YES(O(1), O(n^2)) 277.55/89.17 YES(O(1), O(n^2)) 277.83/89.21 277.83/89.21 277.83/89.21 277.83/89.21 277.83/89.21 277.83/89.21 Runtime Complexity (innermost) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml.xml 277.83/89.21 277.83/89.21 277.83/89.21
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277.83/89.21
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(n^2)).

0 CpxTRS
277.83/89.21 
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳2 CdtProblem
277.83/89.21 
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳4 CdtProblem
277.83/89.21 
↳5 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳6 CdtProblem
277.83/89.21 
↳7 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳8 CdtProblem
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↳9 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳10 CdtProblem
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↳11 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳12 CdtProblem
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↳13 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳14 CdtProblem
277.83/89.21 
↳15 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳16 CdtProblem
277.83/89.21 
↳17 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳18 CdtProblem
277.83/89.21 
↳19 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳20 CdtProblem
277.83/89.21 
↳21 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳22 CdtProblem
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↳23 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳24 CdtProblem
277.83/89.21 
↳25 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳26 CdtProblem
277.83/89.21 
↳27 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳28 CdtProblem
277.83/89.21 
↳29 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳30 CdtProblem
277.83/89.21 
↳31 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳32 CdtProblem
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↳33 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳34 CdtProblem
277.83/89.21 
↳35 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳36 CdtProblem
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↳37 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳38 CdtProblem
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↳39 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳40 CdtProblem
277.83/89.21 
↳41 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳42 CdtProblem
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↳43 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳44 CdtProblem
277.83/89.21 
↳45 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳46 CdtProblem
277.83/89.21 
↳47 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳48 CdtProblem
277.83/89.21 
↳49 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳50 CdtProblem
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↳51 CdtUnreachableProof (⇔)
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↳52 CdtProblem
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↳53 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳54 CdtProblem
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↳55 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
277.83/89.21 
↳56 CdtProblem
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↳57 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
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↳58 CdtProblem
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↳59 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
277.83/89.21 
↳60 CdtProblem
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↳61 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
277.83/89.21 
↳62 CdtProblem
277.83/89.21 
↳63 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
277.83/89.21 
↳64 CdtProblem
277.83/89.21 
↳65 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
277.83/89.21 
↳66 CdtProblem
277.83/89.21 
↳67 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
277.83/89.21 
↳68 CdtProblem
277.83/89.21 
↳69 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))
277.83/89.21 
↳70 CdtProblem
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↳71 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
277.83/89.29 
↳72 CdtProblem
277.83/89.29 
↳73 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
277.83/89.29 
↳74 CdtProblem
277.83/89.29 
↳75 SIsEmptyProof (BOTH BOUNDS(ID, ID))
277.83/89.29 
↳76 BOUNDS(O(1), O(1))
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277.83/89.29

(0) Obligation:

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

active(from(X)) → mark(cons(X, from(s(X)))) 277.83/89.29
active(head(cons(X, XS))) → mark(X) 277.83/89.29
active(2nd(cons(X, XS))) → mark(head(XS)) 277.83/89.29
active(take(0, XS)) → mark(nil) 277.83/89.29
active(take(s(N), cons(X, XS))) → mark(cons(X, take(N, XS))) 277.83/89.29
active(sel(0, cons(X, XS))) → mark(X) 277.83/89.29
active(sel(s(N), cons(X, XS))) → mark(sel(N, XS)) 277.83/89.29
active(from(X)) → from(active(X)) 277.83/89.29
active(cons(X1, X2)) → cons(active(X1), X2) 277.83/89.29
active(s(X)) → s(active(X)) 277.83/89.29
active(head(X)) → head(active(X)) 277.83/89.29
active(2nd(X)) → 2nd(active(X)) 277.83/89.29
active(take(X1, X2)) → take(active(X1), X2) 277.83/89.29
active(take(X1, X2)) → take(X1, active(X2)) 277.83/89.29
active(sel(X1, X2)) → sel(active(X1), X2) 277.83/89.29
active(sel(X1, X2)) → sel(X1, active(X2)) 277.83/89.29
from(mark(X)) → mark(from(X)) 277.83/89.29
cons(mark(X1), X2) → mark(cons(X1, X2)) 277.83/89.29
s(mark(X)) → mark(s(X)) 277.83/89.29
head(mark(X)) → mark(head(X)) 277.83/89.29
2nd(mark(X)) → mark(2nd(X)) 277.83/89.29
take(mark(X1), X2) → mark(take(X1, X2)) 277.83/89.29
take(X1, mark(X2)) → mark(take(X1, X2)) 277.83/89.29
sel(mark(X1), X2) → mark(sel(X1, X2)) 277.83/89.29
sel(X1, mark(X2)) → mark(sel(X1, X2)) 277.83/89.29
proper(from(X)) → from(proper(X)) 277.83/89.29
proper(cons(X1, X2)) → cons(proper(X1), proper(X2)) 277.83/89.29
proper(s(X)) → s(proper(X)) 277.83/89.29
proper(head(X)) → head(proper(X)) 277.83/89.29
proper(2nd(X)) → 2nd(proper(X)) 277.83/89.29
proper(take(X1, X2)) → take(proper(X1), proper(X2)) 277.83/89.29
proper(0) → ok(0) 277.83/89.29
proper(nil) → ok(nil) 277.83/89.29
proper(sel(X1, X2)) → sel(proper(X1), proper(X2)) 277.83/89.29
from(ok(X)) → ok(from(X)) 277.83/89.29
cons(ok(X1), ok(X2)) → ok(cons(X1, X2)) 277.83/89.29
s(ok(X)) → ok(s(X)) 277.83/89.29
head(ok(X)) → ok(head(X)) 277.83/89.29
2nd(ok(X)) → ok(2nd(X)) 277.83/89.29
take(ok(X1), ok(X2)) → ok(take(X1, X2)) 277.83/89.29
sel(ok(X1), ok(X2)) → ok(sel(X1, X2)) 277.83/89.29
top(mark(X)) → top(proper(X)) 277.83/89.29
top(ok(X)) → top(active(X))

Rewrite Strategy: INNERMOST
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277.83/89.29

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

Converted CpxTRS to CDT
277.83/89.29
277.83/89.29

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 277.83/89.29
active(head(cons(z0, z1))) → mark(z0) 277.83/89.29
active(2nd(cons(z0, z1))) → mark(head(z1)) 277.83/89.29
active(take(0, z0)) → mark(nil) 277.83/89.29
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 277.83/89.29
active(sel(0, cons(z0, z1))) → mark(z0) 277.83/89.29
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 277.83/89.29
active(from(z0)) → from(active(z0)) 277.83/89.29
active(cons(z0, z1)) → cons(active(z0), z1) 277.83/89.29
active(s(z0)) → s(active(z0)) 277.83/89.29
active(head(z0)) → head(active(z0)) 277.83/89.29
active(2nd(z0)) → 2nd(active(z0)) 277.83/89.29
active(take(z0, z1)) → take(active(z0), z1) 277.83/89.29
active(take(z0, z1)) → take(z0, active(z1)) 277.83/89.29
active(sel(z0, z1)) → sel(active(z0), z1) 277.83/89.29
active(sel(z0, z1)) → sel(z0, active(z1)) 277.83/89.29
from(mark(z0)) → mark(from(z0)) 277.83/89.29
from(ok(z0)) → ok(from(z0)) 277.83/89.29
cons(mark(z0), z1) → mark(cons(z0, z1)) 277.83/89.29
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 277.83/89.29
s(mark(z0)) → mark(s(z0)) 277.83/89.29
s(ok(z0)) → ok(s(z0)) 277.83/89.29
head(mark(z0)) → mark(head(z0)) 277.83/89.29
head(ok(z0)) → ok(head(z0)) 277.83/89.29
2nd(mark(z0)) → mark(2nd(z0)) 277.83/89.29
2nd(ok(z0)) → ok(2nd(z0)) 277.83/89.29
take(mark(z0), z1) → mark(take(z0, z1)) 277.83/89.29
take(z0, mark(z1)) → mark(take(z0, z1)) 277.83/89.29
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 277.83/89.29
sel(mark(z0), z1) → mark(sel(z0, z1)) 277.83/89.29
sel(z0, mark(z1)) → mark(sel(z0, z1)) 277.83/89.29
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 277.83/89.29
proper(from(z0)) → from(proper(z0)) 277.83/89.29
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 277.83/89.29
proper(s(z0)) → s(proper(z0)) 277.83/89.29
proper(head(z0)) → head(proper(z0)) 277.83/89.29
proper(2nd(z0)) → 2nd(proper(z0)) 277.83/89.29
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 277.83/89.29
proper(0) → ok(0) 277.83/89.29
proper(nil) → ok(nil) 277.83/89.29
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 277.83/89.29
top(mark(z0)) → top(proper(z0)) 277.83/89.29
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(from(z0)) → c(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0)) 277.83/89.29
ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 277.83/89.29
ACTIVE(take(s(z0), cons(z1, z2))) → c4(CONS(z1, take(z0, z2)), TAKE(z0, z2)) 277.83/89.29
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 277.83/89.29
ACTIVE(from(z0)) → c7(FROM(active(z0)), ACTIVE(z0)) 277.83/89.29
ACTIVE(cons(z0, z1)) → c8(CONS(active(z0), z1), ACTIVE(z0)) 277.83/89.29
ACTIVE(s(z0)) → c9(S(active(z0)), ACTIVE(z0)) 277.83/89.29
ACTIVE(head(z0)) → c10(HEAD(active(z0)), ACTIVE(z0)) 277.83/89.29
ACTIVE(2nd(z0)) → c11(2ND(active(z0)), ACTIVE(z0)) 277.83/89.29
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 277.83/89.29
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 277.83/89.29
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 277.83/89.29
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 277.83/89.29
FROM(mark(z0)) → c16(FROM(z0)) 277.83/89.29
FROM(ok(z0)) → c17(FROM(z0)) 277.83/89.29
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 277.83/89.29
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 277.83/89.29
S(mark(z0)) → c20(S(z0)) 277.83/89.29
S(ok(z0)) → c21(S(z0)) 277.83/89.29
HEAD(mark(z0)) → c22(HEAD(z0)) 277.83/89.29
HEAD(ok(z0)) → c23(HEAD(z0)) 277.83/89.29
2ND(mark(z0)) → c24(2ND(z0)) 277.83/89.29
2ND(ok(z0)) → c25(2ND(z0)) 277.83/89.29
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 277.83/89.29
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 277.83/89.29
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 277.83/89.29
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 277.83/89.29
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 277.83/89.29
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 277.83/89.29
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 277.83/89.29
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 277.83/89.29
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 277.83/89.29
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 277.83/89.29
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 277.83/89.29
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 277.83/89.29
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 277.83/89.29
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 277.83/89.29
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0))
S tuples:

ACTIVE(from(z0)) → c(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0)) 277.83/89.29
ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 277.83/89.29
ACTIVE(take(s(z0), cons(z1, z2))) → c4(CONS(z1, take(z0, z2)), TAKE(z0, z2)) 277.83/89.29
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 277.83/89.29
ACTIVE(from(z0)) → c7(FROM(active(z0)), ACTIVE(z0)) 277.83/89.29
ACTIVE(cons(z0, z1)) → c8(CONS(active(z0), z1), ACTIVE(z0)) 277.83/89.29
ACTIVE(s(z0)) → c9(S(active(z0)), ACTIVE(z0)) 277.83/89.29
ACTIVE(head(z0)) → c10(HEAD(active(z0)), ACTIVE(z0)) 277.83/89.29
ACTIVE(2nd(z0)) → c11(2ND(active(z0)), ACTIVE(z0)) 277.83/89.29
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 277.83/89.29
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 277.83/89.29
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 277.83/89.29
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 277.83/89.29
FROM(mark(z0)) → c16(FROM(z0)) 277.83/89.29
FROM(ok(z0)) → c17(FROM(z0)) 277.83/89.29
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.41
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.41
S(mark(z0)) → c20(S(z0)) 278.63/89.41
S(ok(z0)) → c21(S(z0)) 278.63/89.41
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.41
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.41
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.41
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.41
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.41
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.41
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.41
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.41
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.41
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.41
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.41
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.41
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.41
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.41
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c, c2, c4, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c40, c41, c42

