
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.87
PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.87
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.87
S(ok(z0)) → c32(S(z0)) 268.22/85.87
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.87
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.87
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.87
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.87
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.87
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.87
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.87
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.87
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.87
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.87
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.87
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.87
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.87
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.87
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.87
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.87
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.87
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.87
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.87
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.87
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.87
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.87
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.87
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.87
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.88
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.88
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.88
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.88
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.88
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.88
PROPER(dbls(nil)) → c26(DBLS(ok(nil)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c28, c29, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23, c25, c25, c26, c26

268.22/85.88
268.22/85.88

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

Use narrowing to replace PROPER(cons(z0, z1)) → c28(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 268.22/85.88
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 268.22/85.88
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 268.22/85.88
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 268.22/85.88
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
268.22/85.88
268.22/85.88

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.88
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.88
active(dbls(nil)) → mark(nil) 268.22/85.88
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.88
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.88
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.88
active(indx(nil, z0)) → mark(nil) 268.22/85.88
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.88
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.88
active(dbl(z0)) → dbl(active(z0)) 268.22/85.88
active(dbls(z0)) → dbls(active(z0)) 268.22/85.88
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.88
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.88
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.88
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.88
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.88
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.88
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.88
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.88
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.88
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.88
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.88
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.88
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.88
proper(0) → ok(0) 268.22/85.88
proper(s(z0)) → s(proper(z0)) 268.22/85.88
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.88
proper(nil) → ok(nil) 268.22/85.88
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.88
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.88
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.88
proper(from(z0)) → from(proper(z0)) 268.22/85.88
s(ok(z0)) → ok(s(z0)) 268.22/85.88
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.88
from(ok(z0)) → ok(from(z0)) 268.22/85.88
top(mark(z0)) → top(proper(z0)) 268.22/85.88
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.88
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.88
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.88
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.88
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.88
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.88
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.88
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.88
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.88
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.88
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.88
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.88
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.88
S(ok(z0)) → c32(S(z0)) 268.22/85.88
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.88
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.88
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.88
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.88
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.88
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.88
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.88
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.88
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.88
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.88
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.88
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.88
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.88
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.88
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 268.22/85.88
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 268.22/85.88
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 268.22/85.88
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 268.22/85.88
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.88
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.88
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.88
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.88
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.88
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.88
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.88
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.88
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.88
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.88
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.88
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.88
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.88
S(ok(z0)) → c32(S(z0)) 268.22/85.88
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.88
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.88
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.88
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.88
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.88
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.88
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.88
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.88
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.88
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.88
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.88
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.88
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.88
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.88
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 268.22/85.88
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 268.22/85.88
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 268.22/85.88
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 268.22/85.88
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c29, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23, c25, c25, c26, c26, c28

268.22/85.88
268.22/85.88

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

Removed 4 trailing tuple parts
268.22/85.88
268.22/85.88

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.88
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.88
active(dbls(nil)) → mark(nil) 268.22/85.88
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.88
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.88
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.88
active(indx(nil, z0)) → mark(nil) 268.22/85.88
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.88
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.88
active(dbl(z0)) → dbl(active(z0)) 268.22/85.88
active(dbls(z0)) → dbls(active(z0)) 268.22/85.88
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.88
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.88
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.88
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.88
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.88
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.88
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.88
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.88
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.88
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.88
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.88
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.88
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.88
proper(0) → ok(0) 268.22/85.88
proper(s(z0)) → s(proper(z0)) 268.22/85.88
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.88
proper(nil) → ok(nil) 268.22/85.88
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.88
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.88
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.88
proper(from(z0)) → from(proper(z0)) 268.22/85.88
s(ok(z0)) → ok(s(z0)) 268.22/85.88
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.88
from(ok(z0)) → ok(from(z0)) 268.22/85.88
top(mark(z0)) → top(proper(z0)) 268.22/85.88
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.88
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.88
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.88
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.88
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.88
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.88
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.88
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.88
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.88
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.88
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.88
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.88
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.88
S(ok(z0)) → c32(S(z0)) 268.22/85.88
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.88
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.88
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.88
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.88
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.88
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.88
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.88
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.88
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.88
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.88
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.88
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.88
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.88
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.88
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.22/85.88
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.88
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.22/85.88
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.88
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.88
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.88
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.88
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.88
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.88
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.88
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.88
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.88
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.88
PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.88
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.88
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.88
S(ok(z0)) → c32(S(z0)) 268.22/85.88
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.88
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.88
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.88
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.88
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.88
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.88
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.88
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.88
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.88
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.88
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.88
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.88
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.88
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.88
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.22/85.88
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.88
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.22/85.88
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c29, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23, c25, c25, c26, c26, c28, c28

268.22/85.88
268.22/85.88

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

Use narrowing to replace PROPER(sel(z0, z1)) → c29(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 268.22/85.88
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 268.22/85.88
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 268.22/85.88
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 268.22/85.88
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
268.22/85.88
268.22/85.88

(42) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.88
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.88
active(dbls(nil)) → mark(nil) 268.22/85.88
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.88
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.88
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.88
active(indx(nil, z0)) → mark(nil) 268.22/85.88
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.88
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.88
active(dbl(z0)) → dbl(active(z0)) 268.22/85.88
active(dbls(z0)) → dbls(active(z0)) 268.22/85.88
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.88
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.88
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.88
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.88
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.88
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.88
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.88
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.88
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.88
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.88
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.88
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.88
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.88
proper(0) → ok(0) 268.22/85.88
proper(s(z0)) → s(proper(z0)) 268.22/85.88
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.88
proper(nil) → ok(nil) 268.22/85.88
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.88
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.88
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.88
proper(from(z0)) → from(proper(z0)) 268.22/85.88
s(ok(z0)) → ok(s(z0)) 268.22/85.88
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.88
from(ok(z0)) → ok(from(z0)) 268.22/85.88
top(mark(z0)) → top(proper(z0)) 268.22/85.88
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.88
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.88
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.88
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.88
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.88
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.88
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.88
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.88
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.88
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.88
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.88
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.88
S(ok(z0)) → c32(S(z0)) 268.22/85.88
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.88
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.88
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.88
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.88
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.88
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.88
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.88
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.88
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.88
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.88
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.88
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.88
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.88
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.88
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.22/85.88
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.88
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.22/85.88
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.88
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 268.22/85.88
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 268.22/85.88
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 268.22/85.88
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 268.22/85.88
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.88
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.88
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.88
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.88
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.88
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.88
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.88
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.88
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.88
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.88
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.88
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.88
S(ok(z0)) → c32(S(z0)) 268.22/85.88
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.88
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.88
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.88
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.88
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.88
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.88
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.88
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.88
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.88
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.88
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.88
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.88
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.88
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.88
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.22/85.88
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.88
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.22/85.88
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.88
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 268.22/85.88
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 268.22/85.88
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 268.22/85.88
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 268.22/85.88
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23, c25, c25, c26, c26, c28, c28, c29

268.22/85.88
268.22/85.88

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

Removed 4 trailing tuple parts
268.22/85.88
268.22/85.88

(44) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.88
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.88
active(dbls(nil)) → mark(nil) 268.22/85.88
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.88
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.88
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.88
active(indx(nil, z0)) → mark(nil) 268.22/85.88
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.88
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.88
active(dbl(z0)) → dbl(active(z0)) 268.22/85.88
active(dbls(z0)) → dbls(active(z0)) 268.22/85.88
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.88
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.88
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.88
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.88
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.88
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.88
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.88
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.88
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.88
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.88
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.88
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.88
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.88
proper(0) → ok(0) 268.22/85.88
proper(s(z0)) → s(proper(z0)) 268.22/85.88
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.88
proper(nil) → ok(nil) 268.22/85.88
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.88
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.88
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.88
proper(from(z0)) → from(proper(z0)) 268.22/85.88
s(ok(z0)) → ok(s(z0)) 268.22/85.88
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.88
from(ok(z0)) → ok(from(z0)) 268.22/85.88
top(mark(z0)) → top(proper(z0)) 268.22/85.88
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.88
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.88
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.88
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.88
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.88
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.88
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.88
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.88
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.88
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.88
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.88
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.88
S(ok(z0)) → c32(S(z0)) 268.22/85.88
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.88
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.88
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.88
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.88
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.88
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.88
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.88
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.88
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.88
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.88
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.88
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.88
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.88
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.88
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.22/85.88
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.88
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.22/85.88
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.88
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.22/85.88
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.88
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.22/85.88
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.88
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.88
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.88
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.88
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.88
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.88
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.88
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.88
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.88
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.88
PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 268.22/85.88
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.88
S(ok(z0)) → c32(S(z0)) 268.22/85.88
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.88
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.88
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.88
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.88
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.88
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.88
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.88
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.88
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.88
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.88
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.88
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.88
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.88
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.88
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.22/85.88
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.88
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.22/85.88
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.88
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.22/85.88
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.88
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.22/85.88
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23, c25, c25, c26, c26, c28, c28, c29, c29

268.22/85.88
268.22/85.88

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

Use narrowing to replace PROPER(indx(z0, z1)) → c30(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 268.22/85.88
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 268.22/85.88
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 268.22/85.88
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 268.22/85.88
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
268.22/85.88
268.22/85.88

(46) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.88
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.88
active(dbls(nil)) → mark(nil) 268.22/85.88
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.88
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.88
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.88
active(indx(nil, z0)) → mark(nil) 268.22/85.88
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.88
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.88
active(dbl(z0)) → dbl(active(z0)) 268.22/85.88
active(dbls(z0)) → dbls(active(z0)) 268.22/85.88
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.88
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.88
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.88
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.88
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.88
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.88
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.88
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.88
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.88
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.88
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.88
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.88
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.88
proper(0) → ok(0) 268.22/85.88
proper(s(z0)) → s(proper(z0)) 268.22/85.88
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.88
proper(nil) → ok(nil) 268.22/85.88
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.88
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.88
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.88
proper(from(z0)) → from(proper(z0)) 268.22/85.88
s(ok(z0)) → ok(s(z0)) 268.22/85.88
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.88
from(ok(z0)) → ok(from(z0)) 268.22/85.88
top(mark(z0)) → top(proper(z0)) 268.22/85.88
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.88
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.88
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.88
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.88
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.88
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.88
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.88
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.88
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.88
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.88
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.88
S(ok(z0)) → c32(S(z0)) 268.22/85.88
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.88
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.88
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.88
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.88
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.88
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.88
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.88
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.88
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.88
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.88
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.88
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.88
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.88
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.88
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.88
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.88
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.88
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.88
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.88
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.88
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.22/85.88
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.88
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.22/85.88
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.88
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.88
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.22/85.88
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.88
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.22/85.88
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.88
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.88
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 268.22/85.88
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.88
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.88
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 268.22/85.88
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.88
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.88
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.88
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.88
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.88
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 268.22/85.88
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.88
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.88
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 268.22/85.88
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.88
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.88
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.88
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.88
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.88
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.88
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.88
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.88
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.88
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.88
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.88
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.88
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.88
S(ok(z0)) → c32(S(z0)) 268.22/85.88
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.88
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.88
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.88
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.88
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.88
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.88
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.88
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.88
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.88
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.88
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.88
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.88
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.88
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.88
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.88
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.88
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.88
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.88
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.88
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.88
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.88
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.88
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.88
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.88
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.89
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.89
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.89
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.89
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.89
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.89
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.89
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.89
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 268.22/85.89
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 268.22/85.89
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 268.22/85.89
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 268.22/85.89
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23, c25, c25, c26, c26, c28, c28, c29, c29, c30

268.22/85.89
268.22/85.89

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

Removed 4 trailing tuple parts
268.22/85.89
268.22/85.89

(48) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.89
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.89
active(dbls(nil)) → mark(nil) 268.22/85.89
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.89
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.89
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.89
active(indx(nil, z0)) → mark(nil) 268.22/85.89
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.89
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.89
active(dbl(z0)) → dbl(active(z0)) 268.22/85.89
active(dbls(z0)) → dbls(active(z0)) 268.22/85.89
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.89
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.89
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.89
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.89
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.89
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.89
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.89
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.89
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.89
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.89
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.89
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.89
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.89
proper(0) → ok(0) 268.22/85.89
proper(s(z0)) → s(proper(z0)) 268.22/85.89
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.89
proper(nil) → ok(nil) 268.22/85.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.89
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.89
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.89
proper(from(z0)) → from(proper(z0)) 268.22/85.89
s(ok(z0)) → ok(s(z0)) 268.22/85.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.89
from(ok(z0)) → ok(from(z0)) 268.22/85.89
top(mark(z0)) → top(proper(z0)) 268.22/85.89
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.89
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.89
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.89
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.89
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.89
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.89
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.89
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.89
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.89
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.89
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.89
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.89
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.89
S(ok(z0)) → c32(S(z0)) 268.22/85.89
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.89
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.89
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.89
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.89
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.89
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.89
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.89
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.89
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.89
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.89
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.89
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.89
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.89
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.89
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.89
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.89
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.89
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.89
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.89
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.89
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.89
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.89
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.89
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.89
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.89
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.89
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.89
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.89
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.89
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.89
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.89
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.89
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.89
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.89
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.89
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.89
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.89
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.89
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.89
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.89
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.89
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.89
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.89
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.89
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.89
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.89
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 268.22/85.89
S(ok(z0)) → c32(S(z0)) 268.22/85.89
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.89
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.89
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.89
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.89
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.89
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.89
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.89
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.89
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.89
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.89
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.89
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.89
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.89
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.89
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.89
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.89
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.89
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.89
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.89
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.89
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.89
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.89
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.89
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.89
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.89
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.89
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.89
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.89
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.89
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.89
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.89
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.89
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.89
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.89
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, PROPER, S, CONS, FROM, TOP

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c31, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23, c25, c25, c26, c26, c28, c28, c29, c29, c30, c30

268.22/85.89
268.22/85.89

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

Use narrowing to replace PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) by

PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(from(0)) → c31(FROM(ok(0)), PROPER(0)) 268.22/85.89
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(from(nil)) → c31(FROM(ok(nil)), PROPER(nil)) 268.22/85.89
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0)))
268.22/85.89
268.22/85.89