278.63/89.41
278.63/89.41

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

Removed 2 trailing tuple parts
278.63/89.41
278.63/89.41

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.63/89.41
active(head(cons(z0, z1))) → mark(z0) 278.63/89.41
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.63/89.41
active(take(0, z0)) → mark(nil) 278.63/89.41
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.63/89.41
active(sel(0, cons(z0, z1))) → mark(z0) 278.63/89.41
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.63/89.41
active(from(z0)) → from(active(z0)) 278.63/89.41
active(cons(z0, z1)) → cons(active(z0), z1) 278.63/89.41
active(s(z0)) → s(active(z0)) 278.63/89.41
active(head(z0)) → head(active(z0)) 278.63/89.41
active(2nd(z0)) → 2nd(active(z0)) 278.63/89.41
active(take(z0, z1)) → take(active(z0), z1) 278.63/89.41
active(take(z0, z1)) → take(z0, active(z1)) 278.63/89.41
active(sel(z0, z1)) → sel(active(z0), z1) 278.63/89.41
active(sel(z0, z1)) → sel(z0, active(z1)) 278.63/89.41
from(mark(z0)) → mark(from(z0)) 278.63/89.41
from(ok(z0)) → ok(from(z0)) 278.63/89.41
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.63/89.41
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.63/89.41
s(mark(z0)) → mark(s(z0)) 278.63/89.41
s(ok(z0)) → ok(s(z0)) 278.63/89.41
head(mark(z0)) → mark(head(z0)) 278.63/89.41
head(ok(z0)) → ok(head(z0)) 278.63/89.41
2nd(mark(z0)) → mark(2nd(z0)) 278.63/89.41
2nd(ok(z0)) → ok(2nd(z0)) 278.63/89.41
take(mark(z0), z1) → mark(take(z0, z1)) 278.63/89.41
take(z0, mark(z1)) → mark(take(z0, z1)) 278.63/89.41
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.63/89.41
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.63/89.41
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.63/89.41
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.63/89.41
proper(from(z0)) → from(proper(z0)) 278.63/89.41
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.63/89.41
proper(s(z0)) → s(proper(z0)) 278.63/89.41
proper(head(z0)) → head(proper(z0)) 278.63/89.41
proper(2nd(z0)) → 2nd(proper(z0)) 278.63/89.41
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.63/89.41
proper(0) → ok(0) 278.63/89.41
proper(nil) → ok(nil) 278.63/89.41
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.63/89.41
top(mark(z0)) → top(proper(z0)) 278.63/89.41
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.41
ACTIVE(take(s(z0), cons(z1, z2))) → c4(CONS(z1, take(z0, z2)), TAKE(z0, z2)) 278.63/89.41
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.41
ACTIVE(from(z0)) → c7(FROM(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(cons(z0, z1)) → c8(CONS(active(z0), z1), ACTIVE(z0)) 278.63/89.41
ACTIVE(s(z0)) → c9(S(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(head(z0)) → c10(HEAD(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(2nd(z0)) → c11(2ND(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.41
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.41
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.41
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.41
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.41
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.41
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.41
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.41
S(mark(z0)) → c20(S(z0)) 278.63/89.41
S(ok(z0)) → c21(S(z0)) 278.63/89.41
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.41
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.41
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.41
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.41
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.41
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.41
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.41
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.41
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.41
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.41
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.41
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.41
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.41
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.41
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(from(z0)) → c(S(z0))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.41
ACTIVE(take(s(z0), cons(z1, z2))) → c4(CONS(z1, take(z0, z2)), TAKE(z0, z2)) 278.63/89.41
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.41
ACTIVE(from(z0)) → c7(FROM(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(cons(z0, z1)) → c8(CONS(active(z0), z1), ACTIVE(z0)) 278.63/89.41
ACTIVE(s(z0)) → c9(S(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(head(z0)) → c10(HEAD(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(2nd(z0)) → c11(2ND(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.41
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.41
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.41
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.41
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.41
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.41
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.41
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.41
S(mark(z0)) → c20(S(z0)) 278.63/89.41
S(ok(z0)) → c21(S(z0)) 278.63/89.41
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.41
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.41
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.41
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.41
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.41
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.41
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.41
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.41
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.41
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.41
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.41
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.41
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.41
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.41
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(from(z0)) → c(S(z0))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c4, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c40, c41, c42, c

278.63/89.41
278.63/89.41

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

Split RHS of tuples not part of any SCC
278.63/89.41
278.63/89.41

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.63/89.41
active(head(cons(z0, z1))) → mark(z0) 278.63/89.41
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.63/89.41
active(take(0, z0)) → mark(nil) 278.63/89.41
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.63/89.41
active(sel(0, cons(z0, z1))) → mark(z0) 278.63/89.41
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.63/89.41
active(from(z0)) → from(active(z0)) 278.63/89.41
active(cons(z0, z1)) → cons(active(z0), z1) 278.63/89.41
active(s(z0)) → s(active(z0)) 278.63/89.41
active(head(z0)) → head(active(z0)) 278.63/89.41
active(2nd(z0)) → 2nd(active(z0)) 278.63/89.41
active(take(z0, z1)) → take(active(z0), z1) 278.63/89.41
active(take(z0, z1)) → take(z0, active(z1)) 278.63/89.41
active(sel(z0, z1)) → sel(active(z0), z1) 278.63/89.41
active(sel(z0, z1)) → sel(z0, active(z1)) 278.63/89.41
from(mark(z0)) → mark(from(z0)) 278.63/89.41
from(ok(z0)) → ok(from(z0)) 278.63/89.41
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.63/89.41
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.63/89.41
s(mark(z0)) → mark(s(z0)) 278.63/89.41
s(ok(z0)) → ok(s(z0)) 278.63/89.41
head(mark(z0)) → mark(head(z0)) 278.63/89.41
head(ok(z0)) → ok(head(z0)) 278.63/89.41
2nd(mark(z0)) → mark(2nd(z0)) 278.63/89.41
2nd(ok(z0)) → ok(2nd(z0)) 278.63/89.41
take(mark(z0), z1) → mark(take(z0, z1)) 278.63/89.41
take(z0, mark(z1)) → mark(take(z0, z1)) 278.63/89.41
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.63/89.41
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.63/89.41
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.63/89.41
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.63/89.41
proper(from(z0)) → from(proper(z0)) 278.63/89.41
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.63/89.41
proper(s(z0)) → s(proper(z0)) 278.63/89.41
proper(head(z0)) → head(proper(z0)) 278.63/89.41
proper(2nd(z0)) → 2nd(proper(z0)) 278.63/89.41
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.63/89.41
proper(0) → ok(0) 278.63/89.41
proper(nil) → ok(nil) 278.63/89.41
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.63/89.41
top(mark(z0)) → top(proper(z0)) 278.63/89.41
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.41
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.41
ACTIVE(from(z0)) → c7(FROM(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(cons(z0, z1)) → c8(CONS(active(z0), z1), ACTIVE(z0)) 278.63/89.41
ACTIVE(s(z0)) → c9(S(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(head(z0)) → c10(HEAD(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(2nd(z0)) → c11(2ND(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.41
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.41
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.41
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.41
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.41
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.41
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.41
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.41
S(mark(z0)) → c20(S(z0)) 278.63/89.41
S(ok(z0)) → c21(S(z0)) 278.63/89.41
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.41
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.41
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.41
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.41
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.41
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.41
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.41
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.41
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.41
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.41
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.41
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.41
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.41
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.41
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.41
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.41
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.41
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.41
ACTIVE(from(z0)) → c7(FROM(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(cons(z0, z1)) → c8(CONS(active(z0), z1), ACTIVE(z0)) 278.63/89.41
ACTIVE(s(z0)) → c9(S(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(head(z0)) → c10(HEAD(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(2nd(z0)) → c11(2ND(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.41
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.41
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.41
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.41
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.41
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.41
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.41
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.41
S(mark(z0)) → c20(S(z0)) 278.63/89.41
S(ok(z0)) → c21(S(z0)) 278.63/89.41
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.41
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.41
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.41
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.41
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.41
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.41
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.41
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.41
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.41
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.41
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.41
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.41
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.41
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.41
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.41
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.41
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.41
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.41
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c40, c41, c42, c, c1

278.63/89.41
278.63/89.41

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

Use narrowing to replace ACTIVE(from(z0)) → c7(FROM(active(z0)), ACTIVE(z0)) by

ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.41
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.41
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.41
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.41
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.41
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.41
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.41
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.41
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.41
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.41
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.41
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.41
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.41
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.41
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.41
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
278.63/89.41
278.63/89.41

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.63/89.41
active(head(cons(z0, z1))) → mark(z0) 278.63/89.41
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.63/89.41
active(take(0, z0)) → mark(nil) 278.63/89.41
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.63/89.41
active(sel(0, cons(z0, z1))) → mark(z0) 278.63/89.41
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.63/89.41
active(from(z0)) → from(active(z0)) 278.63/89.41
active(cons(z0, z1)) → cons(active(z0), z1) 278.63/89.41
active(s(z0)) → s(active(z0)) 278.63/89.41
active(head(z0)) → head(active(z0)) 278.63/89.41
active(2nd(z0)) → 2nd(active(z0)) 278.63/89.41
active(take(z0, z1)) → take(active(z0), z1) 278.63/89.41
active(take(z0, z1)) → take(z0, active(z1)) 278.63/89.41
active(sel(z0, z1)) → sel(active(z0), z1) 278.63/89.41
active(sel(z0, z1)) → sel(z0, active(z1)) 278.63/89.41
from(mark(z0)) → mark(from(z0)) 278.63/89.41
from(ok(z0)) → ok(from(z0)) 278.63/89.41
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.63/89.41
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.63/89.41
s(mark(z0)) → mark(s(z0)) 278.63/89.41
s(ok(z0)) → ok(s(z0)) 278.63/89.41
head(mark(z0)) → mark(head(z0)) 278.63/89.41
head(ok(z0)) → ok(head(z0)) 278.63/89.41
2nd(mark(z0)) → mark(2nd(z0)) 278.63/89.41
2nd(ok(z0)) → ok(2nd(z0)) 278.63/89.41
take(mark(z0), z1) → mark(take(z0, z1)) 278.63/89.41
take(z0, mark(z1)) → mark(take(z0, z1)) 278.63/89.41
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.63/89.41
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.63/89.41
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.63/89.41
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.63/89.41
proper(from(z0)) → from(proper(z0)) 278.63/89.41
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.63/89.42
proper(s(z0)) → s(proper(z0)) 278.63/89.42
proper(head(z0)) → head(proper(z0)) 278.63/89.42
proper(2nd(z0)) → 2nd(proper(z0)) 278.63/89.42
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.63/89.42
proper(0) → ok(0) 278.63/89.42
proper(nil) → ok(nil) 278.63/89.42
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.63/89.42
top(mark(z0)) → top(proper(z0)) 278.63/89.42
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.42
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.42
ACTIVE(cons(z0, z1)) → c8(CONS(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(s(z0)) → c9(S(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(head(z0)) → c10(HEAD(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(2nd(z0)) → c11(2ND(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.42
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.42
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.42
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.42
S(mark(z0)) → c20(S(z0)) 278.63/89.42
S(ok(z0)) → c21(S(z0)) 278.63/89.42
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.42
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.42
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.42
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.42
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.42
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.42
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.42
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.42
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.42
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.42
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.42
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.42
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.42
ACTIVE(cons(z0, z1)) → c8(CONS(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(s(z0)) → c9(S(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(head(z0)) → c10(HEAD(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(2nd(z0)) → c11(2ND(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.42
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.42
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.42
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.42
S(mark(z0)) → c20(S(z0)) 278.63/89.42
S(ok(z0)) → c21(S(z0)) 278.63/89.42
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.42
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.42
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.42
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.42
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.42
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.42
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.42
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.42
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.42
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.42
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.42
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c40, c41, c42, c, c1, c7

278.63/89.42
278.63/89.42

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

Use narrowing to replace ACTIVE(cons(z0, z1)) → c8(CONS(active(z0), z1), ACTIVE(z0)) by

ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
278.63/89.42
278.63/89.42

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.63/89.42
active(head(cons(z0, z1))) → mark(z0) 278.63/89.42
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.63/89.42
active(take(0, z0)) → mark(nil) 278.63/89.42
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.63/89.42
active(sel(0, cons(z0, z1))) → mark(z0) 278.63/89.42
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.63/89.42
active(from(z0)) → from(active(z0)) 278.63/89.42
active(cons(z0, z1)) → cons(active(z0), z1) 278.63/89.42
active(s(z0)) → s(active(z0)) 278.63/89.42
active(head(z0)) → head(active(z0)) 278.63/89.42
active(2nd(z0)) → 2nd(active(z0)) 278.63/89.42
active(take(z0, z1)) → take(active(z0), z1) 278.63/89.42
active(take(z0, z1)) → take(z0, active(z1)) 278.63/89.42
active(sel(z0, z1)) → sel(active(z0), z1) 278.63/89.42
active(sel(z0, z1)) → sel(z0, active(z1)) 278.63/89.42
from(mark(z0)) → mark(from(z0)) 278.63/89.42
from(ok(z0)) → ok(from(z0)) 278.63/89.42
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.63/89.42
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.63/89.42
s(mark(z0)) → mark(s(z0)) 278.63/89.42
s(ok(z0)) → ok(s(z0)) 278.63/89.42
head(mark(z0)) → mark(head(z0)) 278.63/89.42
head(ok(z0)) → ok(head(z0)) 278.63/89.42
2nd(mark(z0)) → mark(2nd(z0)) 278.63/89.42
2nd(ok(z0)) → ok(2nd(z0)) 278.63/89.42
take(mark(z0), z1) → mark(take(z0, z1)) 278.63/89.42
take(z0, mark(z1)) → mark(take(z0, z1)) 278.63/89.42
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.63/89.42
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.63/89.42
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.63/89.42
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.63/89.42
proper(from(z0)) → from(proper(z0)) 278.63/89.42
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.63/89.42
proper(s(z0)) → s(proper(z0)) 278.63/89.42
proper(head(z0)) → head(proper(z0)) 278.63/89.42
proper(2nd(z0)) → 2nd(proper(z0)) 278.63/89.42
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.63/89.42
proper(0) → ok(0) 278.63/89.42
proper(nil) → ok(nil) 278.63/89.42
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.63/89.42
top(mark(z0)) → top(proper(z0)) 278.63/89.42
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.42
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.42
ACTIVE(s(z0)) → c9(S(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(head(z0)) → c10(HEAD(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(2nd(z0)) → c11(2ND(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.42
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.42
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.42
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.42
S(mark(z0)) → c20(S(z0)) 278.63/89.42
S(ok(z0)) → c21(S(z0)) 278.63/89.42
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.42
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.42
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.42
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.42
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.42
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.42
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.42
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.42
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.42
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.42
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.42
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.42
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.42
ACTIVE(s(z0)) → c9(S(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(head(z0)) → c10(HEAD(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(2nd(z0)) → c11(2ND(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.42
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.42
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.42
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.42
S(mark(z0)) → c20(S(z0)) 278.63/89.42
S(ok(z0)) → c21(S(z0)) 278.63/89.42
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.42
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.42
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.42
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.42
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.42
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.42
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.42
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.42
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.42
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.42
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.42
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c40, c41, c42, c, c1, c7, c8

278.63/89.42
278.63/89.42

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

Use narrowing to replace ACTIVE(s(z0)) → c9(S(active(z0)), ACTIVE(z0)) by

ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
278.63/89.42
278.63/89.42

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.63/89.42
active(head(cons(z0, z1))) → mark(z0) 278.63/89.42
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.63/89.42
active(take(0, z0)) → mark(nil) 278.63/89.42
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.63/89.42
active(sel(0, cons(z0, z1))) → mark(z0) 278.63/89.42
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.63/89.42
active(from(z0)) → from(active(z0)) 278.63/89.42
active(cons(z0, z1)) → cons(active(z0), z1) 278.63/89.42
active(s(z0)) → s(active(z0)) 278.63/89.42
active(head(z0)) → head(active(z0)) 278.63/89.42
active(2nd(z0)) → 2nd(active(z0)) 278.63/89.42
active(take(z0, z1)) → take(active(z0), z1) 278.63/89.42
active(take(z0, z1)) → take(z0, active(z1)) 278.63/89.42
active(sel(z0, z1)) → sel(active(z0), z1) 278.63/89.42
active(sel(z0, z1)) → sel(z0, active(z1)) 278.63/89.42
from(mark(z0)) → mark(from(z0)) 278.63/89.42
from(ok(z0)) → ok(from(z0)) 278.63/89.42
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.63/89.42
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.63/89.42
s(mark(z0)) → mark(s(z0)) 278.63/89.42
s(ok(z0)) → ok(s(z0)) 278.63/89.42
head(mark(z0)) → mark(head(z0)) 278.63/89.42
head(ok(z0)) → ok(head(z0)) 278.63/89.42
2nd(mark(z0)) → mark(2nd(z0)) 278.63/89.42
2nd(ok(z0)) → ok(2nd(z0)) 278.63/89.42
take(mark(z0), z1) → mark(take(z0, z1)) 278.63/89.42
take(z0, mark(z1)) → mark(take(z0, z1)) 278.63/89.42
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.63/89.42
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.63/89.42
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.63/89.42
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.63/89.42
proper(from(z0)) → from(proper(z0)) 278.63/89.42
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.63/89.42
proper(s(z0)) → s(proper(z0)) 278.63/89.42
proper(head(z0)) → head(proper(z0)) 278.63/89.42
proper(2nd(z0)) → 2nd(proper(z0)) 278.63/89.42
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.63/89.42
proper(0) → ok(0) 278.63/89.42
proper(nil) → ok(nil) 278.63/89.42
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.63/89.42
top(mark(z0)) → top(proper(z0)) 278.63/89.42
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.42
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.42
ACTIVE(head(z0)) → c10(HEAD(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(2nd(z0)) → c11(2ND(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.42
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.42
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.42
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.42
S(mark(z0)) → c20(S(z0)) 278.63/89.42
S(ok(z0)) → c21(S(z0)) 278.63/89.42
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.42
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.42
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.42
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.42
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.42
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.42
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.42
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.42
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.42
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.42
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.42
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.42
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.42
ACTIVE(head(z0)) → c10(HEAD(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(2nd(z0)) → c11(2ND(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.42
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.42
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.42
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.42
S(mark(z0)) → c20(S(z0)) 278.63/89.42
S(ok(z0)) → c21(S(z0)) 278.63/89.42
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.42
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.42
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.42
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.42
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.42
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.42
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.42
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.42
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.42
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.42
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.42
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c40, c41, c42, c, c1, c7, c8, c9

278.63/89.42
278.63/89.42

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

Use narrowing to replace ACTIVE(head(z0)) → c10(HEAD(active(z0)), ACTIVE(z0)) by

ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
278.63/89.42
278.63/89.42

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.63/89.42
active(head(cons(z0, z1))) → mark(z0) 278.63/89.42
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.63/89.42
active(take(0, z0)) → mark(nil) 278.63/89.42
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.63/89.42
active(sel(0, cons(z0, z1))) → mark(z0) 278.63/89.42
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.63/89.42
active(from(z0)) → from(active(z0)) 278.63/89.42
active(cons(z0, z1)) → cons(active(z0), z1) 278.63/89.42
active(s(z0)) → s(active(z0)) 278.63/89.42
active(head(z0)) → head(active(z0)) 278.63/89.42
active(2nd(z0)) → 2nd(active(z0)) 278.63/89.42
active(take(z0, z1)) → take(active(z0), z1) 278.63/89.42
active(take(z0, z1)) → take(z0, active(z1)) 278.63/89.42
active(sel(z0, z1)) → sel(active(z0), z1) 278.63/89.42
active(sel(z0, z1)) → sel(z0, active(z1)) 278.63/89.42
from(mark(z0)) → mark(from(z0)) 278.63/89.42
from(ok(z0)) → ok(from(z0)) 278.63/89.42
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.63/89.42
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.63/89.42
s(mark(z0)) → mark(s(z0)) 278.63/89.42
s(ok(z0)) → ok(s(z0)) 278.63/89.42
head(mark(z0)) → mark(head(z0)) 278.63/89.42
head(ok(z0)) → ok(head(z0)) 278.63/89.42
2nd(mark(z0)) → mark(2nd(z0)) 278.63/89.42
2nd(ok(z0)) → ok(2nd(z0)) 278.63/89.42
take(mark(z0), z1) → mark(take(z0, z1)) 278.63/89.42
take(z0, mark(z1)) → mark(take(z0, z1)) 278.63/89.42
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.63/89.42
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.63/89.42
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.63/89.42
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.63/89.42
proper(from(z0)) → from(proper(z0)) 278.63/89.42
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.63/89.42
proper(s(z0)) → s(proper(z0)) 278.63/89.42
proper(head(z0)) → head(proper(z0)) 278.63/89.42
proper(2nd(z0)) → 2nd(proper(z0)) 278.63/89.42
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.63/89.42
proper(0) → ok(0) 278.63/89.42
proper(nil) → ok(nil) 278.63/89.42
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.63/89.42
top(mark(z0)) → top(proper(z0)) 278.63/89.42
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.42
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.42
ACTIVE(2nd(z0)) → c11(2ND(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.42
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.42
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.42
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.42
S(mark(z0)) → c20(S(z0)) 278.63/89.42
S(ok(z0)) → c21(S(z0)) 278.63/89.42
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.42
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.42
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.42
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.42
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.42
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.42
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.42
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.42
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.42
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.42
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.42
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.42
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.42
ACTIVE(2nd(z0)) → c11(2ND(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.42
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.42
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.42
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.42
S(mark(z0)) → c20(S(z0)) 278.63/89.42
S(ok(z0)) → c21(S(z0)) 278.63/89.42
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.42
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.42
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.42
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.42
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.42
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.42
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.42
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.42
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.42
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.42
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.42
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c40, c41, c42, c, c1, c7, c8, c9, c10