(50) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.89
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.89
active(dbls(nil)) → mark(nil) 268.22/85.89
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.89
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.89
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.89
active(indx(nil, z0)) → mark(nil) 268.22/85.89
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.89
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.89
active(dbl(z0)) → dbl(active(z0)) 268.22/85.89
active(dbls(z0)) → dbls(active(z0)) 268.22/85.89
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.89
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.89
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.89
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.89
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.89
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.89
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.89
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.89
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.89
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.89
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.89
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.89
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.89
proper(0) → ok(0) 268.22/85.89
proper(s(z0)) → s(proper(z0)) 268.22/85.89
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.89
proper(nil) → ok(nil) 268.22/85.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.89
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.89
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.89
proper(from(z0)) → from(proper(z0)) 268.22/85.89
s(ok(z0)) → ok(s(z0)) 268.22/85.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.89
from(ok(z0)) → ok(from(z0)) 268.22/85.89
top(mark(z0)) → top(proper(z0)) 268.22/85.89
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.89
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.89
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.89
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.89
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.89
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.89
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.89
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.89
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.89
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.89
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.89
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.89
S(ok(z0)) → c32(S(z0)) 268.22/85.89
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.89
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.89
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.89
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.89
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.89
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.89
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.89
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.89
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.89
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.89
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.89
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.89
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.89
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.89
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.89
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.89
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.89
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.89
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.89
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.89
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.89
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.89
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.89
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.89
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.89
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.89
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.89
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.89
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.89
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.89
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.89
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.89
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.89
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.89
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(from(0)) → c31(FROM(ok(0)), PROPER(0)) 268.22/85.89
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(from(nil)) → c31(FROM(ok(nil)), PROPER(nil)) 268.22/85.89
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.89
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.89
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.89
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.89
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.89
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.89
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.89
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.89
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.89
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.89
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.89
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.89
S(ok(z0)) → c32(S(z0)) 268.22/85.89
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.89
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.89
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.89
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.89
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.89
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.89
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.89
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.89
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.89
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.89
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.89
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.89
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.89
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.89
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.89
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.89
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.89
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.89
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.89
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.89
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.89
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.89
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.89
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.89
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.89
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.89
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.89
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.89
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.89
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.89
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.89
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.89
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.89
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.89
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(from(0)) → c31(FROM(ok(0)), PROPER(0)) 268.22/85.89
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(from(nil)) → c31(FROM(ok(nil)), PROPER(nil)) 268.22/85.89
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, S, CONS, FROM, TOP, PROPER

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23, c25, c25, c26, c26, c28, c28, c29, c29, c30, c30, c31

268.22/85.89
268.22/85.89

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

Removed 2 trailing tuple parts
268.22/85.89
268.22/85.89

(52) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.89
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.89
active(dbls(nil)) → mark(nil) 268.22/85.89
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.89
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.89
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.89
active(indx(nil, z0)) → mark(nil) 268.22/85.89
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.89
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.89
active(dbl(z0)) → dbl(active(z0)) 268.22/85.89
active(dbls(z0)) → dbls(active(z0)) 268.22/85.89
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.89
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.89
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.89
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.89
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.89
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.89
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.89
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.89
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.89
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.89
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.89
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.89
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.89
proper(0) → ok(0) 268.22/85.89
proper(s(z0)) → s(proper(z0)) 268.22/85.89
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.89
proper(nil) → ok(nil) 268.22/85.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.89
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.89
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.89
proper(from(z0)) → from(proper(z0)) 268.22/85.89
s(ok(z0)) → ok(s(z0)) 268.22/85.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.89
from(ok(z0)) → ok(from(z0)) 268.22/85.89
top(mark(z0)) → top(proper(z0)) 268.22/85.89
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.89
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.89
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.89
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.89
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.89
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.89
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.89
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.89
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.89
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.89
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.89
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.89
S(ok(z0)) → c32(S(z0)) 268.22/85.89
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.89
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.89
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.89
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.89
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.89
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.89
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.89
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.89
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.89
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.89
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.89
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.89
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.89
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.89
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.89
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.89
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.89
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.89
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.89
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.89
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.89
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.89
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.89
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.89
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.89
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.89
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.89
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.89
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.89
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.89
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.89
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.89
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.89
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.89
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(from(0)) → c31(FROM(ok(0))) 268.22/85.89
PROPER(from(nil)) → c31(FROM(ok(nil)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.89
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.89
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.89
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.89
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.89
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.89
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.89
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.89
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.89
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.89
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.89
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.89
S(ok(z0)) → c32(S(z0)) 268.22/85.89
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.89
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.89
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 268.22/85.89
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.89
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.89
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.89
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.89
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.89
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.89
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.89
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.89
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.89
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.89
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.89
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.89
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.89
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.89
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.89
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.89
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.89
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.89
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.89
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.89
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.89
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.89
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.89
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.89
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.89
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.89
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.89
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.89
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.89
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.89
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.89
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(from(0)) → c31(FROM(ok(0))) 268.22/85.89
PROPER(from(nil)) → c31(FROM(ok(nil)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, S, CONS, FROM, TOP, PROPER

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34, c35, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23, c25, c25, c26, c26, c28, c28, c29, c29, c30, c30, c31, c31

268.22/85.89
268.22/85.89

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

Use narrowing to replace TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) by

TOP(mark(dbl(z0))) → c35(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
TOP(mark(0)) → c35(TOP(ok(0)), PROPER(0)) 268.22/85.89
TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
TOP(mark(dbls(z0))) → c35(TOP(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
TOP(mark(nil)) → c35(TOP(ok(nil)), PROPER(nil)) 268.22/85.89
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
TOP(mark(sel(z0, z1))) → c35(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
TOP(mark(indx(z0, z1))) → c35(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0)))
268.22/85.89
268.22/85.89

(54) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.89
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.89
active(dbls(nil)) → mark(nil) 268.22/85.89
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.89
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.89
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.89
active(indx(nil, z0)) → mark(nil) 268.22/85.89
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.89
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.89
active(dbl(z0)) → dbl(active(z0)) 268.22/85.89
active(dbls(z0)) → dbls(active(z0)) 268.22/85.89
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.89
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.89
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.89
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.89
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.89
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.89
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.89
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.89
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.89
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.89
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.89
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.89
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.89
proper(0) → ok(0) 268.22/85.89
proper(s(z0)) → s(proper(z0)) 268.22/85.89
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.89
proper(nil) → ok(nil) 268.22/85.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.89
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.89
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.89
proper(from(z0)) → from(proper(z0)) 268.22/85.89
s(ok(z0)) → ok(s(z0)) 268.22/85.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.89
from(ok(z0)) → ok(from(z0)) 268.22/85.89
top(mark(z0)) → top(proper(z0)) 268.22/85.89
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.89
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.89
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.89
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.89
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.89
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.89
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.89
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.89
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.89
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.89
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.89
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.89
S(ok(z0)) → c32(S(z0)) 268.22/85.89
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.89
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.89
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.89
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.89
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.89
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.89
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.89
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.89
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.89
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.89
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.89
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.89
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.89
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.89
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.89
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.89
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.89
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.89
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.89
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.89
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.89
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.89
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.89
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.89
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.89
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.89
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.89
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.89
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.89
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.89
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.89
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.89
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.89
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(from(0)) → c31(FROM(ok(0))) 268.22/85.89
PROPER(from(nil)) → c31(FROM(ok(nil))) 268.22/85.89
TOP(mark(dbl(z0))) → c35(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
TOP(mark(0)) → c35(TOP(ok(0)), PROPER(0)) 268.22/85.89
TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
TOP(mark(dbls(z0))) → c35(TOP(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
TOP(mark(nil)) → c35(TOP(ok(nil)), PROPER(nil)) 268.22/85.89
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
TOP(mark(sel(z0, z1))) → c35(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
TOP(mark(indx(z0, z1))) → c35(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.89
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.89
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.89
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.89
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.89
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.89
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.89
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.89
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.89
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.89
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.89
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.89
S(ok(z0)) → c32(S(z0)) 268.22/85.89
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.89
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.89
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.89
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.89
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.89
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.89
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.89
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.89
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.89
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.89
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.89
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.89
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.89
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.89
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.89
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.89
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.89
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.89
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.89
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.89
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.89
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.89
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.89
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.89
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.89
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.89
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.89
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.89
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.89
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.89
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.89
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.89
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.89
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.89
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.89
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.89
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.89
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.89
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.89
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.89
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.89
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.89
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.89
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.89
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.89
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.89
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.89
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.89
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.89
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.89
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.22/85.89
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.89
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.89
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.89
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.89
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.89
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.89
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.89
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.89
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.89
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.89
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.89
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.90
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.22/85.90
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.90
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.22/85.90
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.90
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.90
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.90
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.90
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.90
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.90
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.90
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.90
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.90
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.90
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.90
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.90
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.90
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.90
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.90
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.22/85.90
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.90
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.22/85.90
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.90
PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.90
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.22/85.90
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.90
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.90
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.90
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.90
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 268.22/85.90
PROPER(from(0)) → c31(FROM(ok(0))) 268.22/85.90
PROPER(from(nil)) → c31(FROM(ok(nil))) 268.22/85.90
TOP(mark(dbl(z0))) → c35(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.90
TOP(mark(0)) → c35(TOP(ok(0)), PROPER(0)) 268.22/85.90
TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 268.22/85.90
TOP(mark(dbls(z0))) → c35(TOP(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.90
TOP(mark(nil)) → c35(TOP(ok(nil)), PROPER(nil)) 268.22/85.90
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.90
TOP(mark(sel(z0, z1))) → c35(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.90
TOP(mark(indx(z0, z1))) → c35(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.90
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, S, CONS, FROM, TOP, PROPER

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23, c25, c25, c26, c26, c28, c28, c29, c29, c30, c30, c31, c31, c35

268.22/85.90
268.22/85.90

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

Removed 2 trailing tuple parts
268.22/85.90
268.22/85.90

(56) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.22/85.90
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.22/85.90
active(dbls(nil)) → mark(nil) 268.22/85.90
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.22/85.90
active(sel(0, cons(z0, z1))) → mark(z0) 268.22/85.90
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.22/85.90
active(indx(nil, z0)) → mark(nil) 268.22/85.90
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.22/85.90
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.22/85.90
active(dbl(z0)) → dbl(active(z0)) 268.22/85.90
active(dbls(z0)) → dbls(active(z0)) 268.22/85.90
active(sel(z0, z1)) → sel(active(z0), z1) 268.22/85.90
active(sel(z0, z1)) → sel(z0, active(z1)) 268.22/85.90
active(indx(z0, z1)) → indx(active(z0), z1) 268.22/85.90
dbl(mark(z0)) → mark(dbl(z0)) 268.22/85.90
dbl(ok(z0)) → ok(dbl(z0)) 268.22/85.90
dbls(mark(z0)) → mark(dbls(z0)) 268.22/85.90
dbls(ok(z0)) → ok(dbls(z0)) 268.22/85.90
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.22/85.90
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.22/85.90
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.22/85.90
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.22/85.90
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.22/85.90
proper(dbl(z0)) → dbl(proper(z0)) 268.22/85.90
proper(0) → ok(0) 268.22/85.90
proper(s(z0)) → s(proper(z0)) 268.22/85.90
proper(dbls(z0)) → dbls(proper(z0)) 268.22/85.90
proper(nil) → ok(nil) 268.22/85.90
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.22/85.90
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.22/85.90
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.22/85.90
proper(from(z0)) → from(proper(z0)) 268.22/85.90
s(ok(z0)) → ok(s(z0)) 268.22/85.90
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.22/85.90
from(ok(z0)) → ok(from(z0)) 268.22/85.90
top(mark(z0)) → top(proper(z0)) 268.22/85.90
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.90
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.90
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.90
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.90
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.90
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.90
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.90
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.90
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.90
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.90
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.90
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.90
S(ok(z0)) → c32(S(z0)) 268.22/85.90
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.90
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.90
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.90
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.90
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.90
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.90
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.22/85.90
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.22/85.90
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.22/85.90
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.22/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.22/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.22/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.22/85.90
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.90
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.90
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.90
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.90
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.90
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.90
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.90
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.22/85.90
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.22/85.90
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.22/85.90
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.22/85.90
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.22/85.90
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.90
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.90
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.22/85.90
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.22/85.90
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.22/85.90
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.22/85.90
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.22/85.90
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.22/85.90
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.22/85.90
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.22/85.90
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.90
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.90
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.22/85.90
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.22/85.90
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.22/85.90
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.90
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.22/85.90
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.22/85.90
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.22/85.90
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.22/85.90
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.22/85.90
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.22/85.90
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.22/85.90
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.22/85.90
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.22/85.90
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.22/85.90
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.22/85.90
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.22/85.90
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.90
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.22/85.90
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.90
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.90
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.22/85.90
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.90
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.22/85.90
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.22/85.90
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.22/85.90
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.22/85.90
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.22/85.90
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.22/85.90
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.22/85.90
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.22/85.90
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.90
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.22/85.90
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.90
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.90
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.90
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.90
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.22/85.90
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.22/85.90
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.22/85.90
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.90
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.22/85.90
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.90
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.90
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.90
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.90
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.22/85.90
PROPER(s(0)) → c25(S(ok(0))) 268.22/85.90
PROPER(s(nil)) → c25(S(ok(nil))) 268.22/85.90
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.90
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.22/85.90
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.90
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.90
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.90
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.90
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.22/85.90
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.22/85.90
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.22/85.90
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.90
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.90
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.90
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.90
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.90
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.90
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.90
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.90
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.90
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.90
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.90
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.90
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.90
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.90
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.22/85.90
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.90
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.22/85.90
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.90
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.90
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.90
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.90
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.90
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.90
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.90
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.90
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.90
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.90
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.90
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.90
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.90
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.90
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.90
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.22/85.90
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.90
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.22/85.90
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.90
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.22/85.90
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.22/85.90
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.22/85.90
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.22/85.90
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.22/85.90
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.22/85.90
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.22/85.90
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.22/85.90
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.22/85.90
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.22/85.90
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.22/85.90
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.22/85.90
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.22/85.90
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.22/85.90
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.22/85.90
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.22/85.90
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.22/85.90
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1)) 268.22/85.90
PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.90
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.22/85.90
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.90
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.90
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.90
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.90
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 268.22/85.90
PROPER(from(0)) → c31(FROM(ok(0))) 268.22/85.90
PROPER(from(nil)) → c31(FROM(ok(nil))) 268.22/85.90
TOP(mark(dbl(z0))) → c35(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 268.22/85.90
TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 268.22/85.90
TOP(mark(dbls(z0))) → c35(TOP(dbls(proper(z0))), PROPER(dbls(z0))) 268.22/85.90
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.22/85.90
TOP(mark(sel(z0, z1))) → c35(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.22/85.90
TOP(mark(indx(z0, z1))) → c35(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.22/85.90
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0))) 268.22/85.90
TOP(mark(0)) → c35(TOP(ok(0))) 268.22/85.90
TOP(mark(nil)) → c35(TOP(ok(nil)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.22/85.90
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.22/85.90
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.22/85.90
DBL(mark(z0)) → c14(DBL(z0)) 268.22/85.90
DBL(ok(z0)) → c15(DBL(z0)) 268.22/85.90
DBLS(mark(z0)) → c16(DBLS(z0)) 268.22/85.90
DBLS(ok(z0)) → c17(DBLS(z0)) 268.22/85.90
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.22/85.90
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.22/85.90
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.22/85.90
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.22/85.90
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.22/85.90
S(ok(z0)) → c32(S(z0)) 268.22/85.90
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.22/85.90
FROM(ok(z0)) → c34(FROM(z0)) 268.22/85.90
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.22/85.90
ACTIVE(from(z0)) → c8(S(z0)) 268.22/85.90
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.22/85.90
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.22/85.90
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.47/85.90
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.90
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.90
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.90
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.90
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.90
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.47/85.90
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.47/85.90
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.47/85.90
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.47/85.90
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.47/85.90
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.90
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.90
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.90
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.90
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.90
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.47/85.90
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.47/85.90
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.47/85.90
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.90
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.90
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.47/85.90
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.47/85.90
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.90
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.90
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.47/85.90
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.47/85.90
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.90
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.90
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.47/85.90
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.47/85.90
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.47/85.90
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.47/85.90
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.47/85.90
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.47/85.90
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.90
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.90
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.90
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.90
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.90
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.90
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.47/85.90
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.47/85.90
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.47/85.90
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.90
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.47/85.90
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.90
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.47/85.90
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.47/85.90
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.47/85.90
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.47/85.90
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(s(0)) → c25(S(ok(0))) 268.47/85.90
PROPER(s(nil)) → c25(S(ok(nil))) 268.47/85.90
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.47/85.90
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.47/85.90
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.90
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.90
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.90
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.90
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.47/85.90
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.90
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.90
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.90
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.90
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.90
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.47/85.90
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.90
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.90
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.90
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.90
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.90
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.47/85.90
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.90
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(from(0)) → c31(FROM(ok(0))) 268.47/85.90
PROPER(from(nil)) → c31(FROM(ok(nil))) 268.47/85.90
TOP(mark(dbl(z0))) → c35(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
TOP(mark(dbls(z0))) → c35(TOP(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
TOP(mark(sel(z0, z1))) → c35(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
TOP(mark(indx(z0, z1))) → c35(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
TOP(mark(0)) → c35(TOP(ok(0))) 268.47/85.90
TOP(mark(nil)) → c35(TOP(ok(nil)))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, S, CONS, FROM, TOP, PROPER

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23, c25, c25, c26, c26, c28, c28, c29, c29, c30, c30, c31, c31, c35, c35

268.47/85.90
268.47/85.90

(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.

TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
TOP(mark(nil)) → c35(TOP(ok(nil)))
We considered the (Usable) Rules:

proper(dbl(z0)) → dbl(proper(z0)) 268.47/85.90
proper(0) → ok(0) 268.47/85.90
proper(s(z0)) → s(proper(z0)) 268.47/85.90
proper(dbls(z0)) → dbls(proper(z0)) 268.47/85.90
proper(nil) → ok(nil) 268.47/85.90
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.47/85.90
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.47/85.90
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.47/85.90
proper(from(z0)) → from(proper(z0)) 268.47/85.90
from(ok(z0)) → ok(from(z0)) 268.47/85.90
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.47/85.90
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.47/85.90
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.47/85.90
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.47/85.90
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.47/85.90
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.47/85.90
dbls(mark(z0)) → mark(dbls(z0)) 268.47/85.90
dbls(ok(z0)) → ok(dbls(z0)) 268.47/85.90
s(ok(z0)) → ok(s(z0)) 268.47/85.90
dbl(mark(z0)) → mark(dbl(z0)) 268.47/85.90
dbl(ok(z0)) → ok(dbl(z0)) 268.47/85.90
active(dbl(0)) → mark(0) 268.47/85.90
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.47/85.90
active(dbls(nil)) → mark(nil) 268.47/85.90
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.47/85.90
active(sel(0, cons(z0, z1))) → mark(z0) 268.47/85.90
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.47/85.90
active(indx(nil, z0)) → mark(nil) 268.47/85.90
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.47/85.90
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.47/85.90
active(dbl(z0)) → dbl(active(z0)) 268.47/85.90
active(dbls(z0)) → dbls(active(z0)) 268.47/85.90
active(sel(z0, z1)) → sel(active(z0), z1) 268.47/85.90
active(sel(z0, z1)) → sel(z0, active(z1)) 268.47/85.90
active(indx(z0, z1)) → indx(active(z0), z1)
And the Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.47/85.90
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.47/85.90
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.47/85.90
DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.90
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.90
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.90
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.90
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.90
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.90
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.90
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.90
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.90
S(ok(z0)) → c32(S(z0)) 268.47/85.90
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.90
FROM(ok(z0)) → c34(FROM(z0)) 268.47/85.90
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.47/85.90
ACTIVE(from(z0)) → c8(S(z0)) 268.47/85.90
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.47/85.90
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.47/85.90
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.47/85.90
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.90
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.90
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.90
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.90
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.90
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.47/85.90
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.47/85.90
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.47/85.90
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.47/85.90
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.47/85.90
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.90
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.90
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.90
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.90
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.90
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.47/85.90
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.47/85.90
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.47/85.90
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.90
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.90
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.47/85.90
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.47/85.90
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.90
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.90
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.47/85.90
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.47/85.90
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.90
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.90
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.47/85.90
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.47/85.90
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.47/85.90
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.47/85.90
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.47/85.90
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.47/85.90
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.90
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.90
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.90
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.90
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.90
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.90
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.47/85.90
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.47/85.90
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.47/85.90
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.90
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.47/85.90
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.90
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.47/85.90
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.47/85.90
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.47/85.90
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.47/85.90
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(s(0)) → c25(S(ok(0))) 268.47/85.90
PROPER(s(nil)) → c25(S(ok(nil))) 268.47/85.90
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.47/85.90
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.47/85.90
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.90
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.90
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.90
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.90
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.47/85.90
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.90
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.90
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.90
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.90
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.90
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.47/85.90
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.90
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.90
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.90
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.90
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.90
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.47/85.90
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.90
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(from(0)) → c31(FROM(ok(0))) 268.47/85.90
PROPER(from(nil)) → c31(FROM(ok(nil))) 268.47/85.90
TOP(mark(dbl(z0))) → c35(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
TOP(mark(dbls(z0))) → c35(TOP(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
TOP(mark(sel(z0, z1))) → c35(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
TOP(mark(indx(z0, z1))) → c35(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
TOP(mark(0)) → c35(TOP(ok(0))) 268.47/85.90
TOP(mark(nil)) → c35(TOP(ok(nil)))
The order we found is given by the following interpretation:
Polynomial interpretation : 268.47/85.90

POL(0) = [2]    268.47/85.90
POL(ACTIVE(x1)) = 0    268.47/85.90
POL(CONS(x1, x2)) = 0    268.47/85.90
POL(DBL(x1)) = 0    268.47/85.90
POL(DBLS(x1)) = 0    268.47/85.90
POL(FROM(x1)) = 0    268.47/85.90
POL(INDX(x1, x2)) = 0    268.47/85.90
POL(PROPER(x1)) = 0    268.47/85.90
POL(S(x1)) = 0    268.47/85.90
POL(SEL(x1, x2)) = 0    268.47/85.90
POL(TOP(x1)) = x1    268.47/85.90
POL(active(x1)) = x1    268.47/85.90
POL(c(x1)) = x1    268.47/85.90
POL(c1(x1)) = x1    268.47/85.90
POL(c10(x1)) = x1    268.47/85.90
POL(c10(x1, x2)) = x1 + x2    268.47/85.90
POL(c11(x1, x2)) = x1 + x2    268.47/85.90
POL(c12(x1, x2)) = x1 + x2    268.47/85.90
POL(c13(x1)) = x1    268.47/85.90
POL(c13(x1, x2)) = x1 + x2    268.47/85.90
POL(c14(x1)) = x1    268.47/85.90
POL(c15(x1)) = x1    268.47/85.90
POL(c16(x1)) = x1    268.47/85.90
POL(c17(x1)) = x1    268.47/85.90
POL(c18(x1)) = x1    268.47/85.90
POL(c19(x1)) = x1    268.47/85.90
POL(c2(x1)) = x1    268.47/85.90
POL(c20(x1)) = x1    268.47/85.90
POL(c21(x1)) = x1    268.47/85.90
POL(c22(x1)) = x1    268.47/85.90
POL(c23(x1)) = x1    268.47/85.90
POL(c23(x1, x2)) = x1 + x2    268.47/85.90
POL(c25(x1)) = x1    268.47/85.90
POL(c25(x1, x2)) = x1 + x2    268.47/85.90
POL(c26(x1)) = x1    268.47/85.90
POL(c26(x1, x2)) = x1 + x2    268.47/85.90
POL(c28(x1, x2)) = x1 + x2    268.47/85.90
POL(c28(x1, x2, x3)) = x1 + x2 + x3    268.47/85.90
POL(c29(x1, x2)) = x1 + x2    268.47/85.90
POL(c29(x1, x2, x3)) = x1 + x2 + x3    268.47/85.90
POL(c3(x1)) = x1    268.47/85.90
POL(c30(x1, x2)) = x1 + x2    268.47/85.90
POL(c30(x1, x2, x3)) = x1 + x2 + x3    268.47/85.90
POL(c31(x1)) = x1    268.47/85.90
POL(c31(x1, x2)) = x1 + x2    268.47/85.90
POL(c32(x1)) = x1    268.47/85.90
POL(c33(x1)) = x1    268.47/85.90
POL(c34(x1)) = x1    268.47/85.90
POL(c35(x1)) = x1    268.47/85.90
POL(c35(x1, x2)) = x1 + x2    268.47/85.90
POL(c36(x1, x2)) = x1 + x2    268.47/85.90
POL(c5(x1)) = x1    268.47/85.90
POL(c8(x1)) = x1    268.47/85.90
POL(c9(x1)) = x1    268.47/85.90
POL(c9(x1, x2)) = x1 + x2    268.47/85.90
POL(cons(x1, x2)) = 0    268.47/85.90
POL(dbl(x1)) = [2]    268.47/85.90
POL(dbls(x1)) = [2]    268.47/85.90
POL(from(x1)) = [2]    268.47/85.90
POL(indx(x1, x2)) = [2]    268.47/85.90
POL(mark(x1)) = [2]    268.47/85.90
POL(nil) = 0    268.47/85.90
POL(ok(x1)) = x1    268.47/85.90
POL(proper(x1)) = [2]x1    268.47/85.90
POL(s(x1)) = 0    268.47/85.90
POL(sel(x1, x2)) = [2]   
268.47/85.90
268.47/85.90

(58) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.47/85.90
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.47/85.90
active(dbls(nil)) → mark(nil) 268.47/85.90
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.47/85.90
active(sel(0, cons(z0, z1))) → mark(z0) 268.47/85.90
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.47/85.90
active(indx(nil, z0)) → mark(nil) 268.47/85.90
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.47/85.90
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.47/85.90
active(dbl(z0)) → dbl(active(z0)) 268.47/85.90
active(dbls(z0)) → dbls(active(z0)) 268.47/85.90
active(sel(z0, z1)) → sel(active(z0), z1) 268.47/85.90
active(sel(z0, z1)) → sel(z0, active(z1)) 268.47/85.90
active(indx(z0, z1)) → indx(active(z0), z1) 268.47/85.90
dbl(mark(z0)) → mark(dbl(z0)) 268.47/85.90
dbl(ok(z0)) → ok(dbl(z0)) 268.47/85.90
dbls(mark(z0)) → mark(dbls(z0)) 268.47/85.90
dbls(ok(z0)) → ok(dbls(z0)) 268.47/85.90
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.47/85.90
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.47/85.90
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.47/85.90
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.47/85.90
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.47/85.90
proper(dbl(z0)) → dbl(proper(z0)) 268.47/85.90
proper(0) → ok(0) 268.47/85.90
proper(s(z0)) → s(proper(z0)) 268.47/85.90
proper(dbls(z0)) → dbls(proper(z0)) 268.47/85.90
proper(nil) → ok(nil) 268.47/85.90
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.47/85.90
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.47/85.90
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.47/85.90
proper(from(z0)) → from(proper(z0)) 268.47/85.90
s(ok(z0)) → ok(s(z0)) 268.47/85.90
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.47/85.90
from(ok(z0)) → ok(from(z0)) 268.47/85.90
top(mark(z0)) → top(proper(z0)) 268.47/85.90
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.47/85.90
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.47/85.90
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.47/85.90
DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.90
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.90
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.90
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.90
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.90
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.90
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.90
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.90
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.90
S(ok(z0)) → c32(S(z0)) 268.47/85.90
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.90
FROM(ok(z0)) → c34(FROM(z0)) 268.47/85.90
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.47/85.90
ACTIVE(from(z0)) → c8(S(z0)) 268.47/85.90
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.47/85.90
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.47/85.90
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.47/85.90
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.90
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.90
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.90
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.90
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.90
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.47/85.90
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.47/85.90
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.47/85.90
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.47/85.90
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.47/85.90
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.90
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.90
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.90
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.90
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.90
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.47/85.90
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.47/85.90
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.47/85.90
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.90
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.90
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.47/85.90
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.47/85.90
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.90
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.90
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.47/85.90
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.47/85.90
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.90
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.90
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.47/85.90
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.47/85.90
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.47/85.90
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.47/85.90
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.47/85.90
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.47/85.90
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.90
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.90
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.90
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.90
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.90
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.90
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.47/85.90
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.47/85.90
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.47/85.90
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.90
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.47/85.90
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.90
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.47/85.90
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.47/85.90
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.47/85.90
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.47/85.90
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(s(0)) → c25(S(ok(0))) 268.47/85.90
PROPER(s(nil)) → c25(S(ok(nil))) 268.47/85.90
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.47/85.90
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.47/85.90
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.90
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.90
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.90
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.90
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.47/85.90
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.90
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.90
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.90
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.90
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.90
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.47/85.90
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.90
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.90
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.90
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.90
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.90
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.47/85.90
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.90
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(from(0)) → c31(FROM(ok(0))) 268.47/85.90
PROPER(from(nil)) → c31(FROM(ok(nil))) 268.47/85.90
TOP(mark(dbl(z0))) → c35(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
TOP(mark(dbls(z0))) → c35(TOP(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
TOP(mark(sel(z0, z1))) → c35(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
TOP(mark(indx(z0, z1))) → c35(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
TOP(mark(0)) → c35(TOP(ok(0))) 268.47/85.90
TOP(mark(nil)) → c35(TOP(ok(nil)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.47/85.90
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.47/85.90
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.47/85.90
DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.90
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.90
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.90
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.90
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.90
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.90
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.90
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.90
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.90
S(ok(z0)) → c32(S(z0)) 268.47/85.90
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.90
FROM(ok(z0)) → c34(FROM(z0)) 268.47/85.90
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.47/85.90
ACTIVE(from(z0)) → c8(S(z0)) 268.47/85.90
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.47/85.90
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.47/85.90
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.47/85.90
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.90
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.90
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.90
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.90
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.90
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.47/85.90
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.47/85.90
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.47/85.90
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.47/85.90
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.47/85.90
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.90
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.90
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.90
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.90
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.90
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.47/85.90
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.47/85.90
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.47/85.90
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.90
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.90
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.47/85.90
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.47/85.90
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.90
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.90
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.47/85.90
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.47/85.90
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.90
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.90
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.47/85.90
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.47/85.90
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.47/85.90
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.47/85.90
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.47/85.90
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.47/85.90
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.90
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.90
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.90
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.90
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.90
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.90
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.47/85.90
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.47/85.90
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.47/85.90
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.90
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.47/85.90
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.90
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.47/85.90
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.47/85.90
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.47/85.90
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.47/85.90
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(s(0)) → c25(S(ok(0))) 268.47/85.90
PROPER(s(nil)) → c25(S(ok(nil))) 268.47/85.90
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.47/85.90
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.47/85.90
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.90
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.90
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.90
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.90
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.47/85.90
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.90
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.90
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.90
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.90
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.90
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.47/85.90
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.90
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.90
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.90
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.90
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.90
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.47/85.90
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.90
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(from(0)) → c31(FROM(ok(0))) 268.47/85.90
PROPER(from(nil)) → c31(FROM(ok(nil))) 268.47/85.90
TOP(mark(dbl(z0))) → c35(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
TOP(mark(dbls(z0))) → c35(TOP(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
TOP(mark(sel(z0, z1))) → c35(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
TOP(mark(indx(z0, z1))) → c35(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
TOP(mark(0)) → c35(TOP(ok(0)))
K tuples:

TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
TOP(mark(nil)) → c35(TOP(ok(nil)))
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, S, CONS, FROM, TOP, PROPER

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23, c25, c25, c26, c26, c28, c28, c29, c29, c30, c30, c31, c31, c35, c35

268.47/85.90
268.47/85.90

(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.