278.63/89.42
278.63/89.42

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

Use narrowing to replace ACTIVE(2nd(z0)) → c11(2ND(active(z0)), ACTIVE(z0)) by

ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
278.63/89.42
278.63/89.42

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.63/89.42
active(head(cons(z0, z1))) → mark(z0) 278.63/89.42
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.63/89.42
active(take(0, z0)) → mark(nil) 278.63/89.42
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.63/89.42
active(sel(0, cons(z0, z1))) → mark(z0) 278.63/89.42
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.63/89.42
active(from(z0)) → from(active(z0)) 278.63/89.42
active(cons(z0, z1)) → cons(active(z0), z1) 278.63/89.42
active(s(z0)) → s(active(z0)) 278.63/89.42
active(head(z0)) → head(active(z0)) 278.63/89.42
active(2nd(z0)) → 2nd(active(z0)) 278.63/89.42
active(take(z0, z1)) → take(active(z0), z1) 278.63/89.42
active(take(z0, z1)) → take(z0, active(z1)) 278.63/89.42
active(sel(z0, z1)) → sel(active(z0), z1) 278.63/89.42
active(sel(z0, z1)) → sel(z0, active(z1)) 278.63/89.42
from(mark(z0)) → mark(from(z0)) 278.63/89.42
from(ok(z0)) → ok(from(z0)) 278.63/89.42
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.63/89.42
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.63/89.42
s(mark(z0)) → mark(s(z0)) 278.63/89.42
s(ok(z0)) → ok(s(z0)) 278.63/89.42
head(mark(z0)) → mark(head(z0)) 278.63/89.42
head(ok(z0)) → ok(head(z0)) 278.63/89.42
2nd(mark(z0)) → mark(2nd(z0)) 278.63/89.42
2nd(ok(z0)) → ok(2nd(z0)) 278.63/89.42
take(mark(z0), z1) → mark(take(z0, z1)) 278.63/89.42
take(z0, mark(z1)) → mark(take(z0, z1)) 278.63/89.42
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.63/89.42
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.63/89.42
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.63/89.42
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.63/89.42
proper(from(z0)) → from(proper(z0)) 278.63/89.42
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.63/89.42
proper(s(z0)) → s(proper(z0)) 278.63/89.42
proper(head(z0)) → head(proper(z0)) 278.63/89.42
proper(2nd(z0)) → 2nd(proper(z0)) 278.63/89.42
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.63/89.42
proper(0) → ok(0) 278.63/89.42
proper(nil) → ok(nil) 278.63/89.42
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.63/89.42
top(mark(z0)) → top(proper(z0)) 278.63/89.42
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.42
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.42
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.42
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.42
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.42
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.42
S(mark(z0)) → c20(S(z0)) 278.63/89.42
S(ok(z0)) → c21(S(z0)) 278.63/89.42
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.42
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.42
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.42
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.42
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.42
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.42
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.42
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.42
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.42
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.42
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.42
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.42
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.42
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.42
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.42
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.42
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.42
S(mark(z0)) → c20(S(z0)) 278.63/89.42
S(ok(z0)) → c21(S(z0)) 278.63/89.42
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.42
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.42
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.42
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.42
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.42
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.42
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.42
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.42
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.42
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.42
PROPER(from(z0)) → c32(FROM(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.42
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c40, c41, c42, c, c1, c7, c8, c9, c10, c11

278.63/89.42
278.63/89.42

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

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

PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.63/89.42
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.42
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.63/89.42
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.63/89.42
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.42
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.42
PROPER(from(0)) → c32(FROM(ok(0)), PROPER(0)) 278.63/89.42
PROPER(from(nil)) → c32(FROM(ok(nil)), PROPER(nil)) 278.63/89.42
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
278.63/89.42
278.63/89.42

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.63/89.42
active(head(cons(z0, z1))) → mark(z0) 278.63/89.42
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.63/89.42
active(take(0, z0)) → mark(nil) 278.63/89.42
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.63/89.42
active(sel(0, cons(z0, z1))) → mark(z0) 278.63/89.42
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.63/89.42
active(from(z0)) → from(active(z0)) 278.63/89.42
active(cons(z0, z1)) → cons(active(z0), z1) 278.63/89.42
active(s(z0)) → s(active(z0)) 278.63/89.42
active(head(z0)) → head(active(z0)) 278.63/89.42
active(2nd(z0)) → 2nd(active(z0)) 278.63/89.42
active(take(z0, z1)) → take(active(z0), z1) 278.63/89.42
active(take(z0, z1)) → take(z0, active(z1)) 278.63/89.42
active(sel(z0, z1)) → sel(active(z0), z1) 278.63/89.42
active(sel(z0, z1)) → sel(z0, active(z1)) 278.63/89.42
from(mark(z0)) → mark(from(z0)) 278.63/89.42
from(ok(z0)) → ok(from(z0)) 278.63/89.42
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.63/89.42
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.63/89.42
s(mark(z0)) → mark(s(z0)) 278.63/89.42
s(ok(z0)) → ok(s(z0)) 278.63/89.42
head(mark(z0)) → mark(head(z0)) 278.63/89.42
head(ok(z0)) → ok(head(z0)) 278.63/89.42
2nd(mark(z0)) → mark(2nd(z0)) 278.63/89.42
2nd(ok(z0)) → ok(2nd(z0)) 278.63/89.42
take(mark(z0), z1) → mark(take(z0, z1)) 278.63/89.42
take(z0, mark(z1)) → mark(take(z0, z1)) 278.63/89.42
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.63/89.42
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.63/89.42
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.63/89.42
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.63/89.42
proper(from(z0)) → from(proper(z0)) 278.63/89.42
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.63/89.42
proper(s(z0)) → s(proper(z0)) 278.63/89.42
proper(head(z0)) → head(proper(z0)) 278.63/89.42
proper(2nd(z0)) → 2nd(proper(z0)) 278.63/89.42
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.63/89.42
proper(0) → ok(0) 278.63/89.42
proper(nil) → ok(nil) 278.63/89.42
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.63/89.42
top(mark(z0)) → top(proper(z0)) 278.63/89.42
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.42
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.42
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.42
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.42
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.42
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.42
S(mark(z0)) → c20(S(z0)) 278.63/89.42
S(ok(z0)) → c21(S(z0)) 278.63/89.42
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.42
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.42
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.42
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.42
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.42
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.42
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.42
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.42
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.42
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.42
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.42
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.63/89.42
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.42
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.63/89.42
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.63/89.42
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.42
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.42
PROPER(from(0)) → c32(FROM(ok(0)), PROPER(0)) 278.63/89.42
PROPER(from(nil)) → c32(FROM(ok(nil)), PROPER(nil)) 278.63/89.42
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.42
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.42
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.42
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.42
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.42
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.42
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.42
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.42
S(mark(z0)) → c20(S(z0)) 278.63/89.42
S(ok(z0)) → c21(S(z0)) 278.63/89.42
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.42
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.42
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.42
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.42
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.42
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.42
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.42
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.42
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.42
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.42
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.42
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.42
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.42
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.42
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.42
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.42
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.42
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.42
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.42
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.42
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.42
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.42
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.42
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.42
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.43
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.43
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.43
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.43
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.43
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.43
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.43
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.43
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.43
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.43
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.43
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.43
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.43
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.43
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.43
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.43
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.43
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.43
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.43
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.43
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.43
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.43
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.43
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.43
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.43
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.43
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.43
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.43
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.43
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.43
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.43
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.43
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.43
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.43
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.43
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.43
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.63/89.43
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.43
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.63/89.43
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.63/89.43
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.43
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.43
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.43
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.43
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.43
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.43
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.43
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.43
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.43
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.43
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.43
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.43
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.63/89.43
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.43
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.63/89.43
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.63/89.43
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.43
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.43
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.43
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.43
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.43
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.63/89.43
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.43
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.63/89.43
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.63/89.43
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.43
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.43
PROPER(from(0)) → c32(FROM(ok(0)), PROPER(0)) 278.63/89.43
PROPER(from(nil)) → c32(FROM(ok(nil)), PROPER(nil)) 278.63/89.43
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c33, c34, c35, c36, c37, c40, c41, c42, c, c1, c7, c8, c9, c10, c11, c32

278.63/89.43
278.63/89.43

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

Removed 2 trailing tuple parts
278.63/89.43
278.63/89.43

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.63/89.43
active(head(cons(z0, z1))) → mark(z0) 278.63/89.43
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.63/89.43
active(take(0, z0)) → mark(nil) 278.63/89.43
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.63/89.43
active(sel(0, cons(z0, z1))) → mark(z0) 278.63/89.43
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.63/89.43
active(from(z0)) → from(active(z0)) 278.63/89.43
active(cons(z0, z1)) → cons(active(z0), z1) 278.63/89.43
active(s(z0)) → s(active(z0)) 278.63/89.43
active(head(z0)) → head(active(z0)) 278.63/89.43
active(2nd(z0)) → 2nd(active(z0)) 278.63/89.43
active(take(z0, z1)) → take(active(z0), z1) 278.63/89.43
active(take(z0, z1)) → take(z0, active(z1)) 278.63/89.43
active(sel(z0, z1)) → sel(active(z0), z1) 278.63/89.43
active(sel(z0, z1)) → sel(z0, active(z1)) 278.63/89.43
from(mark(z0)) → mark(from(z0)) 278.63/89.43
from(ok(z0)) → ok(from(z0)) 278.63/89.43
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.63/89.43
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.63/89.43
s(mark(z0)) → mark(s(z0)) 278.63/89.43
s(ok(z0)) → ok(s(z0)) 278.63/89.43
head(mark(z0)) → mark(head(z0)) 278.63/89.43
head(ok(z0)) → ok(head(z0)) 278.63/89.43
2nd(mark(z0)) → mark(2nd(z0)) 278.63/89.43
2nd(ok(z0)) → ok(2nd(z0)) 278.63/89.43
take(mark(z0), z1) → mark(take(z0, z1)) 278.63/89.43
take(z0, mark(z1)) → mark(take(z0, z1)) 278.63/89.43
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.63/89.43
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.63/89.43
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.63/89.43
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.63/89.43
proper(from(z0)) → from(proper(z0)) 278.63/89.43
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.63/89.43
proper(s(z0)) → s(proper(z0)) 278.63/89.43
proper(head(z0)) → head(proper(z0)) 278.63/89.43
proper(2nd(z0)) → 2nd(proper(z0)) 278.63/89.43
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.63/89.43
proper(0) → ok(0) 278.63/89.43
proper(nil) → ok(nil) 278.63/89.43
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.63/89.43
top(mark(z0)) → top(proper(z0)) 278.63/89.43
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.43
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.44
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.44
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.44
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.44
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.44
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.44
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.44
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.44
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.44
S(mark(z0)) → c20(S(z0)) 278.63/89.44
S(ok(z0)) → c21(S(z0)) 278.63/89.44
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.44
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.44
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.44
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.44
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.44
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.44
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.44
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.44
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.44
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.44
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.44
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.44
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.44
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.44
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.44
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.44
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.44
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.44
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.44
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.44
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.44
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.44
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.44
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.44
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.44
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.44
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.44
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.44
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.44
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.44
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.44
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.44
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.44
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.44
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.44
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.44
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.44
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.44
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.44
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.44
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.44
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.44
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.44
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.44
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.44
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.44
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.44
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.44
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.44
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.44
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.44
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.44
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.44
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.44
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.44
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.44
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.44
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.44
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.44
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.44
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.44
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.44
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.44
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.44
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.44
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.44
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.44
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.44
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.44
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.44
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.44
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.44
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.44
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.44
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.44
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.44
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.63/89.44
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.44
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.63/89.44
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.63/89.44
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.44
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.44
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.44
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.44
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.44
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.44
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.44
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.44
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.44
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.44
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.44
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.44
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.63/89.44
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.44
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.63/89.44
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.63/89.44
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.44
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.44
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.44
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.44
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.44
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.63/89.44
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.44
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.63/89.44
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.63/89.44
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.44
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.44
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.63/89.44
PROPER(from(0)) → c32(FROM(ok(0))) 278.63/89.44
PROPER(from(nil)) → c32(FROM(ok(nil)))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.44
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.44
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.44
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.44
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.44
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.44
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.44
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.44
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.44
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.44
S(mark(z0)) → c20(S(z0)) 278.63/89.44
S(ok(z0)) → c21(S(z0)) 278.63/89.44
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.44
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.44
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.44
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.44
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.44
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.44
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.44
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.44
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.44
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.44
PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.44
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.44
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.44
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.44
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.44
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.44
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.44
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.44
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.44
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.44
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.44
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.44
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.44
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.44
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.44
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.44
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.44
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.44
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.44
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.44
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.44
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.44
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.49
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.63/89.49
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.49
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.63/89.49
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.63/89.49
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.49
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.49
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.63/89.49
PROPER(from(0)) → c32(FROM(ok(0))) 278.63/89.49
PROPER(from(nil)) → c32(FROM(ok(nil)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c33, c34, c35, c36, c37, c40, c41, c42, c, c1, c7, c8, c9, c10, c11, c32, c32