TOP(mark(0)) → c35(TOP(ok(0)))
We considered the (Usable) Rules:

proper(dbl(z0)) → dbl(proper(z0)) 268.47/85.90
proper(0) → ok(0) 268.47/85.90
proper(s(z0)) → s(proper(z0)) 268.47/85.90
proper(dbls(z0)) → dbls(proper(z0)) 268.47/85.90
proper(nil) → ok(nil) 268.47/85.90
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.47/85.90
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.47/85.90
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.47/85.90
proper(from(z0)) → from(proper(z0)) 268.47/85.90
from(ok(z0)) → ok(from(z0)) 268.47/85.90
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.47/85.90
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.47/85.90
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.47/85.90
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.47/85.90
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.47/85.90
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.47/85.90
dbls(mark(z0)) → mark(dbls(z0)) 268.47/85.90
dbls(ok(z0)) → ok(dbls(z0)) 268.47/85.90
s(ok(z0)) → ok(s(z0)) 268.47/85.90
dbl(mark(z0)) → mark(dbl(z0)) 268.47/85.90
dbl(ok(z0)) → ok(dbl(z0)) 268.47/85.90
active(dbl(0)) → mark(0) 268.47/85.90
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.47/85.90
active(dbls(nil)) → mark(nil) 268.47/85.90
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.47/85.90
active(sel(0, cons(z0, z1))) → mark(z0) 268.47/85.90
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.47/85.90
active(indx(nil, z0)) → mark(nil) 268.47/85.90
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.47/85.90
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.47/85.90
active(dbl(z0)) → dbl(active(z0)) 268.47/85.90
active(dbls(z0)) → dbls(active(z0)) 268.47/85.90
active(sel(z0, z1)) → sel(active(z0), z1) 268.47/85.90
active(sel(z0, z1)) → sel(z0, active(z1)) 268.47/85.90
active(indx(z0, z1)) → indx(active(z0), z1)
And the Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.47/85.90
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.47/85.90
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.47/85.90
DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.90
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.90
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.90
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.90
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.90
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.90
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.90
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.90
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.90
S(ok(z0)) → c32(S(z0)) 268.47/85.90
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.90
FROM(ok(z0)) → c34(FROM(z0)) 268.47/85.90
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.47/85.90
ACTIVE(from(z0)) → c8(S(z0)) 268.47/85.90
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.47/85.90
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.47/85.90
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.47/85.90
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.90
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.90
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.90
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.90
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.90
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.47/85.90
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.47/85.90
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.47/85.90
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.47/85.90
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.47/85.90
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.90
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.90
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.90
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.90
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.90
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.47/85.90
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.47/85.90
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.47/85.90
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.90
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.90
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.47/85.90
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.47/85.90
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.90
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.90
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.47/85.90
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.47/85.90
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.90
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.90
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.47/85.90
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.47/85.90
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.47/85.90
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.47/85.90
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.47/85.90
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.47/85.90
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.90
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.90
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.90
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.90
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.90
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.90
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.47/85.90
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.47/85.90
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.47/85.90
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.90
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.47/85.90
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.90
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.47/85.90
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.47/85.90
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.47/85.90
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.47/85.90
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(s(0)) → c25(S(ok(0))) 268.47/85.90
PROPER(s(nil)) → c25(S(ok(nil))) 268.47/85.90
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.47/85.90
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.47/85.90
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.90
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.90
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.90
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.90
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.90
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.47/85.90
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.90
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.90
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.90
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.90
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.90
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.90
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.47/85.90
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.90
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.90
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.90
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.90
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.90
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.90
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.90
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.47/85.90
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.90
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.90
PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
PROPER(from(0)) → c31(FROM(ok(0))) 268.47/85.90
PROPER(from(nil)) → c31(FROM(ok(nil))) 268.47/85.90
TOP(mark(dbl(z0))) → c35(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.90
TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 268.47/85.90
TOP(mark(dbls(z0))) → c35(TOP(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.90
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.90
TOP(mark(sel(z0, z1))) → c35(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.90
TOP(mark(indx(z0, z1))) → c35(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.90
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0))) 268.47/85.90
TOP(mark(0)) → c35(TOP(ok(0))) 268.47/85.90
TOP(mark(nil)) → c35(TOP(ok(nil)))
The order we found is given by the following interpretation:
Polynomial interpretation : 268.47/85.90

POL(0) = 0    268.47/85.90
POL(ACTIVE(x1)) = 0    268.47/85.90
POL(CONS(x1, x2)) = 0    268.47/85.90
POL(DBL(x1)) = 0    268.47/85.90
POL(DBLS(x1)) = 0    268.47/85.90
POL(FROM(x1)) = 0    268.47/85.90
POL(INDX(x1, x2)) = 0    268.47/85.90
POL(PROPER(x1)) = 0    268.47/85.90
POL(S(x1)) = 0    268.47/85.90
POL(SEL(x1, x2)) = 0    268.47/85.90
POL(TOP(x1)) = [2]x1    268.47/85.90
POL(active(x1)) = x1    268.47/85.90
POL(c(x1)) = x1    268.47/85.90
POL(c1(x1)) = x1    268.47/85.90
POL(c10(x1)) = x1    268.47/85.90
POL(c10(x1, x2)) = x1 + x2    268.47/85.90
POL(c11(x1, x2)) = x1 + x2    268.47/85.90
POL(c12(x1, x2)) = x1 + x2    268.47/85.90
POL(c13(x1)) = x1    268.47/85.90
POL(c13(x1, x2)) = x1 + x2    268.47/85.90
POL(c14(x1)) = x1    268.47/85.90
POL(c15(x1)) = x1    268.47/85.90
POL(c16(x1)) = x1    268.47/85.90
POL(c17(x1)) = x1    268.47/85.90
POL(c18(x1)) = x1    268.47/85.90
POL(c19(x1)) = x1    268.47/85.90
POL(c2(x1)) = x1    268.47/85.90
POL(c20(x1)) = x1    268.47/85.90
POL(c21(x1)) = x1    268.47/85.90
POL(c22(x1)) = x1    268.47/85.90
POL(c23(x1)) = x1    268.47/85.90
POL(c23(x1, x2)) = x1 + x2    268.47/85.90
POL(c25(x1)) = x1    268.47/85.90
POL(c25(x1, x2)) = x1 + x2    268.47/85.90
POL(c26(x1)) = x1    268.47/85.90
POL(c26(x1, x2)) = x1 + x2    268.47/85.90
POL(c28(x1, x2)) = x1 + x2    268.47/85.90
POL(c28(x1, x2, x3)) = x1 + x2 + x3    268.47/85.90
POL(c29(x1, x2)) = x1 + x2    268.47/85.90
POL(c29(x1, x2, x3)) = x1 + x2 + x3    268.47/85.90
POL(c3(x1)) = x1    268.47/85.90
POL(c30(x1, x2)) = x1 + x2    268.47/85.90
POL(c30(x1, x2, x3)) = x1 + x2 + x3    268.47/85.90
POL(c31(x1)) = x1    268.47/85.90
POL(c31(x1, x2)) = x1 + x2    268.47/85.90
POL(c32(x1)) = x1    268.47/85.90
POL(c33(x1)) = x1    268.47/85.90
POL(c34(x1)) = x1    268.47/85.90
POL(c35(x1)) = x1    268.47/85.90
POL(c35(x1, x2)) = x1 + x2    268.47/85.90
POL(c36(x1, x2)) = x1 + x2    268.47/85.90
POL(c5(x1)) = x1    268.47/85.90
POL(c8(x1)) = x1    268.47/85.90
POL(c9(x1)) = x1    268.47/85.90
POL(c9(x1, x2)) = x1 + x2    268.47/85.90
POL(cons(x1, x2)) = 0    268.47/85.90
POL(dbl(x1)) = [2]    268.47/85.90
POL(dbls(x1)) = [2]    268.47/85.90
POL(from(x1)) = [2]    268.47/85.90
POL(indx(x1, x2)) = [2]    268.47/85.90
POL(mark(x1)) = [2]    268.47/85.90
POL(nil) = 0    268.47/85.90
POL(ok(x1)) = x1    268.47/85.90
POL(proper(x1)) = 0    268.47/85.90
POL(s(x1)) = 0    268.47/85.90
POL(sel(x1, x2)) = [2]   
268.47/85.90
268.47/85.90

(60) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.47/85.90
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.47/85.90
active(dbls(nil)) → mark(nil) 268.47/85.90
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.47/85.90
active(sel(0, cons(z0, z1))) → mark(z0) 268.47/85.90
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.47/85.90
active(indx(nil, z0)) → mark(nil) 268.47/85.90
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.47/85.90
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.47/85.90
active(dbl(z0)) → dbl(active(z0)) 268.47/85.90
active(dbls(z0)) → dbls(active(z0)) 268.47/85.90
active(sel(z0, z1)) → sel(active(z0), z1) 268.47/85.90
active(sel(z0, z1)) → sel(z0, active(z1)) 268.47/85.90
active(indx(z0, z1)) → indx(active(z0), z1) 268.47/85.90
dbl(mark(z0)) → mark(dbl(z0)) 268.47/85.90
dbl(ok(z0)) → ok(dbl(z0)) 268.47/85.90
dbls(mark(z0)) → mark(dbls(z0)) 268.47/85.90
dbls(ok(z0)) → ok(dbls(z0)) 268.47/85.90
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.47/85.90
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.47/85.90
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.47/85.90
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.47/85.90
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.47/85.90
proper(dbl(z0)) → dbl(proper(z0)) 268.47/85.90
proper(0) → ok(0) 268.47/85.90
proper(s(z0)) → s(proper(z0)) 268.47/85.90
proper(dbls(z0)) → dbls(proper(z0)) 268.47/85.90
proper(nil) → ok(nil) 268.47/85.90
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.47/85.90
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.47/85.90
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.47/85.90
proper(from(z0)) → from(proper(z0)) 268.47/85.90
s(ok(z0)) → ok(s(z0)) 268.47/85.90
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.47/85.90
from(ok(z0)) → ok(from(z0)) 268.47/85.90
top(mark(z0)) → top(proper(z0)) 268.47/85.90
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.47/85.90
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.47/85.90
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.47/85.90
DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.90
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.90
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.90
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.90
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.90
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.90
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.90
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.90
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.90
S(ok(z0)) → c32(S(z0)) 268.47/85.90
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.90
FROM(ok(z0)) → c34(FROM(z0)) 268.47/85.90
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.47/85.90
ACTIVE(from(z0)) → c8(S(z0)) 268.47/85.90
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.47/85.90
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.47/85.90
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.47/85.90
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.47/85.90
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.47/85.90
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.90
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.90
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.90
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.90
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.90
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.90
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.47/85.90
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.47/85.90
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.47/85.90
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.47/85.90
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.47/85.90
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.91
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.91
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.91
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.47/85.91
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.47/85.91
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.47/85.91
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.91
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.47/85.91
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.47/85.91
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.91
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.47/85.91
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.47/85.91
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.47/85.91
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.47/85.91
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.47/85.91
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.47/85.91
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.47/85.91
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.47/85.91
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.91
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.91
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.91
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.91
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.47/85.91
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.47/85.91
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.47/85.91
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.47/85.91
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.47/85.91
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.47/85.91
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.47/85.91
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.47/85.91
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(s(0)) → c25(S(ok(0))) 268.47/85.91
PROPER(s(nil)) → c25(S(ok(nil))) 268.47/85.91
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.47/85.91
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.47/85.91
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.91
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.91
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.91
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.91
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.47/85.91
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.91
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.91
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.91
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.91
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.91
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.47/85.91
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.91
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.91
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.91
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.91
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.91
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.47/85.91
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.91
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(from(0)) → c31(FROM(ok(0))) 268.47/85.91
PROPER(from(nil)) → c31(FROM(ok(nil))) 268.47/85.91
TOP(mark(dbl(z0))) → c35(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
TOP(mark(dbls(z0))) → c35(TOP(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
TOP(mark(sel(z0, z1))) → c35(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
TOP(mark(indx(z0, z1))) → c35(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
TOP(mark(0)) → c35(TOP(ok(0))) 268.47/85.91
TOP(mark(nil)) → c35(TOP(ok(nil)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.47/85.91
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.47/85.91
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.47/85.91
DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0)) 268.47/85.91
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 268.47/85.91
ACTIVE(from(z0)) → c8(S(z0)) 268.47/85.91
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.47/85.91
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.47/85.91
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.47/85.91
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.47/85.91
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.47/85.91
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.47/85.91
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.47/85.91
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.47/85.91
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.47/85.91
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.91
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.91
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.91
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.47/85.91
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.47/85.91
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.47/85.91
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.47/85.91
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.47/85.91
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.91
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.91
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.91
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.47/85.91
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.47/85.91
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.47/85.91
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.91
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.47/85.91
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.47/85.91
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.91
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.47/85.91
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.47/85.91
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.47/85.91
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.47/85.91
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.47/85.91
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.47/85.91
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.47/85.91
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.47/85.91
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.91
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.91
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.91
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.91
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.47/85.91
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.47/85.91
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.47/85.91
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.47/85.91
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.47/85.91
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.47/85.91
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.47/85.91
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.47/85.91
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(s(0)) → c25(S(ok(0))) 268.47/85.91
PROPER(s(nil)) → c25(S(ok(nil))) 268.47/85.91
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.47/85.91
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.47/85.91
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.91
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.91
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.91
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.91
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.47/85.91
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.91
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.91
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.91
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.91
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.91
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.47/85.91
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.91
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.91
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.91
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.91
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.91
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.47/85.91
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.91
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(from(0)) → c31(FROM(ok(0))) 268.47/85.91
PROPER(from(nil)) → c31(FROM(ok(nil))) 268.47/85.91
TOP(mark(dbl(z0))) → c35(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
TOP(mark(dbls(z0))) → c35(TOP(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
TOP(mark(sel(z0, z1))) → c35(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
TOP(mark(indx(z0, z1))) → c35(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0)))
K tuples:

TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
TOP(mark(nil)) → c35(TOP(ok(nil))) 268.47/85.91
TOP(mark(0)) → c35(TOP(ok(0)))
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, S, CONS, FROM, TOP, PROPER

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34, c36, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23, c25, c25, c26, c26, c28, c28, c29, c29, c30, c30, c31, c31, c35, c35

268.47/85.91
268.47/85.91

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

Use narrowing to replace TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) by

TOP(ok(dbl(0))) → c36(TOP(mark(0)), ACTIVE(dbl(0))) 268.47/85.91
TOP(ok(dbl(s(z0)))) → c36(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 268.47/85.91
TOP(ok(dbls(nil))) → c36(TOP(mark(nil)), ACTIVE(dbls(nil))) 268.47/85.91
TOP(ok(dbls(cons(z0, z1)))) → c36(TOP(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
TOP(ok(sel(0, cons(z0, z1)))) → c36(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
TOP(ok(sel(s(z0), cons(z1, z2)))) → c36(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
TOP(ok(indx(nil, z0))) → c36(TOP(mark(nil)), ACTIVE(indx(nil, z0))) 268.47/85.91
TOP(ok(indx(cons(z0, z1), z2))) → c36(TOP(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
TOP(ok(from(z0))) → c36(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 268.47/85.91
TOP(ok(dbl(z0))) → c36(TOP(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.91
TOP(ok(dbls(z0))) → c36(TOP(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.91
TOP(ok(sel(z0, z1))) → c36(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.91
TOP(ok(sel(z0, z1))) → c36(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.91
TOP(ok(indx(z0, z1))) → c36(TOP(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
268.47/85.91
268.47/85.91

(62) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.47/85.91
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.47/85.91
active(dbls(nil)) → mark(nil) 268.47/85.91
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.47/85.91
active(sel(0, cons(z0, z1))) → mark(z0) 268.47/85.91
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.47/85.91
active(indx(nil, z0)) → mark(nil) 268.47/85.91
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.47/85.91
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.47/85.91
active(dbl(z0)) → dbl(active(z0)) 268.47/85.91
active(dbls(z0)) → dbls(active(z0)) 268.47/85.91
active(sel(z0, z1)) → sel(active(z0), z1) 268.47/85.91
active(sel(z0, z1)) → sel(z0, active(z1)) 268.47/85.91
active(indx(z0, z1)) → indx(active(z0), z1) 268.47/85.91
dbl(mark(z0)) → mark(dbl(z0)) 268.47/85.91
dbl(ok(z0)) → ok(dbl(z0)) 268.47/85.91
dbls(mark(z0)) → mark(dbls(z0)) 268.47/85.91
dbls(ok(z0)) → ok(dbls(z0)) 268.47/85.91
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.47/85.91
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.47/85.91
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.47/85.91
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.47/85.91
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.47/85.91
proper(dbl(z0)) → dbl(proper(z0)) 268.47/85.91
proper(0) → ok(0) 268.47/85.91
proper(s(z0)) → s(proper(z0)) 268.47/85.91
proper(dbls(z0)) → dbls(proper(z0)) 268.47/85.91
proper(nil) → ok(nil) 268.47/85.91
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.47/85.91
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.47/85.91
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.47/85.91
proper(from(z0)) → from(proper(z0)) 268.47/85.91
s(ok(z0)) → ok(s(z0)) 268.47/85.91
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.47/85.91
from(ok(z0)) → ok(from(z0)) 268.47/85.91
top(mark(z0)) → top(proper(z0)) 268.47/85.91
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.47/85.91
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.47/85.91
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.47/85.91
DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0)) 268.47/85.91
ACTIVE(from(z0)) → c8(S(z0)) 268.47/85.91
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.47/85.91
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.47/85.91
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.47/85.91
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.47/85.91
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.47/85.91
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.47/85.91
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.47/85.91
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.47/85.91
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.47/85.91
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.91
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.91
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.91
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.47/85.91
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.47/85.91
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.47/85.91
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.47/85.91
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.47/85.91
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.91
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.91
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.91
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.47/85.91
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.47/85.91
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.47/85.91
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.91
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.47/85.91
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.47/85.91
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.91
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.47/85.91
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.47/85.91
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.47/85.91
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.47/85.91
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.47/85.91
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.47/85.91
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.47/85.91
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.47/85.91
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.91
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.91
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.91
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.91
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.47/85.91
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.47/85.91
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.47/85.91
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.47/85.91
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.47/85.91
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.47/85.91
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.47/85.91
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.47/85.91
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(s(0)) → c25(S(ok(0))) 268.47/85.91
PROPER(s(nil)) → c25(S(ok(nil))) 268.47/85.91
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.47/85.91
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.47/85.91
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.91
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.91
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.91
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.91
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.47/85.91
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.91
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.91
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.91
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.91
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.91
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.47/85.91
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.91
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.91
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.91
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.91
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.91
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.47/85.91
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.91
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(from(0)) → c31(FROM(ok(0))) 268.47/85.91
PROPER(from(nil)) → c31(FROM(ok(nil))) 268.47/85.91
TOP(mark(dbl(z0))) → c35(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
TOP(mark(dbls(z0))) → c35(TOP(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
TOP(mark(sel(z0, z1))) → c35(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
TOP(mark(indx(z0, z1))) → c35(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
TOP(mark(0)) → c35(TOP(ok(0))) 268.47/85.91
TOP(mark(nil)) → c35(TOP(ok(nil))) 268.47/85.91
TOP(ok(dbl(0))) → c36(TOP(mark(0)), ACTIVE(dbl(0))) 268.47/85.91
TOP(ok(dbl(s(z0)))) → c36(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 268.47/85.91
TOP(ok(dbls(nil))) → c36(TOP(mark(nil)), ACTIVE(dbls(nil))) 268.47/85.91
TOP(ok(dbls(cons(z0, z1)))) → c36(TOP(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
TOP(ok(sel(0, cons(z0, z1)))) → c36(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
TOP(ok(sel(s(z0), cons(z1, z2)))) → c36(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
TOP(ok(indx(nil, z0))) → c36(TOP(mark(nil)), ACTIVE(indx(nil, z0))) 268.47/85.91
TOP(ok(indx(cons(z0, z1), z2))) → c36(TOP(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
TOP(ok(from(z0))) → c36(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 268.47/85.91
TOP(ok(dbl(z0))) → c36(TOP(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.91
TOP(ok(dbls(z0))) → c36(TOP(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.91
TOP(ok(sel(z0, z1))) → c36(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.91
TOP(ok(sel(z0, z1))) → c36(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.91
TOP(ok(indx(z0, z1))) → c36(TOP(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.47/85.91
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.47/85.91
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.47/85.91
DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0)) 268.47/85.91
ACTIVE(from(z0)) → c8(S(z0)) 268.47/85.91
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.47/85.91
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.47/85.91
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.47/85.91
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.47/85.91
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.47/85.91
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.47/85.91
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.47/85.91
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.47/85.91
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.47/85.91
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.91
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.91
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.91
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.47/85.91
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.47/85.91
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.47/85.91
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.47/85.91
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.47/85.91
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.91
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.91
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.91
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.47/85.91
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.47/85.91
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.47/85.91
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.91
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.47/85.91
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.47/85.91
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.91
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.47/85.91
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.47/85.91
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.47/85.91
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.47/85.91
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.47/85.91
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.47/85.91
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.47/85.91
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.47/85.91
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.91
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.91
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.91
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.91
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.47/85.91
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.47/85.91
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.47/85.91
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.47/85.91
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.47/85.91
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.47/85.91
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.47/85.91
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.47/85.91
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(s(0)) → c25(S(ok(0))) 268.47/85.91
PROPER(s(nil)) → c25(S(ok(nil))) 268.47/85.91
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.47/85.91
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.47/85.91
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.91
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.91
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.91
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.91
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.47/85.91
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.91
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.91
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.91
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.91
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.91
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.47/85.91
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.91
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.91
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.91
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.91
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.91
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.47/85.91
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.91
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(from(0)) → c31(FROM(ok(0))) 268.47/85.91
PROPER(from(nil)) → c31(FROM(ok(nil))) 268.47/85.91
TOP(mark(dbl(z0))) → c35(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
TOP(mark(dbls(z0))) → c35(TOP(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
TOP(mark(sel(z0, z1))) → c35(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
TOP(mark(indx(z0, z1))) → c35(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
TOP(ok(dbl(0))) → c36(TOP(mark(0)), ACTIVE(dbl(0))) 268.47/85.91
TOP(ok(dbl(s(z0)))) → c36(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 268.47/85.91
TOP(ok(dbls(nil))) → c36(TOP(mark(nil)), ACTIVE(dbls(nil))) 268.47/85.91
TOP(ok(dbls(cons(z0, z1)))) → c36(TOP(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
TOP(ok(sel(0, cons(z0, z1)))) → c36(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
TOP(ok(sel(s(z0), cons(z1, z2)))) → c36(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
TOP(ok(indx(nil, z0))) → c36(TOP(mark(nil)), ACTIVE(indx(nil, z0))) 268.47/85.91
TOP(ok(indx(cons(z0, z1), z2))) → c36(TOP(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
TOP(ok(from(z0))) → c36(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 268.47/85.91
TOP(ok(dbl(z0))) → c36(TOP(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.91
TOP(ok(dbls(z0))) → c36(TOP(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.91
TOP(ok(sel(z0, z1))) → c36(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.91
TOP(ok(sel(z0, z1))) → c36(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.91
TOP(ok(indx(z0, z1))) → c36(TOP(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
K tuples:

TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
TOP(mark(nil)) → c35(TOP(ok(nil))) 268.47/85.91
TOP(mark(0)) → c35(TOP(ok(0)))
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

ACTIVE, DBL, DBLS, SEL, INDX, S, CONS, FROM, PROPER, TOP

Compound Symbols:

c5, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34, c8, c, c9, c9, c1, c10, c10, c2, c13, c13, c3, c23, c23, c25, c25, c26, c26, c28, c28, c29, c29, c30, c30, c31, c31, c35, c35, c36

268.47/85.91
268.47/85.91

(63) CdtUnreachableProof (EQUIVALENT transformation)