278.63/89.49
278.63/89.49

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

Use narrowing to replace PROPER(cons(z0, z1)) → c33(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.63/89.49
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.63/89.49
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.63/89.49
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.63/89.49
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.63/89.49
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.63/89.49
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 278.63/89.49
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 278.63/89.49
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.63/89.49
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.63/89.49
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.63/89.49
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.63/89.49
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.63/89.49
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.63/89.49
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.63/89.49
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 278.63/89.49
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 278.63/89.49
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
278.63/89.49
278.63/89.49

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.63/89.49
active(head(cons(z0, z1))) → mark(z0) 278.63/89.49
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.63/89.49
active(take(0, z0)) → mark(nil) 278.63/89.49
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.63/89.49
active(sel(0, cons(z0, z1))) → mark(z0) 278.63/89.49
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.63/89.49
active(from(z0)) → from(active(z0)) 278.63/89.49
active(cons(z0, z1)) → cons(active(z0), z1) 278.63/89.49
active(s(z0)) → s(active(z0)) 278.63/89.49
active(head(z0)) → head(active(z0)) 278.63/89.49
active(2nd(z0)) → 2nd(active(z0)) 278.63/89.49
active(take(z0, z1)) → take(active(z0), z1) 278.63/89.49
active(take(z0, z1)) → take(z0, active(z1)) 278.63/89.49
active(sel(z0, z1)) → sel(active(z0), z1) 278.63/89.49
active(sel(z0, z1)) → sel(z0, active(z1)) 278.63/89.49
from(mark(z0)) → mark(from(z0)) 278.63/89.49
from(ok(z0)) → ok(from(z0)) 278.63/89.49
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.63/89.49
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.63/89.49
s(mark(z0)) → mark(s(z0)) 278.63/89.49
s(ok(z0)) → ok(s(z0)) 278.63/89.49
head(mark(z0)) → mark(head(z0)) 278.63/89.49
head(ok(z0)) → ok(head(z0)) 278.63/89.49
2nd(mark(z0)) → mark(2nd(z0)) 278.63/89.49
2nd(ok(z0)) → ok(2nd(z0)) 278.63/89.49
take(mark(z0), z1) → mark(take(z0, z1)) 278.63/89.49
take(z0, mark(z1)) → mark(take(z0, z1)) 278.63/89.49
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.63/89.49
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.63/89.49
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.63/89.49
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.63/89.49
proper(from(z0)) → from(proper(z0)) 278.63/89.49
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.63/89.49
proper(s(z0)) → s(proper(z0)) 278.63/89.49
proper(head(z0)) → head(proper(z0)) 278.63/89.49
proper(2nd(z0)) → 2nd(proper(z0)) 278.63/89.49
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.63/89.49
proper(0) → ok(0) 278.63/89.49
proper(nil) → ok(nil) 278.63/89.49
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.63/89.49
top(mark(z0)) → top(proper(z0)) 278.63/89.49
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.49
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.49
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.49
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.49
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.49
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.49
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.49
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.49
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.49
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.49
S(mark(z0)) → c20(S(z0)) 278.63/89.49
S(ok(z0)) → c21(S(z0)) 278.63/89.49
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.49
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.49
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.49
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.49
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.49
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.49
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.49
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.49
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.49
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.49
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.49
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.49
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.49
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.49
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.49
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.49
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.49
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.49
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.49
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.49
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.49
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.63/89.49
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.49
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.63/89.49
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.63/89.49
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.49
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.49
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.63/89.49
PROPER(from(0)) → c32(FROM(ok(0))) 278.63/89.49
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.63/89.49
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.63/89.49
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.63/89.49
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.63/89.49
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.63/89.49
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.63/89.49
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.63/89.49
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 278.63/89.49
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 278.63/89.49
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.63/89.49
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.63/89.49
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.63/89.49
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.63/89.49
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.63/89.49
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.63/89.49
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.63/89.49
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 278.63/89.49
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 278.63/89.49
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.49
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.49
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.49
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.49
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.49
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.49
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.49
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.49
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.49
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.49
S(mark(z0)) → c20(S(z0)) 278.63/89.49
S(ok(z0)) → c21(S(z0)) 278.63/89.49
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.49
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.49
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.49
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.49
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.49
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.49
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.49
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.49
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.49
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.49
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.49
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.49
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.49
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.49
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.49
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.49
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.49
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.49
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.49
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.49
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.49
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.63/89.49
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.49
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.63/89.49
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.63/89.49
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.49
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.49
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.63/89.49
PROPER(from(0)) → c32(FROM(ok(0))) 278.63/89.49
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.63/89.49
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.63/89.49
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.63/89.49
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.63/89.49
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.63/89.49
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.63/89.49
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.63/89.49
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 278.63/89.49
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 278.63/89.49
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.63/89.49
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.63/89.49
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.63/89.49
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.63/89.49
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.63/89.49
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.63/89.49
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.63/89.49
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 278.63/89.49
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 278.63/89.49
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c34, c35, c36, c37, c40, c41, c42, c, c1, c7, c8, c9, c10, c11, c32, c32, c33

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278.63/89.49

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

Removed 4 trailing tuple parts
278.63/89.49
278.63/89.49

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.63/89.49
active(head(cons(z0, z1))) → mark(z0) 278.63/89.49
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.63/89.49
active(take(0, z0)) → mark(nil) 278.63/89.49
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.63/89.49
active(sel(0, cons(z0, z1))) → mark(z0) 278.63/89.49
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.63/89.49
active(from(z0)) → from(active(z0)) 278.63/89.49
active(cons(z0, z1)) → cons(active(z0), z1) 278.63/89.49
active(s(z0)) → s(active(z0)) 278.63/89.49
active(head(z0)) → head(active(z0)) 278.63/89.49
active(2nd(z0)) → 2nd(active(z0)) 278.63/89.49
active(take(z0, z1)) → take(active(z0), z1) 278.63/89.49
active(take(z0, z1)) → take(z0, active(z1)) 278.63/89.49
active(sel(z0, z1)) → sel(active(z0), z1) 278.63/89.49
active(sel(z0, z1)) → sel(z0, active(z1)) 278.63/89.49
from(mark(z0)) → mark(from(z0)) 278.63/89.49
from(ok(z0)) → ok(from(z0)) 278.63/89.49
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.63/89.49
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.63/89.49
s(mark(z0)) → mark(s(z0)) 278.63/89.49
s(ok(z0)) → ok(s(z0)) 278.63/89.49
head(mark(z0)) → mark(head(z0)) 278.63/89.49
head(ok(z0)) → ok(head(z0)) 278.63/89.49
2nd(mark(z0)) → mark(2nd(z0)) 278.63/89.49
2nd(ok(z0)) → ok(2nd(z0)) 278.63/89.49
take(mark(z0), z1) → mark(take(z0, z1)) 278.63/89.49
take(z0, mark(z1)) → mark(take(z0, z1)) 278.63/89.49
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.63/89.49
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.63/89.49
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.63/89.49
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.63/89.49
proper(from(z0)) → from(proper(z0)) 278.63/89.49
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.63/89.49
proper(s(z0)) → s(proper(z0)) 278.63/89.49
proper(head(z0)) → head(proper(z0)) 278.63/89.49
proper(2nd(z0)) → 2nd(proper(z0)) 278.63/89.49
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.63/89.49
proper(0) → ok(0) 278.63/89.49
proper(nil) → ok(nil) 278.63/89.49
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.63/89.49
top(mark(z0)) → top(proper(z0)) 278.63/89.49
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.49
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.49
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.49
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.49
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.49
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.49
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.49
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.49
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.49
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.49
S(mark(z0)) → c20(S(z0)) 278.63/89.49
S(ok(z0)) → c21(S(z0)) 278.63/89.49
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.49
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.49
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.49
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.49
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.49
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.49
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.49
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.49
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.49
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.49
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.49
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.49
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.49
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.49
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.49
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.49
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.49
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.49
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.49
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.49
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.49
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.63/89.49
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.63/89.49
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.49
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.49
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.49
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.49
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.49
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.49
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.49
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.49
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.49
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.63/89.50
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.63/89.50
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.63/89.50
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.50
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.50
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.63/89.50
PROPER(from(0)) → c32(FROM(ok(0))) 278.63/89.50
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.63/89.50
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.63/89.50
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.63/89.50
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.63/89.50
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.63/89.50
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.63/89.50
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.63/89.50
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.63/89.50
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.63/89.50
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.63/89.50
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.50
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.50
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.50
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.50
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.50
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.50
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.50
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.50
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.50
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.50
S(mark(z0)) → c20(S(z0)) 278.63/89.50
S(ok(z0)) → c21(S(z0)) 278.63/89.50
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.50
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.50
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.50
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.50
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.50
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.50
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.50
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.50
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.50
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.50
PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) 278.63/89.50
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.50
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.50
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.50
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.50
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.50
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.50
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.50
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.50
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.50
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.63/89.50
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.63/89.50
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.63/89.50
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.50
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.50
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.63/89.50
PROPER(from(0)) → c32(FROM(ok(0))) 278.63/89.50
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.63/89.50
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.63/89.50
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.63/89.50
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.63/89.50
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.63/89.50
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.63/89.50
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.63/89.50
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.63/89.50
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.63/89.50
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.63/89.50
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c34, c35, c36, c37, c40, c41, c42, c, c1, c7, c8, c9, c10, c11, c32, c32, c33, c33

278.63/89.50
278.63/89.50

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

Use narrowing to replace PROPER(s(z0)) → c34(S(proper(z0)), PROPER(z0)) by

PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.63/89.50
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.63/89.50
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.63/89.50
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.50
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.50
PROPER(s(0)) → c34(S(ok(0)), PROPER(0)) 278.63/89.50
PROPER(s(nil)) → c34(S(ok(nil)), PROPER(nil)) 278.63/89.50
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
278.63/89.50
278.63/89.50

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.63/89.50
active(head(cons(z0, z1))) → mark(z0) 278.63/89.50
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.63/89.50
active(take(0, z0)) → mark(nil) 278.63/89.50
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.63/89.50
active(sel(0, cons(z0, z1))) → mark(z0) 278.63/89.50
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.63/89.50
active(from(z0)) → from(active(z0)) 278.63/89.50
active(cons(z0, z1)) → cons(active(z0), z1) 278.63/89.50
active(s(z0)) → s(active(z0)) 278.63/89.50
active(head(z0)) → head(active(z0)) 278.63/89.50
active(2nd(z0)) → 2nd(active(z0)) 278.63/89.50
active(take(z0, z1)) → take(active(z0), z1) 278.63/89.50
active(take(z0, z1)) → take(z0, active(z1)) 278.63/89.50
active(sel(z0, z1)) → sel(active(z0), z1) 278.63/89.50
active(sel(z0, z1)) → sel(z0, active(z1)) 278.63/89.50
from(mark(z0)) → mark(from(z0)) 278.63/89.50
from(ok(z0)) → ok(from(z0)) 278.63/89.50
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.63/89.50
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.63/89.50
s(mark(z0)) → mark(s(z0)) 278.63/89.50
s(ok(z0)) → ok(s(z0)) 278.63/89.50
head(mark(z0)) → mark(head(z0)) 278.63/89.50
head(ok(z0)) → ok(head(z0)) 278.63/89.50
2nd(mark(z0)) → mark(2nd(z0)) 278.63/89.50
2nd(ok(z0)) → ok(2nd(z0)) 278.63/89.50
take(mark(z0), z1) → mark(take(z0, z1)) 278.63/89.50
take(z0, mark(z1)) → mark(take(z0, z1)) 278.63/89.50
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.63/89.50
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.63/89.50
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.63/89.50
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.63/89.50
proper(from(z0)) → from(proper(z0)) 278.63/89.50
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.63/89.50
proper(s(z0)) → s(proper(z0)) 278.63/89.50
proper(head(z0)) → head(proper(z0)) 278.63/89.50
proper(2nd(z0)) → 2nd(proper(z0)) 278.63/89.50
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.63/89.50
proper(0) → ok(0) 278.63/89.50
proper(nil) → ok(nil) 278.63/89.50
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.63/89.50
top(mark(z0)) → top(proper(z0)) 278.63/89.50
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.50
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.50
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.50
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.50
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.50
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.50
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.50
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.50
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.50
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.50
S(mark(z0)) → c20(S(z0)) 278.63/89.50
S(ok(z0)) → c21(S(z0)) 278.63/89.50
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.50
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.50
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.50
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.50
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.50
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.50
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.50
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.50
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.50
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.50
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.50
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.50
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.50
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.50
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.50
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.50
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.50
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.50
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.50
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.63/89.50
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.63/89.50
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.63/89.50
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.50
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.50
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.63/89.50
PROPER(from(0)) → c32(FROM(ok(0))) 278.63/89.50
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.63/89.50
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.63/89.50
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.63/89.50
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.63/89.50
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.63/89.50
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.63/89.50
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.63/89.50
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.63/89.50
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.63/89.50
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.63/89.50
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.63/89.50
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.63/89.50
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.63/89.50
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.63/89.50
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.50
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.50
PROPER(s(0)) → c34(S(ok(0)), PROPER(0)) 278.63/89.50
PROPER(s(nil)) → c34(S(ok(nil)), PROPER(nil)) 278.63/89.50
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.50
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.50
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.50
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.50
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.50
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.50
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.50
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.50
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.50
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.50
S(mark(z0)) → c20(S(z0)) 278.63/89.50
S(ok(z0)) → c21(S(z0)) 278.63/89.50
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.50
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.50
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.50
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.50
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.50
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.50
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.50
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.50
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.50
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.50
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.50
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.50
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.50
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.50
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.50
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.50
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.50
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.50
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.50
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.63/89.50
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.63/89.50
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.63/89.50
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.50
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.50
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.63/89.50
PROPER(from(0)) → c32(FROM(ok(0))) 278.63/89.50
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.63/89.50
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.63/89.50
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.63/89.50
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.63/89.50
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.63/89.50
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.63/89.50
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.63/89.50
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.63/89.50
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.63/89.50
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.63/89.50
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.63/89.50
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.63/89.50
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.63/89.50
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.63/89.50
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.50
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.50
PROPER(s(0)) → c34(S(ok(0)), PROPER(0)) 278.63/89.50
PROPER(s(nil)) → c34(S(ok(nil)), PROPER(nil)) 278.63/89.50
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c35, c36, c37, c40, c41, c42, c, c1, c7, c8, c9, c10, c11, c32, c32, c33, c33, c34

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278.63/89.50

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

Removed 2 trailing tuple parts
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278.63/89.50

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.63/89.50
active(head(cons(z0, z1))) → mark(z0) 278.63/89.50
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.63/89.50
active(take(0, z0)) → mark(nil) 278.63/89.50
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.63/89.50
active(sel(0, cons(z0, z1))) → mark(z0) 278.63/89.50
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.63/89.50
active(from(z0)) → from(active(z0)) 278.63/89.50
active(cons(z0, z1)) → cons(active(z0), z1) 278.63/89.50
active(s(z0)) → s(active(z0)) 278.63/89.50
active(head(z0)) → head(active(z0)) 278.63/89.50
active(2nd(z0)) → 2nd(active(z0)) 278.63/89.50
active(take(z0, z1)) → take(active(z0), z1) 278.63/89.50
active(take(z0, z1)) → take(z0, active(z1)) 278.63/89.50
active(sel(z0, z1)) → sel(active(z0), z1) 278.63/89.50
active(sel(z0, z1)) → sel(z0, active(z1)) 278.63/89.50
from(mark(z0)) → mark(from(z0)) 278.63/89.50
from(ok(z0)) → ok(from(z0)) 278.63/89.50
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.63/89.50
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.63/89.50
s(mark(z0)) → mark(s(z0)) 278.63/89.50
s(ok(z0)) → ok(s(z0)) 278.63/89.50
head(mark(z0)) → mark(head(z0)) 278.63/89.50
head(ok(z0)) → ok(head(z0)) 278.63/89.50
2nd(mark(z0)) → mark(2nd(z0)) 278.63/89.50
2nd(ok(z0)) → ok(2nd(z0)) 278.63/89.50
take(mark(z0), z1) → mark(take(z0, z1)) 278.63/89.50
take(z0, mark(z1)) → mark(take(z0, z1)) 278.63/89.50
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.63/89.50
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.63/89.50
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.63/89.50
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.63/89.50
proper(from(z0)) → from(proper(z0)) 278.63/89.50
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.63/89.50
proper(s(z0)) → s(proper(z0)) 278.63/89.50
proper(head(z0)) → head(proper(z0)) 278.63/89.50
proper(2nd(z0)) → 2nd(proper(z0)) 278.63/89.50
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.63/89.50
proper(0) → ok(0) 278.63/89.50
proper(nil) → ok(nil) 278.63/89.50
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.63/89.50
top(mark(z0)) → top(proper(z0)) 278.63/89.50
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.50
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.50
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.50
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.50
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.50
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.50
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.50
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.50
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.50
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.50
S(mark(z0)) → c20(S(z0)) 278.63/89.50
S(ok(z0)) → c21(S(z0)) 278.63/89.50
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.50
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.50
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.50
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.50
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.50
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.50
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.50
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.50
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.50
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.50
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.50
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.50
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.50
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.50
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.50
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.50
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.50
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.50
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.50
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.63/89.50
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.63/89.50
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.63/89.50
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.50
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.50
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.63/89.50
PROPER(from(0)) → c32(FROM(ok(0))) 278.63/89.50
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.63/89.50
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.63/89.50
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.63/89.50
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.63/89.50
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.63/89.50
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.63/89.50
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.63/89.50
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.63/89.50
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.63/89.50
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.63/89.50
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.63/89.50
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.63/89.50
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.63/89.50
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.63/89.50
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.50
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.50
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.63/89.50
PROPER(s(0)) → c34(S(ok(0))) 278.63/89.50
PROPER(s(nil)) → c34(S(ok(nil)))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.63/89.50
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.63/89.50
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.63/89.50
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.63/89.50
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.63/89.50
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.63/89.50
FROM(mark(z0)) → c16(FROM(z0)) 278.63/89.50
FROM(ok(z0)) → c17(FROM(z0)) 278.63/89.50
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.63/89.50
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.63/89.50
S(mark(z0)) → c20(S(z0)) 278.63/89.50
S(ok(z0)) → c21(S(z0)) 278.63/89.50
HEAD(mark(z0)) → c22(HEAD(z0)) 278.63/89.50
HEAD(ok(z0)) → c23(HEAD(z0)) 278.63/89.50
2ND(mark(z0)) → c24(2ND(z0)) 278.63/89.50
2ND(ok(z0)) → c25(2ND(z0)) 278.63/89.50
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.63/89.50
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.63/89.50
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.63/89.50
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.63/89.50
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.63/89.50
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.63/89.50
PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) 278.63/89.50
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.63/89.50
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.50
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.63/89.50
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.63/89.50
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.63/89.50
ACTIVE(from(z0)) → c(S(z0)) 278.63/89.50
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.63/89.50
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.63/89.50
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.63/89.50
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.63/89.50
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.63/89.50
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.63/89.50
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.63/89.50
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.63/89.50
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.63/89.50
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.63/89.50
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.63/89.50
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.63/89.50
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.63/89.50
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.63/89.50
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.63/89.50
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.63/89.50
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.63/89.50
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.63/89.50
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.50
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.50
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.63/89.50
PROPER(from(0)) → c32(FROM(ok(0))) 278.63/89.50
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.63/89.50
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.63/89.50
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.63/89.50
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.63/89.50
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.63/89.50
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.63/89.50
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.63/89.50
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.63/89.50
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.63/89.50
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.63/89.50
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.63/89.50
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.63/89.50
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.63/89.50
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.63/89.50
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.63/89.50
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.63/89.50
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.50
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.50
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.63/89.50
PROPER(s(0)) → c34(S(ok(0))) 278.63/89.50
PROPER(s(nil)) → c34(S(ok(nil)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c35, c36, c37, c40, c41, c42, c, c1, c7, c8, c9, c10, c11, c32, c32, c33, c33, c34, c34

278.63/89.50
278.63/89.50

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

Use narrowing to replace PROPER(head(z0)) → c35(HEAD(proper(z0)), PROPER(z0)) by

PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.63/89.50
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.63/89.50
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.63/89.50
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.63/89.50
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.63/89.50
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.63/89.50
PROPER(head(0)) → c35(HEAD(ok(0)), PROPER(0)) 278.63/89.50
PROPER(head(nil)) → c35(HEAD(ok(nil)), PROPER(nil)) 278.63/89.50
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
278.63/89.50
278.63/89.50