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

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 268.47/85.91
ACTIVE(sel(z0, z1)) → c11(SEL(active(z0), z1), ACTIVE(z0)) 268.47/85.91
ACTIVE(sel(z0, z1)) → c12(SEL(z0, active(z1)), ACTIVE(z1)) 268.47/85.91
ACTIVE(from(z0)) → c8(S(z0)) 268.47/85.91
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0)))) 268.47/85.91
ACTIVE(dbl(s(z0))) → c(S(dbl(z0))) 268.47/85.91
ACTIVE(dbl(s(z0))) → c(DBL(z0)) 268.47/85.91
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1))) 268.47/85.91
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0)) 268.47/85.91
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1)) 268.47/85.91
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2))) 268.47/85.91
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2)) 268.47/85.91
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2)) 268.47/85.91
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c9(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c9(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
ACTIVE(dbl(dbl(z0))) → c9(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.91
ACTIVE(dbl(dbls(z0))) → c9(DBL(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.91
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbl(sel(z0, z1))) → c9(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbl(indx(z0, z1))) → c9(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.91
ACTIVE(dbl(dbl(0))) → c9(DBL(mark(0))) 268.47/85.91
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0)))))) 268.47/85.91
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0)))) 268.47/85.91
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0)))))) 268.47/85.91
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0))) 268.47/85.91
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c10(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c10(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
ACTIVE(dbls(dbl(z0))) → c10(DBLS(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.91
ACTIVE(dbls(dbls(z0))) → c10(DBLS(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.91
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbls(sel(z0, z1))) → c10(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(dbls(indx(z0, z1))) → c10(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1))) 268.47/85.91
ACTIVE(dbl(dbls(nil))) → c9(DBL(mark(nil))) 268.47/85.91
ACTIVE(dbls(dbl(0))) → c10(DBLS(mark(0))) 268.47/85.91
ACTIVE(dbls(dbls(nil))) → c10(DBLS(mark(nil))) 268.47/85.91
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.91
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0)))))) 268.47/85.91
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 268.47/85.91
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1))))) 268.47/85.91
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0)))))) 268.47/85.91
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0))) 268.47/85.91
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c13(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c13(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
ACTIVE(indx(dbl(z0), x1)) → c13(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 268.47/85.91
ACTIVE(indx(dbls(z0), x1)) → c13(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0))) 268.47/85.91
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(indx(sel(z0, z1), x1)) → c13(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 268.47/85.91
ACTIVE(indx(indx(z0, z1), x1)) → c13(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1))) 268.47/85.91
ACTIVE(dbl(indx(nil, z0))) → c9(DBL(mark(nil))) 268.47/85.91
ACTIVE(dbls(indx(nil, z0))) → c10(DBLS(mark(nil))) 268.47/85.91
ACTIVE(indx(dbl(0), x1)) → c13(INDX(mark(0), x1)) 268.47/85.91
ACTIVE(indx(dbls(nil), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.91
ACTIVE(indx(indx(nil, z0), x1)) → c13(INDX(mark(nil), x1)) 268.47/85.91
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.91
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2))))) 268.47/85.91
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1)) 268.47/85.91
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0)))) 268.47/85.91
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1)) 268.47/85.91
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1)) 268.47/85.91
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1)) 268.47/85.91
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0))) 268.47/85.91
PROPER(dbl(dbl(z0))) → c23(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(dbl(s(z0))) → c23(DBL(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(dbl(dbls(z0))) → c23(DBL(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(dbl(cons(z0, z1))) → c23(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(dbl(sel(z0, z1))) → c23(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(dbl(indx(z0, z1))) → c23(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(dbl(from(z0))) → c23(DBL(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(dbl(0)) → c23(DBL(ok(0))) 268.47/85.91
PROPER(dbl(nil)) → c23(DBL(ok(nil))) 268.47/85.91
PROPER(s(dbl(z0))) → c25(S(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(s(s(z0))) → c25(S(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(s(dbls(z0))) → c25(S(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(s(cons(z0, z1))) → c25(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(s(sel(z0, z1))) → c25(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(s(indx(z0, z1))) → c25(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(s(from(z0))) → c25(S(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(s(0)) → c25(S(ok(0))) 268.47/85.91
PROPER(s(nil)) → c25(S(ok(nil))) 268.47/85.91
PROPER(dbls(dbl(z0))) → c26(DBLS(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(dbls(s(z0))) → c26(DBLS(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(dbls(dbls(z0))) → c26(DBLS(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(dbls(cons(z0, z1))) → c26(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(dbls(sel(z0, z1))) → c26(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(dbls(indx(z0, z1))) → c26(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(dbls(from(z0))) → c26(DBLS(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(dbls(0)) → c26(DBLS(ok(0))) 268.47/85.91
PROPER(dbls(nil)) → c26(DBLS(ok(nil))) 268.47/85.91
PROPER(cons(x0, dbl(z0))) → c28(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.91
PROPER(cons(x0, s(z0))) → c28(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.91
PROPER(cons(x0, dbls(z0))) → c28(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.91
PROPER(cons(x0, cons(z0, z1))) → c28(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(cons(x0, sel(z0, z1))) → c28(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(cons(x0, indx(z0, z1))) → c28(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(cons(x0, from(z0))) → c28(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.91
PROPER(cons(dbl(z0), x1)) → c28(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(s(z0), x1)) → c28(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(dbls(z0), x1)) → c28(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(cons(z0, z1), x1)) → c28(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(cons(sel(z0, z1), x1)) → c28(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(cons(indx(z0, z1), x1)) → c28(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(cons(from(z0), x1)) → c28(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.91
PROPER(cons(x0, 0)) → c28(CONS(proper(x0), ok(0)), PROPER(x0)) 268.47/85.91
PROPER(cons(x0, nil)) → c28(CONS(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.91
PROPER(cons(0, x1)) → c28(CONS(ok(0), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(cons(nil, x1)) → c28(CONS(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(sel(x0, dbl(z0))) → c29(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.91
PROPER(sel(x0, s(z0))) → c29(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.91
PROPER(sel(x0, dbls(z0))) → c29(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.91
PROPER(sel(x0, cons(z0, z1))) → c29(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(sel(x0, sel(z0, z1))) → c29(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(sel(x0, indx(z0, z1))) → c29(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(sel(x0, from(z0))) → c29(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.91
PROPER(sel(dbl(z0), x1)) → c29(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(s(z0), x1)) → c29(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(dbls(z0), x1)) → c29(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(cons(z0, z1), x1)) → c29(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(sel(sel(z0, z1), x1)) → c29(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(sel(indx(z0, z1), x1)) → c29(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(sel(from(z0), x1)) → c29(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.91
PROPER(sel(x0, 0)) → c29(SEL(proper(x0), ok(0)), PROPER(x0)) 268.47/85.91
PROPER(sel(x0, nil)) → c29(SEL(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.91
PROPER(sel(0, x1)) → c29(SEL(ok(0), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(sel(nil, x1)) → c29(SEL(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(indx(x0, dbl(z0))) → c30(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 268.47/85.91
PROPER(indx(x0, s(z0))) → c30(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 268.47/85.91
PROPER(indx(x0, dbls(z0))) → c30(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0))) 268.47/85.91
PROPER(indx(x0, cons(z0, z1))) → c30(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(indx(x0, sel(z0, z1))) → c30(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(indx(x0, indx(z0, z1))) → c30(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(indx(x0, from(z0))) → c30(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 268.47/85.91
PROPER(indx(dbl(z0), x1)) → c30(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(s(z0), x1)) → c30(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(dbls(z0), x1)) → c30(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(cons(z0, z1), x1)) → c30(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(indx(sel(z0, z1), x1)) → c30(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(indx(indx(z0, z1), x1)) → c30(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1)) 268.47/85.91
PROPER(indx(from(z0), x1)) → c30(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 268.47/85.91
PROPER(indx(x0, 0)) → c30(INDX(proper(x0), ok(0)), PROPER(x0)) 268.47/85.91
PROPER(indx(x0, nil)) → c30(INDX(proper(x0), ok(nil)), PROPER(x0)) 268.47/85.91
PROPER(indx(0, x1)) → c30(INDX(ok(0), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(indx(nil, x1)) → c30(INDX(ok(nil), proper(x1)), PROPER(x1)) 268.47/85.91
PROPER(from(dbl(z0))) → c31(FROM(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
PROPER(from(dbls(z0))) → c31(FROM(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
PROPER(from(sel(z0, z1))) → c31(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
PROPER(from(indx(z0, z1))) → c31(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
PROPER(from(0)) → c31(FROM(ok(0))) 268.47/85.91
PROPER(from(nil)) → c31(FROM(ok(nil))) 268.47/85.91
TOP(mark(dbl(z0))) → c35(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 268.47/85.91
TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 268.47/85.91
TOP(mark(dbls(z0))) → c35(TOP(dbls(proper(z0))), PROPER(dbls(z0))) 268.47/85.91
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 268.47/85.91
TOP(mark(sel(z0, z1))) → c35(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 268.47/85.91
TOP(mark(indx(z0, z1))) → c35(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1))) 268.47/85.91
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0))) 268.47/85.91
TOP(ok(dbl(0))) → c36(TOP(mark(0)), ACTIVE(dbl(0))) 268.47/85.91
TOP(ok(dbl(s(z0)))) → c36(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 268.47/85.91
TOP(ok(dbls(nil))) → c36(TOP(mark(nil)), ACTIVE(dbls(nil))) 268.47/85.91
TOP(ok(dbls(cons(z0, z1)))) → c36(TOP(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1)))) 268.47/85.91
TOP(ok(sel(0, cons(z0, z1)))) → c36(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 268.47/85.91
TOP(ok(sel(s(z0), cons(z1, z2)))) → c36(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 268.47/85.91
TOP(ok(indx(nil, z0))) → c36(TOP(mark(nil)), ACTIVE(indx(nil, z0))) 268.47/85.91
TOP(ok(indx(cons(z0, z1), z2))) → c36(TOP(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2))) 268.47/85.91
TOP(ok(from(z0))) → c36(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 268.47/85.91
TOP(ok(dbl(z0))) → c36(TOP(dbl(active(z0))), ACTIVE(dbl(z0))) 268.47/85.91
TOP(ok(dbls(z0))) → c36(TOP(dbls(active(z0))), ACTIVE(dbls(z0))) 268.47/85.91
TOP(ok(sel(z0, z1))) → c36(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 268.47/85.91
TOP(ok(sel(z0, z1))) → c36(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 268.47/85.91
TOP(ok(indx(z0, z1))) → c36(TOP(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
268.47/85.91
268.47/85.91

(64) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.47/85.91
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.47/85.91
active(dbls(nil)) → mark(nil) 268.47/85.91
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.47/85.91
active(sel(0, cons(z0, z1))) → mark(z0) 268.47/85.91
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.47/85.91
active(indx(nil, z0)) → mark(nil) 268.47/85.91
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.47/85.91
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.47/85.91
active(dbl(z0)) → dbl(active(z0)) 268.47/85.91
active(dbls(z0)) → dbls(active(z0)) 268.47/85.91
active(sel(z0, z1)) → sel(active(z0), z1) 268.47/85.91
active(sel(z0, z1)) → sel(z0, active(z1)) 268.47/85.91
active(indx(z0, z1)) → indx(active(z0), z1) 268.47/85.91
dbl(mark(z0)) → mark(dbl(z0)) 268.47/85.91
dbl(ok(z0)) → ok(dbl(z0)) 268.47/85.91
dbls(mark(z0)) → mark(dbls(z0)) 268.47/85.91
dbls(ok(z0)) → ok(dbls(z0)) 268.47/85.91
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.47/85.91
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.47/85.91
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.47/85.91
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.47/85.91
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.47/85.91
proper(dbl(z0)) → dbl(proper(z0)) 268.47/85.91
proper(0) → ok(0) 268.47/85.91
proper(s(z0)) → s(proper(z0)) 268.47/85.91
proper(dbls(z0)) → dbls(proper(z0)) 268.47/85.91
proper(nil) → ok(nil) 268.47/85.91
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.47/85.91
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.47/85.91
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.47/85.91
proper(from(z0)) → from(proper(z0)) 268.47/85.91
s(ok(z0)) → ok(s(z0)) 268.47/85.91
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.47/85.91
from(ok(z0)) → ok(from(z0)) 268.47/85.91
top(mark(z0)) → top(proper(z0)) 268.47/85.91
top(ok(z0)) → top(active(z0))
Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0)) 268.47/85.91
TOP(mark(0)) → c35(TOP(ok(0))) 268.47/85.91
TOP(mark(nil)) → c35(TOP(ok(nil)))
S tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
K tuples:

TOP(mark(nil)) → c35(TOP(ok(nil))) 268.47/85.91
TOP(mark(0)) → c35(TOP(ok(0)))
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

DBL, DBLS, SEL, INDX, S, CONS, FROM, TOP

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34, c35

268.47/85.91
268.47/85.91

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

Removed 2 trailing tuple parts
268.47/85.91
268.47/85.91

(66) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.47/85.91
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.47/85.91
active(dbls(nil)) → mark(nil) 268.47/85.91
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.47/85.91
active(sel(0, cons(z0, z1))) → mark(z0) 268.47/85.91
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.47/85.91
active(indx(nil, z0)) → mark(nil) 268.47/85.91
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.47/85.91
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.47/85.91
active(dbl(z0)) → dbl(active(z0)) 268.47/85.91
active(dbls(z0)) → dbls(active(z0)) 268.47/85.91
active(sel(z0, z1)) → sel(active(z0), z1) 268.47/85.91
active(sel(z0, z1)) → sel(z0, active(z1)) 268.47/85.91
active(indx(z0, z1)) → indx(active(z0), z1) 268.47/85.91
dbl(mark(z0)) → mark(dbl(z0)) 268.47/85.91
dbl(ok(z0)) → ok(dbl(z0)) 268.47/85.91
dbls(mark(z0)) → mark(dbls(z0)) 268.47/85.91
dbls(ok(z0)) → ok(dbls(z0)) 268.47/85.91
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.47/85.91
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.47/85.91
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.47/85.91
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.47/85.91
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.47/85.91
proper(dbl(z0)) → dbl(proper(z0)) 268.47/85.91
proper(0) → ok(0) 268.47/85.91
proper(s(z0)) → s(proper(z0)) 268.47/85.91
proper(dbls(z0)) → dbls(proper(z0)) 268.47/85.91
proper(nil) → ok(nil) 268.47/85.91
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.47/85.91
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.47/85.91
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.47/85.91
proper(from(z0)) → from(proper(z0)) 268.47/85.91
s(ok(z0)) → ok(s(z0)) 268.47/85.91
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.47/85.91
from(ok(z0)) → ok(from(z0)) 268.47/85.91
top(mark(z0)) → top(proper(z0)) 268.47/85.91
top(ok(z0)) → top(active(z0))
Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0)) 268.47/85.91
TOP(mark(0)) → c35 268.47/85.91
TOP(mark(nil)) → c35
S tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
K tuples:

TOP(mark(0)) → c35 268.47/85.91
TOP(mark(nil)) → c35
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

DBL, DBLS, SEL, INDX, S, CONS, FROM, TOP

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34, c35

268.47/85.91
268.47/85.91

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

Removed 2 trailing nodes:

TOP(mark(0)) → c35 268.47/85.91
TOP(mark(nil)) → c35
268.47/85.91
268.47/85.91

(68) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.47/85.91
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.47/85.91
active(dbls(nil)) → mark(nil) 268.47/85.91
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.47/85.91
active(sel(0, cons(z0, z1))) → mark(z0) 268.47/85.91
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.47/85.91
active(indx(nil, z0)) → mark(nil) 268.47/85.91
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.47/85.91
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.47/85.91
active(dbl(z0)) → dbl(active(z0)) 268.47/85.91
active(dbls(z0)) → dbls(active(z0)) 268.47/85.91
active(sel(z0, z1)) → sel(active(z0), z1) 268.47/85.91
active(sel(z0, z1)) → sel(z0, active(z1)) 268.47/85.91
active(indx(z0, z1)) → indx(active(z0), z1) 268.47/85.91
dbl(mark(z0)) → mark(dbl(z0)) 268.47/85.91
dbl(ok(z0)) → ok(dbl(z0)) 268.47/85.91
dbls(mark(z0)) → mark(dbls(z0)) 268.47/85.91
dbls(ok(z0)) → ok(dbls(z0)) 268.47/85.91
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.47/85.91
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.47/85.91
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.47/85.91
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.47/85.91
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.47/85.91
proper(dbl(z0)) → dbl(proper(z0)) 268.47/85.91
proper(0) → ok(0) 268.47/85.91
proper(s(z0)) → s(proper(z0)) 268.47/85.91
proper(dbls(z0)) → dbls(proper(z0)) 268.47/85.91
proper(nil) → ok(nil) 268.47/85.91
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.47/85.91
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.47/85.91
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.47/85.91
proper(from(z0)) → from(proper(z0)) 268.47/85.91
s(ok(z0)) → ok(s(z0)) 268.47/85.91
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.47/85.91
from(ok(z0)) → ok(from(z0)) 268.47/85.91
top(mark(z0)) → top(proper(z0)) 268.47/85.91
top(ok(z0)) → top(active(z0))
Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
S tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
K tuples:none
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

DBL, DBLS, SEL, INDX, S, CONS, FROM

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34

268.47/85.91
268.47/85.91

(69) 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.

INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0))
We considered the (Usable) Rules:none
And the Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 268.47/85.91

POL(CONS(x1, x2)) = 0    268.47/85.91
POL(DBL(x1)) = 0    268.47/85.91
POL(DBLS(x1)) = 0    268.47/85.91
POL(FROM(x1)) = 0    268.47/85.91
POL(INDX(x1, x2)) = x22    268.47/85.91
POL(S(x1)) = x12    268.47/85.91
POL(SEL(x1, x2)) = 0    268.47/85.91
POL(c14(x1)) = x1    268.47/85.91
POL(c15(x1)) = x1    268.47/85.91
POL(c16(x1)) = x1    268.47/85.91
POL(c17(x1)) = x1    268.47/85.91
POL(c18(x1)) = x1    268.47/85.91
POL(c19(x1)) = x1    268.47/85.91
POL(c20(x1)) = x1    268.47/85.91
POL(c21(x1)) = x1    268.47/85.91
POL(c22(x1)) = x1    268.47/85.91
POL(c32(x1)) = x1    268.47/85.91
POL(c33(x1)) = x1    268.47/85.91
POL(c34(x1)) = x1    268.47/85.91
POL(mark(x1)) = 0    268.47/85.91
POL(ok(x1)) = [1] + x1   
268.47/85.91
268.47/85.91

(70) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.47/85.91
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.47/85.91
active(dbls(nil)) → mark(nil) 268.47/85.91
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.47/85.91
active(sel(0, cons(z0, z1))) → mark(z0) 268.47/85.91
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.47/85.91
active(indx(nil, z0)) → mark(nil) 268.47/85.91
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.47/85.91
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.47/85.91
active(dbl(z0)) → dbl(active(z0)) 268.47/85.91
active(dbls(z0)) → dbls(active(z0)) 268.47/85.91
active(sel(z0, z1)) → sel(active(z0), z1) 268.47/85.91
active(sel(z0, z1)) → sel(z0, active(z1)) 268.47/85.91
active(indx(z0, z1)) → indx(active(z0), z1) 268.47/85.91
dbl(mark(z0)) → mark(dbl(z0)) 268.47/85.91
dbl(ok(z0)) → ok(dbl(z0)) 268.47/85.91
dbls(mark(z0)) → mark(dbls(z0)) 268.47/85.91
dbls(ok(z0)) → ok(dbls(z0)) 268.47/85.91
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.47/85.91
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.47/85.91
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.47/85.91
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.47/85.91
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.47/85.91
proper(dbl(z0)) → dbl(proper(z0)) 268.47/85.91
proper(0) → ok(0) 268.47/85.91
proper(s(z0)) → s(proper(z0)) 268.47/85.91
proper(dbls(z0)) → dbls(proper(z0)) 268.47/85.91
proper(nil) → ok(nil) 268.47/85.91
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.47/85.91
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.47/85.91
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.47/85.91
proper(from(z0)) → from(proper(z0)) 268.47/85.91
s(ok(z0)) → ok(s(z0)) 268.47/85.91
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.47/85.91
from(ok(z0)) → ok(from(z0)) 268.47/85.91
top(mark(z0)) → top(proper(z0)) 268.47/85.91
top(ok(z0)) → top(active(z0))
Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
S tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
K tuples:

INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0))
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

DBL, DBLS, SEL, INDX, S, CONS, FROM

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34

268.47/85.91
268.47/85.91

(71) 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.

SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 268.47/85.91

POL(CONS(x1, x2)) = 0    268.47/85.91
POL(DBL(x1)) = 0    268.47/85.91
POL(DBLS(x1)) = 0    268.47/85.91
POL(FROM(x1)) = 0    268.47/85.91
POL(INDX(x1, x2)) = [5]x2    268.47/85.91
POL(S(x1)) = [5]x1    268.47/85.91
POL(SEL(x1, x2)) = x2    268.47/85.91
POL(c14(x1)) = x1    268.47/85.91
POL(c15(x1)) = x1    268.47/85.91
POL(c16(x1)) = x1    268.47/85.91
POL(c17(x1)) = x1    268.47/85.91
POL(c18(x1)) = x1    268.47/85.91
POL(c19(x1)) = x1    268.47/85.91
POL(c20(x1)) = x1    268.47/85.91
POL(c21(x1)) = x1    268.47/85.91
POL(c22(x1)) = x1    268.47/85.91
POL(c32(x1)) = x1    268.47/85.91
POL(c33(x1)) = x1    268.47/85.91
POL(c34(x1)) = x1    268.47/85.91
POL(mark(x1)) = x1    268.47/85.91
POL(ok(x1)) = [1] + x1   
268.47/85.91
268.47/85.91

(72) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.47/85.91
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.47/85.91
active(dbls(nil)) → mark(nil) 268.47/85.91
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.47/85.91
active(sel(0, cons(z0, z1))) → mark(z0) 268.47/85.91
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.47/85.91
active(indx(nil, z0)) → mark(nil) 268.47/85.91
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.47/85.91
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.47/85.91
active(dbl(z0)) → dbl(active(z0)) 268.47/85.91
active(dbls(z0)) → dbls(active(z0)) 268.47/85.91
active(sel(z0, z1)) → sel(active(z0), z1) 268.47/85.91
active(sel(z0, z1)) → sel(z0, active(z1)) 268.47/85.91
active(indx(z0, z1)) → indx(active(z0), z1) 268.47/85.91
dbl(mark(z0)) → mark(dbl(z0)) 268.47/85.91
dbl(ok(z0)) → ok(dbl(z0)) 268.47/85.91
dbls(mark(z0)) → mark(dbls(z0)) 268.47/85.91
dbls(ok(z0)) → ok(dbls(z0)) 268.47/85.91
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.47/85.91
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.47/85.91
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.47/85.91
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.47/85.91
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.47/85.91
proper(dbl(z0)) → dbl(proper(z0)) 268.47/85.91
proper(0) → ok(0) 268.47/85.91
proper(s(z0)) → s(proper(z0)) 268.47/85.91
proper(dbls(z0)) → dbls(proper(z0)) 268.47/85.91
proper(nil) → ok(nil) 268.47/85.91
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.47/85.91
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.47/85.91
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.47/85.91
proper(from(z0)) → from(proper(z0)) 268.47/85.91
s(ok(z0)) → ok(s(z0)) 268.47/85.91
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.47/85.91
from(ok(z0)) → ok(from(z0)) 268.47/85.91
top(mark(z0)) → top(proper(z0)) 268.47/85.91
top(ok(z0)) → top(active(z0))
Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
S tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
K tuples:

INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1))
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

DBL, DBLS, SEL, INDX, S, CONS, FROM

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34

268.47/85.91
268.47/85.91

(73) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^3))) transformation)

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

DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
We considered the (Usable) Rules:none
And the Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 268.47/85.91

POL(CONS(x1, x2)) = x12 + x13 + x12·x2 + x1·x22    268.47/85.91
POL(DBL(x1)) = x1 + x12 + x13    268.47/85.91
POL(DBLS(x1)) = x1 + x12 + x13    268.47/85.91
POL(FROM(x1)) = x1 + x13    268.47/85.91
POL(INDX(x1, x2)) = x2 + x22 + x23    268.47/85.91
POL(S(x1)) = x1 + x12 + x13    268.47/85.91
POL(SEL(x1, x2)) = x1 + x2 + x22 + x1·x2 + x12 + x13 + x12·x2 + x1·x22 + x23    268.47/85.91
POL(c14(x1)) = x1    268.47/85.91
POL(c15(x1)) = x1    268.47/85.91
POL(c16(x1)) = x1    268.47/85.91
POL(c17(x1)) = x1    268.47/85.91
POL(c18(x1)) = x1    268.47/85.91
POL(c19(x1)) = x1    268.47/85.91
POL(c20(x1)) = x1    268.47/85.91
POL(c21(x1)) = x1    268.47/85.91
POL(c22(x1)) = x1    268.47/85.91
POL(c32(x1)) = x1    268.47/85.91
POL(c33(x1)) = x1    268.47/85.91
POL(c34(x1)) = x1    268.47/85.91
POL(mark(x1)) = x1    268.47/85.91
POL(ok(x1)) = [1] + x1   
268.47/85.91
268.47/85.91

(74) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.47/85.91
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.47/85.91
active(dbls(nil)) → mark(nil) 268.47/85.91
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.47/85.91
active(sel(0, cons(z0, z1))) → mark(z0) 268.47/85.91
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.47/85.91
active(indx(nil, z0)) → mark(nil) 268.47/85.91
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.47/85.91
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.47/85.91
active(dbl(z0)) → dbl(active(z0)) 268.47/85.91
active(dbls(z0)) → dbls(active(z0)) 268.47/85.91
active(sel(z0, z1)) → sel(active(z0), z1) 268.47/85.91
active(sel(z0, z1)) → sel(z0, active(z1)) 268.47/85.91
active(indx(z0, z1)) → indx(active(z0), z1) 268.47/85.91
dbl(mark(z0)) → mark(dbl(z0)) 268.47/85.91
dbl(ok(z0)) → ok(dbl(z0)) 268.47/85.91
dbls(mark(z0)) → mark(dbls(z0)) 268.47/85.91
dbls(ok(z0)) → ok(dbls(z0)) 268.47/85.91
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.47/85.91
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.47/85.91
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.47/85.91
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.47/85.91
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.47/85.91
proper(dbl(z0)) → dbl(proper(z0)) 268.47/85.91
proper(0) → ok(0) 268.47/85.91
proper(s(z0)) → s(proper(z0)) 268.47/85.91
proper(dbls(z0)) → dbls(proper(z0)) 268.47/85.91
proper(nil) → ok(nil) 268.47/85.91
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.47/85.91
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.47/85.91
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.47/85.91
proper(from(z0)) → from(proper(z0)) 268.47/85.91
s(ok(z0)) → ok(s(z0)) 268.47/85.91
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.47/85.91
from(ok(z0)) → ok(from(z0)) 268.47/85.91
top(mark(z0)) → top(proper(z0)) 268.47/85.91
top(ok(z0)) → top(active(z0))
Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
S tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1))
K tuples:

INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

DBL, DBLS, SEL, INDX, S, CONS, FROM

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34

268.47/85.91
268.47/85.91

(75) 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.

SEL(z0, mark(z1)) → c19(SEL(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 268.47/85.91

POL(CONS(x1, x2)) = [5]x1 + [5]x2    268.47/85.91
POL(DBL(x1)) = 0    268.47/85.91
POL(DBLS(x1)) = 0    268.47/85.91
POL(FROM(x1)) = [3]x1    268.47/85.91
POL(INDX(x1, x2)) = [5]x2    268.47/85.91
POL(S(x1)) = [5]x1    268.47/85.91
POL(SEL(x1, x2)) = x2    268.47/85.91
POL(c14(x1)) = x1    268.47/85.91
POL(c15(x1)) = x1    268.47/85.91
POL(c16(x1)) = x1    268.47/85.91
POL(c17(x1)) = x1    268.47/85.91
POL(c18(x1)) = x1    268.47/85.91
POL(c19(x1)) = x1    268.47/85.91
POL(c20(x1)) = x1    268.47/85.91
POL(c21(x1)) = x1    268.47/85.91
POL(c22(x1)) = x1    268.47/85.91
POL(c32(x1)) = x1    268.47/85.91
POL(c33(x1)) = x1    268.47/85.91
POL(c34(x1)) = x1    268.47/85.91
POL(mark(x1)) = [1] + x1    268.47/85.91
POL(ok(x1)) = x1   
268.47/85.91
268.47/85.91

(76) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.47/85.91
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.47/85.91
active(dbls(nil)) → mark(nil) 268.47/85.91
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.47/85.91
active(sel(0, cons(z0, z1))) → mark(z0) 268.47/85.91
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.47/85.91
active(indx(nil, z0)) → mark(nil) 268.47/85.91
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.47/85.91
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.47/85.91
active(dbl(z0)) → dbl(active(z0)) 268.47/85.91
active(dbls(z0)) → dbls(active(z0)) 268.47/85.91
active(sel(z0, z1)) → sel(active(z0), z1) 268.47/85.91
active(sel(z0, z1)) → sel(z0, active(z1)) 268.47/85.91
active(indx(z0, z1)) → indx(active(z0), z1) 268.47/85.91
dbl(mark(z0)) → mark(dbl(z0)) 268.47/85.91
dbl(ok(z0)) → ok(dbl(z0)) 268.47/85.91
dbls(mark(z0)) → mark(dbls(z0)) 268.47/85.91
dbls(ok(z0)) → ok(dbls(z0)) 268.47/85.91
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.47/85.91
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.47/85.91
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.47/85.91
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.47/85.91
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.47/85.91
proper(dbl(z0)) → dbl(proper(z0)) 268.47/85.91
proper(0) → ok(0) 268.47/85.91
proper(s(z0)) → s(proper(z0)) 268.47/85.91
proper(dbls(z0)) → dbls(proper(z0)) 268.47/85.91
proper(nil) → ok(nil) 268.47/85.91
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.47/85.91
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.47/85.91
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.47/85.91
proper(from(z0)) → from(proper(z0)) 268.47/85.91
s(ok(z0)) → ok(s(z0)) 268.47/85.91
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.47/85.91
from(ok(z0)) → ok(from(z0)) 268.47/85.91
top(mark(z0)) → top(proper(z0)) 268.47/85.91
top(ok(z0)) → top(active(z0))
Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
S tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1))
K tuples:

INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1))
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

DBL, DBLS, SEL, INDX, S, CONS, FROM

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34

268.47/85.91
268.47/85.91

(77) 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.

DBL(mark(z0)) → c14(DBL(z0))
We considered the (Usable) Rules:none
And the Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 268.47/85.91

POL(CONS(x1, x2)) = [5]x1 + [5]x2    268.47/85.91
POL(DBL(x1)) = [4]x1    268.47/85.91
POL(DBLS(x1)) = 0    268.47/85.91
POL(FROM(x1)) = [5]x1    268.47/85.91
POL(INDX(x1, x2)) = [5]x2    268.47/85.91
POL(S(x1)) = [5]x1    268.47/85.91
POL(SEL(x1, x2)) = [5]x2    268.47/85.91
POL(c14(x1)) = x1    268.47/85.91
POL(c15(x1)) = x1    268.47/85.91
POL(c16(x1)) = x1    268.47/85.91
POL(c17(x1)) = x1    268.47/85.91
POL(c18(x1)) = x1    268.47/85.91
POL(c19(x1)) = x1    268.47/85.91
POL(c20(x1)) = x1    268.47/85.91
POL(c21(x1)) = x1    268.47/85.91
POL(c22(x1)) = x1    268.47/85.91
POL(c32(x1)) = x1    268.47/85.91
POL(c33(x1)) = x1    268.47/85.91
POL(c34(x1)) = x1    268.47/85.91
POL(mark(x1)) = [4] + x1    268.47/85.91
POL(ok(x1)) = x1   
268.47/85.91
268.47/85.91

(78) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.47/85.91
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.47/85.91
active(dbls(nil)) → mark(nil) 268.47/85.91
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.47/85.91
active(sel(0, cons(z0, z1))) → mark(z0) 268.47/85.91
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.47/85.91
active(indx(nil, z0)) → mark(nil) 268.47/85.91
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.47/85.91
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.47/85.91
active(dbl(z0)) → dbl(active(z0)) 268.47/85.91
active(dbls(z0)) → dbls(active(z0)) 268.47/85.91
active(sel(z0, z1)) → sel(active(z0), z1) 268.47/85.91
active(sel(z0, z1)) → sel(z0, active(z1)) 268.47/85.91
active(indx(z0, z1)) → indx(active(z0), z1) 268.47/85.91
dbl(mark(z0)) → mark(dbl(z0)) 268.47/85.91
dbl(ok(z0)) → ok(dbl(z0)) 268.47/85.91
dbls(mark(z0)) → mark(dbls(z0)) 268.47/85.91
dbls(ok(z0)) → ok(dbls(z0)) 268.47/85.91
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.47/85.91
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.47/85.91
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.47/85.91
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.47/85.91
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.47/85.91
proper(dbl(z0)) → dbl(proper(z0)) 268.47/85.91
proper(0) → ok(0) 268.47/85.91
proper(s(z0)) → s(proper(z0)) 268.47/85.91
proper(dbls(z0)) → dbls(proper(z0)) 268.47/85.91
proper(nil) → ok(nil) 268.47/85.91
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.47/85.91
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.47/85.91
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.47/85.91
proper(from(z0)) → from(proper(z0)) 268.47/85.91
s(ok(z0)) → ok(s(z0)) 268.47/85.91
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.47/85.91
from(ok(z0)) → ok(from(z0)) 268.47/85.91
top(mark(z0)) → top(proper(z0)) 268.47/85.91
top(ok(z0)) → top(active(z0))
Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
S tuples:

DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1))
K tuples:

INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
DBL(mark(z0)) → c14(DBL(z0))
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

DBL, DBLS, SEL, INDX, S, CONS, FROM

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34

268.47/85.91
268.47/85.91

(79) 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.