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.63/89.50
active(head(cons(z0, z1))) → mark(z0) 278.63/89.50
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.63/89.50
active(take(0, z0)) → mark(nil) 278.63/89.50
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.63/89.50
active(sel(0, cons(z0, z1))) → mark(z0) 278.63/89.50
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.63/89.50
active(from(z0)) → from(active(z0)) 278.63/89.50
active(cons(z0, z1)) → cons(active(z0), z1) 278.63/89.50
active(s(z0)) → s(active(z0)) 278.63/89.50
active(head(z0)) → head(active(z0)) 278.63/89.50
active(2nd(z0)) → 2nd(active(z0)) 278.63/89.50
active(take(z0, z1)) → take(active(z0), z1) 278.63/89.50
active(take(z0, z1)) → take(z0, active(z1)) 278.63/89.50
active(sel(z0, z1)) → sel(active(z0), z1) 278.63/89.50
active(sel(z0, z1)) → sel(z0, active(z1)) 278.63/89.50
from(mark(z0)) → mark(from(z0)) 278.63/89.50
from(ok(z0)) → ok(from(z0)) 278.63/89.50
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.63/89.50
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.63/89.50
s(mark(z0)) → mark(s(z0)) 278.63/89.50
s(ok(z0)) → ok(s(z0)) 278.63/89.50
head(mark(z0)) → mark(head(z0)) 278.63/89.50
head(ok(z0)) → ok(head(z0)) 278.63/89.50
2nd(mark(z0)) → mark(2nd(z0)) 278.63/89.50
2nd(ok(z0)) → ok(2nd(z0)) 278.63/89.50
take(mark(z0), z1) → mark(take(z0, z1)) 278.63/89.50
take(z0, mark(z1)) → mark(take(z0, z1)) 278.63/89.50
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.63/89.50
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.63/89.50
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.63/89.50
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.63/89.50
proper(from(z0)) → from(proper(z0)) 278.63/89.50
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.63/89.50
proper(s(z0)) → s(proper(z0)) 278.63/89.50
proper(head(z0)) → head(proper(z0)) 278.63/89.50
proper(2nd(z0)) → 2nd(proper(z0)) 278.63/89.50
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.50
proper(0) → ok(0) 278.97/89.50
proper(nil) → ok(nil) 278.97/89.50
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.50
top(mark(z0)) → top(proper(z0)) 278.97/89.50
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.50
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.50
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.50
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.50
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.50
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.50
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.50
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.50
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.50
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.50
S(mark(z0)) → c20(S(z0)) 278.97/89.50
S(ok(z0)) → c21(S(z0)) 278.97/89.50
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.50
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.50
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.50
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.50
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.50
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.50
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.50
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.50
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.50
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.50
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.97/89.50
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.50
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.50
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.97/89.50
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.50
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.50
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.50
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.50
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.50
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.50
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.50
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.50
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.50
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.50
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.50
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.50
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.50
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.50
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.50
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.50
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.50
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.50
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.50
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.50
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.50
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.50
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.50
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.50
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.50
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.50
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.50
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.50
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.50
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.50
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.50
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.50
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.50
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.50
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.50
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.50
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.50
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.50
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.50
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.50
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.50
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.50
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.50
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.50
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.50
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.50
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.50
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.50
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.50
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.50
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.50
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.50
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.50
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.50
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.50
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.50
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.50
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.50
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.50
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.50
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.50
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.50
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.50
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.50
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.50
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.50
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.50
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.50
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.50
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.50
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.50
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.50
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.50
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.50
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.50
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.50
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.50
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.50
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.50
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.50
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.50
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.50
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.50
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.50
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.50
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.50
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.50
PROPER(head(0)) → c35(HEAD(ok(0)), PROPER(0)) 278.97/89.50
PROPER(head(nil)) → c35(HEAD(ok(nil)), PROPER(nil)) 278.97/89.50
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.50
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.50
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.50
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.50
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.50
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.50
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.50
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.50
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.50
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.50
S(mark(z0)) → c20(S(z0)) 278.97/89.50
S(ok(z0)) → c21(S(z0)) 278.97/89.50
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.50
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.50
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.50
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.50
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.50
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.50
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.50
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.50
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.50
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.50
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.97/89.50
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.50
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.50
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.97/89.50
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.50
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.50
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.50
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.50
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.50
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.50
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.50
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.50
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.50
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.50
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.50
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.50
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.50
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.50
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.50
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.50
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.50
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.50
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.50
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.50
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.50
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.50
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.50
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.50
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.50
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.50
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.50
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.50
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.50
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.50
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.50
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.50
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.50
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.50
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.50
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.50
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.50
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.50
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.50
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.50
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.50
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.50
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.50
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.50
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.50
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.50
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.50
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.50
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.50
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.50
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.50
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.50
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.50
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.50
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.50
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.50
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.50
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.50
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.50
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.50
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.50
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.50
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.50
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.50
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.50
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.50
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.50
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.50
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.50
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.50
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.50
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.50
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.50
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.50
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.50
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.50
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.50
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.50
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.50
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.50
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.50
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.50
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.50
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.50
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.50
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.50
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.50
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.50
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.50
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.50
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.50
PROPER(head(0)) → c35(HEAD(ok(0)), PROPER(0)) 278.97/89.50
PROPER(head(nil)) → c35(HEAD(ok(nil)), PROPER(nil)) 278.97/89.50
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c36, c37, c40, c41, c42, c, c1, c7, c8, c9, c10, c11, c32, c32, c33, c33, c34, c34, c35

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278.97/89.50

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

Removed 2 trailing tuple parts
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278.97/89.50

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.50
active(head(cons(z0, z1))) → mark(z0) 278.97/89.50
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.50
active(take(0, z0)) → mark(nil) 278.97/89.50
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.51
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.51
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.51
active(from(z0)) → from(active(z0)) 278.97/89.51
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.51
active(s(z0)) → s(active(z0)) 278.97/89.51
active(head(z0)) → head(active(z0)) 278.97/89.51
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.51
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.51
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.51
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.51
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.51
from(mark(z0)) → mark(from(z0)) 278.97/89.51
from(ok(z0)) → ok(from(z0)) 278.97/89.51
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.51
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.51
s(mark(z0)) → mark(s(z0)) 278.97/89.51
s(ok(z0)) → ok(s(z0)) 278.97/89.51
head(mark(z0)) → mark(head(z0)) 278.97/89.51
head(ok(z0)) → ok(head(z0)) 278.97/89.51
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.51
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.51
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.51
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.51
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.51
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.51
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.51
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.51
proper(from(z0)) → from(proper(z0)) 278.97/89.51
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.51
proper(s(z0)) → s(proper(z0)) 278.97/89.51
proper(head(z0)) → head(proper(z0)) 278.97/89.51
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.51
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.51
proper(0) → ok(0) 278.97/89.51
proper(nil) → ok(nil) 278.97/89.51
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.51
top(mark(z0)) → top(proper(z0)) 278.97/89.51
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.51
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.51
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.51
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.51
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.51
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.51
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.51
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.51
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.51
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.51
S(mark(z0)) → c20(S(z0)) 278.97/89.51
S(ok(z0)) → c21(S(z0)) 278.97/89.51
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.51
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.51
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.51
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.51
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.51
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.51
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.51
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.51
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.51
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.51
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.97/89.51
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.51
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.51
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.97/89.51
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.51
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.51
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.51
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.51
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.51
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.51
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.51
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.51
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.51
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.51
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.51
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.51
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.51
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.51
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.51
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.51
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.51
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.51
PROPER(head(nil)) → c35(HEAD(ok(nil)))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.51
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.51
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.51
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.51
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.51
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.51
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.51
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.51
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.51
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.51
S(mark(z0)) → c20(S(z0)) 278.97/89.51
S(ok(z0)) → c21(S(z0)) 278.97/89.51
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.51
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.51
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.51
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.51
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.51
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.51
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.51
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.51
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.51
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.51
PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) 278.97/89.51
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.51
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.51
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.97/89.51
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.51
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.51
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.51
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.51
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.51
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.51
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.51
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.51
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.51
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.51
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.51
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.51
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.51
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.51
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.51
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.51
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.51
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.51
PROPER(head(nil)) → c35(HEAD(ok(nil)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c36, c37, c40, c41, c42, c, c1, c7, c8, c9, c10, c11, c32, c32, c33, c33, c34, c34, c35, c35

278.97/89.51
278.97/89.51

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

Use narrowing to replace PROPER(2nd(z0)) → c36(2ND(proper(z0)), PROPER(z0)) by

PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(2nd(0)) → c36(2ND(ok(0)), PROPER(0)) 278.97/89.51
PROPER(2nd(nil)) → c36(2ND(ok(nil)), PROPER(nil)) 278.97/89.51
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
278.97/89.51
278.97/89.51

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.51
active(head(cons(z0, z1))) → mark(z0) 278.97/89.51
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.51
active(take(0, z0)) → mark(nil) 278.97/89.51
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.51
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.51
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.51
active(from(z0)) → from(active(z0)) 278.97/89.51
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.51
active(s(z0)) → s(active(z0)) 278.97/89.51
active(head(z0)) → head(active(z0)) 278.97/89.51
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.51
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.51
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.51
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.51
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.51
from(mark(z0)) → mark(from(z0)) 278.97/89.51
from(ok(z0)) → ok(from(z0)) 278.97/89.51
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.51
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.51
s(mark(z0)) → mark(s(z0)) 278.97/89.51
s(ok(z0)) → ok(s(z0)) 278.97/89.51
head(mark(z0)) → mark(head(z0)) 278.97/89.51
head(ok(z0)) → ok(head(z0)) 278.97/89.51
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.51
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.51
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.51
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.51
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.51
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.51
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.51
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.51
proper(from(z0)) → from(proper(z0)) 278.97/89.51
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.51
proper(s(z0)) → s(proper(z0)) 278.97/89.51
proper(head(z0)) → head(proper(z0)) 278.97/89.51
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.51
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.51
proper(0) → ok(0) 278.97/89.51
proper(nil) → ok(nil) 278.97/89.51
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.51
top(mark(z0)) → top(proper(z0)) 278.97/89.51
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.51
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.51
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.51
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.51
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.51
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.51
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.51
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.51
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.51
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.51
S(mark(z0)) → c20(S(z0)) 278.97/89.51
S(ok(z0)) → c21(S(z0)) 278.97/89.51
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.51
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.51
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.51
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.51
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.51
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.51
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.51
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.51
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.51
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.51
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.51
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.51
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.97/89.51
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.51
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.51
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.51
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.51
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.51
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.51
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.51
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.51
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.51
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.51
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.51
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.51
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.51
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.51
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.51
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.51
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.51
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.51
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.51
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(2nd(0)) → c36(2ND(ok(0)), PROPER(0)) 278.97/89.51
PROPER(2nd(nil)) → c36(2ND(ok(nil)), PROPER(nil)) 278.97/89.51
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.51
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.51
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.51
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.51
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.51
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.51
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.51
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.51
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.51
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.51
S(mark(z0)) → c20(S(z0)) 278.97/89.51
S(ok(z0)) → c21(S(z0)) 278.97/89.51
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.51
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.51
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.51
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.51
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.51
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.51
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.51
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.51
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.51
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.51
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.51
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.51
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.97/89.51
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.51
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.51
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.51
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.51
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.51
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.51
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.51
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.51
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.51
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.51
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.51
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.51
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.51
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.51
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.51
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.51
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.51
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.51
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.51
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(2nd(0)) → c36(2ND(ok(0)), PROPER(0)) 278.97/89.51
PROPER(2nd(nil)) → c36(2ND(ok(nil)), PROPER(nil)) 278.97/89.51
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c37, c40, c41, c42, c, c1, c7, c8, c9, c10, c11, c32, c32, c33, c33, c34, c34, c35, c35, c36

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278.97/89.51

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

Removed 2 trailing tuple parts
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278.97/89.51

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.51
active(head(cons(z0, z1))) → mark(z0) 278.97/89.51
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.51
active(take(0, z0)) → mark(nil) 278.97/89.51
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.51
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.51
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.51
active(from(z0)) → from(active(z0)) 278.97/89.51
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.51
active(s(z0)) → s(active(z0)) 278.97/89.51
active(head(z0)) → head(active(z0)) 278.97/89.51
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.51
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.51
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.51
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.51
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.51
from(mark(z0)) → mark(from(z0)) 278.97/89.51
from(ok(z0)) → ok(from(z0)) 278.97/89.51
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.51
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.51
s(mark(z0)) → mark(s(z0)) 278.97/89.51
s(ok(z0)) → ok(s(z0)) 278.97/89.51
head(mark(z0)) → mark(head(z0)) 278.97/89.51
head(ok(z0)) → ok(head(z0)) 278.97/89.51
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.51
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.51
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.51
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.51
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.51
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.51
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.51
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.51
proper(from(z0)) → from(proper(z0)) 278.97/89.51
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.51
proper(s(z0)) → s(proper(z0)) 278.97/89.51
proper(head(z0)) → head(proper(z0)) 278.97/89.51
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.51
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.51
proper(0) → ok(0) 278.97/89.51
proper(nil) → ok(nil) 278.97/89.51
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.51
top(mark(z0)) → top(proper(z0)) 278.97/89.51
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.51
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.51
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.51
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.51
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.51
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.51
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.51
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.51
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.51
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.51
S(mark(z0)) → c20(S(z0)) 278.97/89.51
S(ok(z0)) → c21(S(z0)) 278.97/89.51
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.51
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.51
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.51
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.51
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.51
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.51
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.51
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.51
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.51
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.51
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.51
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.51
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.97/89.51
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.51
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.51
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.51
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.51
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.51
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.51
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.51
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.51
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.51
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.51
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.51
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.51
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.51
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.51
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.51
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.51
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.51
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.51
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.51
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(2nd(0)) → c36(2ND(ok(0))) 278.97/89.51
PROPER(2nd(nil)) → c36(2ND(ok(nil)))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.51
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.51
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.51
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.51
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.51
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.51
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.51
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.51
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.51
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.51
S(mark(z0)) → c20(S(z0)) 278.97/89.51
S(ok(z0)) → c21(S(z0)) 278.97/89.51
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.51
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.51
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.51
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.51
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.51
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.51
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.51
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.51
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.51
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.51
PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.51
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.51
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.97/89.51
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.51
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.51
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.51
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.51
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.51
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.51
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.51
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.51
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.51
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.51
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.51
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.51
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.51
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.51
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.51
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.51
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.51
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.51
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.51
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(2nd(0)) → c36(2ND(ok(0))) 278.97/89.51
PROPER(2nd(nil)) → c36(2ND(ok(nil)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c37, c40, c41, c42, c, c1, c7, c8, c9, c10, c11, c32, c32, c33, c33, c34, c34, c35, c35, c36, c36