DBLS(mark(z0)) → c16(DBLS(z0))
We considered the (Usable) Rules:none
And the Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 268.47/85.91

POL(CONS(x1, x2)) = [5]x1 + [5]x2    268.47/85.91
POL(DBL(x1)) = [5]x1    268.47/85.91
POL(DBLS(x1)) = [2]x1    268.47/85.91
POL(FROM(x1)) = [5]x1    268.47/85.91
POL(INDX(x1, x2)) = [5]x2    268.47/85.91
POL(S(x1)) = [5]x1    268.47/85.91
POL(SEL(x1, x2)) = [5]x2    268.47/85.91
POL(c14(x1)) = x1    268.47/85.91
POL(c15(x1)) = x1    268.47/85.91
POL(c16(x1)) = x1    268.47/85.91
POL(c17(x1)) = x1    268.47/85.91
POL(c18(x1)) = x1    268.47/85.91
POL(c19(x1)) = x1    268.47/85.91
POL(c20(x1)) = x1    268.47/85.91
POL(c21(x1)) = x1    268.47/85.91
POL(c22(x1)) = x1    268.47/85.91
POL(c32(x1)) = x1    268.47/85.91
POL(c33(x1)) = x1    268.47/85.91
POL(c34(x1)) = x1    268.47/85.91
POL(mark(x1)) = [1] + x1    268.47/85.91
POL(ok(x1)) = x1   
268.47/85.91
268.47/85.91

(80) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.47/85.91
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.47/85.91
active(dbls(nil)) → mark(nil) 268.47/85.91
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.47/85.91
active(sel(0, cons(z0, z1))) → mark(z0) 268.47/85.91
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.47/85.91
active(indx(nil, z0)) → mark(nil) 268.47/85.91
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.47/85.91
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.47/85.91
active(dbl(z0)) → dbl(active(z0)) 268.47/85.91
active(dbls(z0)) → dbls(active(z0)) 268.47/85.91
active(sel(z0, z1)) → sel(active(z0), z1) 268.47/85.91
active(sel(z0, z1)) → sel(z0, active(z1)) 268.47/85.91
active(indx(z0, z1)) → indx(active(z0), z1) 268.47/85.91
dbl(mark(z0)) → mark(dbl(z0)) 268.47/85.91
dbl(ok(z0)) → ok(dbl(z0)) 268.47/85.91
dbls(mark(z0)) → mark(dbls(z0)) 268.47/85.91
dbls(ok(z0)) → ok(dbls(z0)) 268.47/85.91
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.47/85.91
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.47/85.91
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.47/85.91
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.47/85.91
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.47/85.91
proper(dbl(z0)) → dbl(proper(z0)) 268.47/85.91
proper(0) → ok(0) 268.47/85.91
proper(s(z0)) → s(proper(z0)) 268.47/85.91
proper(dbls(z0)) → dbls(proper(z0)) 268.47/85.91
proper(nil) → ok(nil) 268.47/85.91
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.47/85.91
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.47/85.91
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.47/85.91
proper(from(z0)) → from(proper(z0)) 268.47/85.91
s(ok(z0)) → ok(s(z0)) 268.47/85.91
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.47/85.91
from(ok(z0)) → ok(from(z0)) 268.47/85.91
top(mark(z0)) → top(proper(z0)) 268.47/85.91
top(ok(z0)) → top(active(z0))
Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
S tuples:

SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1))
K tuples:

INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0))
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

DBL, DBLS, SEL, INDX, S, CONS, FROM

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34

268.47/85.91
268.47/85.91

(81) 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.

SEL(mark(z0), z1) → c18(SEL(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.91
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.91
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.91
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.91
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.91
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.91
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.91
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.91
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.91
S(ok(z0)) → c32(S(z0)) 268.47/85.91
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.91
FROM(ok(z0)) → c34(FROM(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 268.47/85.91

POL(CONS(x1, x2)) = x1 + x2 + [3]x22 + [3]x1·x2 + [3]x12    268.47/85.91
POL(DBL(x1)) = [3]x1 + [3]x12    268.47/85.91
POL(DBLS(x1)) = [3]x1 + [3]x12    268.47/85.91
POL(FROM(x1)) = [3]x1 + [3]x12    268.47/85.91
POL(INDX(x1, x2)) = x2 + [3]x22 + [3]x1·x2    268.47/85.91
POL(S(x1)) = [3]x1 + [3]x12    268.47/85.91
POL(SEL(x1, x2)) = x2 + [3]x22 + [3]x1·x2 + x12    268.47/85.91
POL(c14(x1)) = x1    268.47/85.91
POL(c15(x1)) = x1    268.47/85.91
POL(c16(x1)) = x1    268.47/85.91
POL(c17(x1)) = x1    268.47/85.91
POL(c18(x1)) = x1    268.47/85.91
POL(c19(x1)) = x1    268.47/85.91
POL(c20(x1)) = x1    268.47/85.91
POL(c21(x1)) = x1    268.47/85.91
POL(c22(x1)) = x1    268.47/85.91
POL(c32(x1)) = x1    268.47/85.91
POL(c33(x1)) = x1    268.47/85.91
POL(c34(x1)) = x1    268.47/85.91
POL(mark(x1)) = [1] + x1    268.47/85.91
POL(ok(x1)) = x1   
268.47/85.91
268.47/85.91

(82) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.47/85.91
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.47/85.91
active(dbls(nil)) → mark(nil) 268.47/85.91
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.47/85.91
active(sel(0, cons(z0, z1))) → mark(z0) 268.47/85.91
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.47/85.91
active(indx(nil, z0)) → mark(nil) 268.47/85.91
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.47/85.91
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.47/85.91
active(dbl(z0)) → dbl(active(z0)) 268.47/85.91
active(dbls(z0)) → dbls(active(z0)) 268.47/85.91
active(sel(z0, z1)) → sel(active(z0), z1) 268.47/85.91
active(sel(z0, z1)) → sel(z0, active(z1)) 268.47/85.91
active(indx(z0, z1)) → indx(active(z0), z1) 268.47/85.91
dbl(mark(z0)) → mark(dbl(z0)) 268.47/85.91
dbl(ok(z0)) → ok(dbl(z0)) 268.47/85.92
dbls(mark(z0)) → mark(dbls(z0)) 268.47/85.92
dbls(ok(z0)) → ok(dbls(z0)) 268.47/85.92
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.47/85.92
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.47/85.92
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.47/85.92
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.47/85.92
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.47/85.92
proper(dbl(z0)) → dbl(proper(z0)) 268.47/85.92
proper(0) → ok(0) 268.47/85.92
proper(s(z0)) → s(proper(z0)) 268.47/85.92
proper(dbls(z0)) → dbls(proper(z0)) 268.47/85.92
proper(nil) → ok(nil) 268.47/85.92
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.47/85.92
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.47/85.92
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.47/85.92
proper(from(z0)) → from(proper(z0)) 268.47/85.92
s(ok(z0)) → ok(s(z0)) 268.47/85.92
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.47/85.92
from(ok(z0)) → ok(from(z0)) 268.47/85.92
top(mark(z0)) → top(proper(z0)) 268.47/85.92
top(ok(z0)) → top(active(z0))
Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.92
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.92
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.92
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.92
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.92
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.92
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.92
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.92
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.92
S(ok(z0)) → c32(S(z0)) 268.47/85.92
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.92
FROM(ok(z0)) → c34(FROM(z0))
S tuples:

INDX(mark(z0), z1) → c21(INDX(z0, z1))
K tuples:

INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.92
S(ok(z0)) → c32(S(z0)) 268.47/85.92
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.92
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.92
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.92
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.92
FROM(ok(z0)) → c34(FROM(z0)) 268.47/85.92
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.92
DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.92
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.92
SEL(mark(z0), z1) → c18(SEL(z0, z1))
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

DBL, DBLS, SEL, INDX, S, CONS, FROM

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34

268.47/85.92
268.47/85.92

(83) 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.

INDX(mark(z0), z1) → c21(INDX(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.92
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.92
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.92
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.92
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.92
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.92
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.92
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.92
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.92
S(ok(z0)) → c32(S(z0)) 268.47/85.92
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.92
FROM(ok(z0)) → c34(FROM(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 268.47/85.92

POL(CONS(x1, x2)) = [3]x1 + [5]x2    268.47/85.92
POL(DBL(x1)) = [5]x1    268.47/85.92
POL(DBLS(x1)) = [5]x1    268.47/85.92
POL(FROM(x1)) = [5]x1    268.47/85.92
POL(INDX(x1, x2)) = [3]x1 + [5]x2    268.47/85.92
POL(S(x1)) = [5]x1    268.47/85.92
POL(SEL(x1, x2)) = [3]x1 + [2]x2    268.47/85.92
POL(c14(x1)) = x1    268.47/85.92
POL(c15(x1)) = x1    268.47/85.92
POL(c16(x1)) = x1    268.47/85.92
POL(c17(x1)) = x1    268.47/85.92
POL(c18(x1)) = x1    268.47/85.92
POL(c19(x1)) = x1    268.47/85.92
POL(c20(x1)) = x1    268.47/85.92
POL(c21(x1)) = x1    268.47/85.92
POL(c22(x1)) = x1    268.47/85.92
POL(c32(x1)) = x1    268.47/85.92
POL(c33(x1)) = x1    268.47/85.92
POL(c34(x1)) = x1    268.47/85.92
POL(mark(x1)) = [1] + x1    268.47/85.92
POL(ok(x1)) = x1   
268.47/85.92
268.47/85.92

(84) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(dbl(0)) → mark(0) 268.47/85.92
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 268.47/85.92
active(dbls(nil)) → mark(nil) 268.47/85.92
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1))) 268.47/85.92
active(sel(0, cons(z0, z1))) → mark(z0) 268.47/85.92
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 268.47/85.92
active(indx(nil, z0)) → mark(nil) 268.47/85.92
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2))) 268.47/85.92
active(from(z0)) → mark(cons(z0, from(s(z0)))) 268.47/85.92
active(dbl(z0)) → dbl(active(z0)) 268.47/85.92
active(dbls(z0)) → dbls(active(z0)) 268.47/85.92
active(sel(z0, z1)) → sel(active(z0), z1) 268.47/85.92
active(sel(z0, z1)) → sel(z0, active(z1)) 268.47/85.92
active(indx(z0, z1)) → indx(active(z0), z1) 268.47/85.92
dbl(mark(z0)) → mark(dbl(z0)) 268.47/85.92
dbl(ok(z0)) → ok(dbl(z0)) 268.47/85.92
dbls(mark(z0)) → mark(dbls(z0)) 268.47/85.92
dbls(ok(z0)) → ok(dbls(z0)) 268.47/85.92
sel(mark(z0), z1) → mark(sel(z0, z1)) 268.47/85.92
sel(z0, mark(z1)) → mark(sel(z0, z1)) 268.47/85.92
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 268.47/85.92
indx(mark(z0), z1) → mark(indx(z0, z1)) 268.47/85.92
indx(ok(z0), ok(z1)) → ok(indx(z0, z1)) 268.47/85.92
proper(dbl(z0)) → dbl(proper(z0)) 268.47/85.92
proper(0) → ok(0) 268.47/85.92
proper(s(z0)) → s(proper(z0)) 268.47/85.92
proper(dbls(z0)) → dbls(proper(z0)) 268.47/85.92
proper(nil) → ok(nil) 268.47/85.92
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 268.47/85.92
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 268.47/85.92
proper(indx(z0, z1)) → indx(proper(z0), proper(z1)) 268.47/85.92
proper(from(z0)) → from(proper(z0)) 268.47/85.92
s(ok(z0)) → ok(s(z0)) 268.47/85.92
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 268.47/85.92
from(ok(z0)) → ok(from(z0)) 268.47/85.92
top(mark(z0)) → top(proper(z0)) 268.47/85.92
top(ok(z0)) → top(active(z0))
Tuples:

DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.92
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.92
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.92
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.92
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.92
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.92
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.92
INDX(mark(z0), z1) → c21(INDX(z0, z1)) 268.47/85.92
INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.92
S(ok(z0)) → c32(S(z0)) 268.47/85.92
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.92
FROM(ok(z0)) → c34(FROM(z0))
S tuples:none
K tuples:

INDX(ok(z0), ok(z1)) → c22(INDX(z0, z1)) 268.47/85.92
S(ok(z0)) → c32(S(z0)) 268.47/85.92
SEL(ok(z0), ok(z1)) → c20(SEL(z0, z1)) 268.47/85.92
DBL(ok(z0)) → c15(DBL(z0)) 268.47/85.92
DBLS(ok(z0)) → c17(DBLS(z0)) 268.47/85.92
CONS(ok(z0), ok(z1)) → c33(CONS(z0, z1)) 268.47/85.92
FROM(ok(z0)) → c34(FROM(z0)) 268.47/85.92
SEL(z0, mark(z1)) → c19(SEL(z0, z1)) 268.47/85.92
DBL(mark(z0)) → c14(DBL(z0)) 268.47/85.92
DBLS(mark(z0)) → c16(DBLS(z0)) 268.47/85.92
SEL(mark(z0), z1) → c18(SEL(z0, z1)) 268.47/85.92
INDX(mark(z0), z1) → c21(INDX(z0, z1))
Defined Rule Symbols:

active, dbl, dbls, sel, indx, proper, s, cons, from, top

Defined Pair Symbols:

DBL, DBLS, SEL, INDX, S, CONS, FROM

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c32, c33, c34

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

The set S is empty
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(86) BOUNDS(O(1), O(1))

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268.64/86.03 EOF