278.97/89.51
278.97/89.51

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

Use narrowing to replace PROPER(take(z0, z1)) → c37(TAKE(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(take(x0, from(z0))) → c37(TAKE(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.51
PROPER(take(x0, cons(z0, z1))) → c37(TAKE(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(take(x0, s(z0))) → c37(TAKE(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.51
PROPER(take(x0, head(z0))) → c37(TAKE(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.51
PROPER(take(x0, 2nd(z0))) → c37(TAKE(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.51
PROPER(take(x0, take(z0, z1))) → c37(TAKE(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.51
PROPER(take(x0, 0)) → c37(TAKE(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 278.97/89.51
PROPER(take(x0, nil)) → c37(TAKE(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 278.97/89.51
PROPER(take(x0, sel(z0, z1))) → c37(TAKE(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(take(from(z0), x1)) → c37(TAKE(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.51
PROPER(take(cons(z0, z1), x1)) → c37(TAKE(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(take(s(z0), x1)) → c37(TAKE(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.51
PROPER(take(head(z0), x1)) → c37(TAKE(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.51
PROPER(take(2nd(z0), x1)) → c37(TAKE(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.51
PROPER(take(take(z0, z1), x1)) → c37(TAKE(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(take(0, x1)) → c37(TAKE(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 278.97/89.51
PROPER(take(nil, x1)) → c37(TAKE(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 278.97/89.51
PROPER(take(sel(z0, z1), x1)) → c37(TAKE(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
278.97/89.51
278.97/89.51

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.51
active(head(cons(z0, z1))) → mark(z0) 278.97/89.51
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.51
active(take(0, z0)) → mark(nil) 278.97/89.51
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.51
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.51
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.51
active(from(z0)) → from(active(z0)) 278.97/89.51
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.51
active(s(z0)) → s(active(z0)) 278.97/89.51
active(head(z0)) → head(active(z0)) 278.97/89.51
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.51
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.51
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.51
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.51
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.51
from(mark(z0)) → mark(from(z0)) 278.97/89.51
from(ok(z0)) → ok(from(z0)) 278.97/89.51
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.51
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.51
s(mark(z0)) → mark(s(z0)) 278.97/89.51
s(ok(z0)) → ok(s(z0)) 278.97/89.51
head(mark(z0)) → mark(head(z0)) 278.97/89.51
head(ok(z0)) → ok(head(z0)) 278.97/89.51
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.51
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.51
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.51
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.51
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.51
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.51
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.51
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.51
proper(from(z0)) → from(proper(z0)) 278.97/89.51
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.51
proper(s(z0)) → s(proper(z0)) 278.97/89.51
proper(head(z0)) → head(proper(z0)) 278.97/89.51
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.51
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.51
proper(0) → ok(0) 278.97/89.51
proper(nil) → ok(nil) 278.97/89.51
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.51
top(mark(z0)) → top(proper(z0)) 278.97/89.51
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.51
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.51
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.51
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.51
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.51
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.51
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.51
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.51
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.51
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.51
S(mark(z0)) → c20(S(z0)) 278.97/89.51
S(ok(z0)) → c21(S(z0)) 278.97/89.51
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.51
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.51
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.51
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.51
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.51
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.51
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.51
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.51
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.51
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.51
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.51
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.97/89.51
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.51
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.51
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.51
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.51
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.51
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.51
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.51
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.51
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.51
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.51
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.51
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.51
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.51
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.51
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.51
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.51
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.51
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.51
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.51
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(2nd(0)) → c36(2ND(ok(0))) 278.97/89.51
PROPER(2nd(nil)) → c36(2ND(ok(nil))) 278.97/89.51
PROPER(take(x0, from(z0))) → c37(TAKE(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.51
PROPER(take(x0, cons(z0, z1))) → c37(TAKE(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(take(x0, s(z0))) → c37(TAKE(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.51
PROPER(take(x0, head(z0))) → c37(TAKE(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.51
PROPER(take(x0, 2nd(z0))) → c37(TAKE(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.51
PROPER(take(x0, take(z0, z1))) → c37(TAKE(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.51
PROPER(take(x0, 0)) → c37(TAKE(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 278.97/89.51
PROPER(take(x0, nil)) → c37(TAKE(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 278.97/89.51
PROPER(take(x0, sel(z0, z1))) → c37(TAKE(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(take(from(z0), x1)) → c37(TAKE(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.51
PROPER(take(cons(z0, z1), x1)) → c37(TAKE(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(take(s(z0), x1)) → c37(TAKE(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.51
PROPER(take(head(z0), x1)) → c37(TAKE(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.51
PROPER(take(2nd(z0), x1)) → c37(TAKE(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.51
PROPER(take(take(z0, z1), x1)) → c37(TAKE(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(take(0, x1)) → c37(TAKE(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 278.97/89.51
PROPER(take(nil, x1)) → c37(TAKE(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 278.97/89.51
PROPER(take(sel(z0, z1), x1)) → c37(TAKE(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.51
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.51
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.51
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.51
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.51
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.51
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.51
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.51
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.51
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.51
S(mark(z0)) → c20(S(z0)) 278.97/89.51
S(ok(z0)) → c21(S(z0)) 278.97/89.51
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.51
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.51
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.51
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.51
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.51
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.51
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.51
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.51
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.51
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.51
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.51
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.97/89.51
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.51
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.51
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.51
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.51
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.51
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.51
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.51
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.51
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.51
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.51
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.51
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.51
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.51
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.51
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.51
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.51
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.51
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.51
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.51
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.51
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.51
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.51
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.51
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.51
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.51
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.51
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.51
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.51
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.51
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.51
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.51
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.51
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.51
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.51
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.51
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.51
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(2nd(0)) → c36(2ND(ok(0))) 278.97/89.51
PROPER(2nd(nil)) → c36(2ND(ok(nil))) 278.97/89.51
PROPER(take(x0, from(z0))) → c37(TAKE(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.51
PROPER(take(x0, cons(z0, z1))) → c37(TAKE(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.51
PROPER(take(x0, s(z0))) → c37(TAKE(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.51
PROPER(take(x0, head(z0))) → c37(TAKE(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.51
PROPER(take(x0, 2nd(z0))) → c37(TAKE(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.51
PROPER(take(x0, take(z0, z1))) → c37(TAKE(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.51
PROPER(take(x0, 0)) → c37(TAKE(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 278.97/89.51
PROPER(take(x0, nil)) → c37(TAKE(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 278.97/89.51
PROPER(take(x0, sel(z0, z1))) → c37(TAKE(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.51
PROPER(take(from(z0), x1)) → c37(TAKE(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.51
PROPER(take(cons(z0, z1), x1)) → c37(TAKE(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(take(s(z0), x1)) → c37(TAKE(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.51
PROPER(take(head(z0), x1)) → c37(TAKE(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.51
PROPER(take(2nd(z0), x1)) → c37(TAKE(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.51
PROPER(take(take(z0, z1), x1)) → c37(TAKE(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.51
PROPER(take(0, x1)) → c37(TAKE(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 278.97/89.51
PROPER(take(nil, x1)) → c37(TAKE(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 278.97/89.51
PROPER(take(sel(z0, z1), x1)) → c37(TAKE(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c40, c41, c42, c, c1, c7, c8, c9, c10, c11, c32, c32, c33, c33, c34, c34, c35, c35, c36, c36, c37

278.97/89.51
278.97/89.51

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

Removed 4 trailing tuple parts
278.97/89.51
278.97/89.51

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.51
active(head(cons(z0, z1))) → mark(z0) 278.97/89.51
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.51
active(take(0, z0)) → mark(nil) 278.97/89.51
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.51
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.51
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.51
active(from(z0)) → from(active(z0)) 278.97/89.51
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.51
active(s(z0)) → s(active(z0)) 278.97/89.52
active(head(z0)) → head(active(z0)) 278.97/89.52
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.52
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.52
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.52
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.52
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.52
from(mark(z0)) → mark(from(z0)) 278.97/89.52
from(ok(z0)) → ok(from(z0)) 278.97/89.52
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.52
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.52
s(mark(z0)) → mark(s(z0)) 278.97/89.52
s(ok(z0)) → ok(s(z0)) 278.97/89.52
head(mark(z0)) → mark(head(z0)) 278.97/89.52
head(ok(z0)) → ok(head(z0)) 278.97/89.52
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.52
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.52
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.52
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.52
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.52
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.52
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.52
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.52
proper(from(z0)) → from(proper(z0)) 278.97/89.52
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.52
proper(s(z0)) → s(proper(z0)) 278.97/89.52
proper(head(z0)) → head(proper(z0)) 278.97/89.52
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.52
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.52
proper(0) → ok(0) 278.97/89.52
proper(nil) → ok(nil) 278.97/89.52
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.52
top(mark(z0)) → top(proper(z0)) 278.97/89.52
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.52
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.52
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.52
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.52
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.52
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.52
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.52
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.52
S(mark(z0)) → c20(S(z0)) 278.97/89.52
S(ok(z0)) → c21(S(z0)) 278.97/89.52
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.52
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.52
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.52
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.52
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.52
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.52
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.52
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.52
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.52
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.52
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.52
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.97/89.52
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.52
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.52
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.52
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.52
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.52
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.52
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.52
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.52
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.52
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.52
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.52
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.52
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(2nd(0)) → c36(2ND(ok(0))) 278.97/89.52
PROPER(2nd(nil)) → c36(2ND(ok(nil))) 278.97/89.52
PROPER(take(x0, from(z0))) → c37(TAKE(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(take(x0, cons(z0, z1))) → c37(TAKE(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(take(x0, s(z0))) → c37(TAKE(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(take(x0, head(z0))) → c37(TAKE(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(take(x0, 2nd(z0))) → c37(TAKE(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(take(x0, take(z0, z1))) → c37(TAKE(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(take(x0, sel(z0, z1))) → c37(TAKE(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(take(from(z0), x1)) → c37(TAKE(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(cons(z0, z1), x1)) → c37(TAKE(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(s(z0), x1)) → c37(TAKE(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(head(z0), x1)) → c37(TAKE(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(2nd(z0), x1)) → c37(TAKE(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(take(z0, z1), x1)) → c37(TAKE(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(sel(z0, z1), x1)) → c37(TAKE(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(x0, 0)) → c37(TAKE(proper(x0), ok(0)), PROPER(x0)) 278.97/89.52
PROPER(take(x0, nil)) → c37(TAKE(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.52
PROPER(take(0, x1)) → c37(TAKE(ok(0), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(take(nil, x1)) → c37(TAKE(ok(nil), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.52
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.52
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.52
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.52
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.52
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.52
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.52
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.52
S(mark(z0)) → c20(S(z0)) 278.97/89.52
S(ok(z0)) → c21(S(z0)) 278.97/89.52
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.52
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.52
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.52
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.52
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.52
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.52
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.52
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.52
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.52
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.52
PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 278.97/89.52
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.97/89.52
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.52
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.52
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.52
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.52
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.52
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.52
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.52
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.52
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.52
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.52
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.52
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.52
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(2nd(0)) → c36(2ND(ok(0))) 278.97/89.52
PROPER(2nd(nil)) → c36(2ND(ok(nil))) 278.97/89.52
PROPER(take(x0, from(z0))) → c37(TAKE(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(take(x0, cons(z0, z1))) → c37(TAKE(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(take(x0, s(z0))) → c37(TAKE(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(take(x0, head(z0))) → c37(TAKE(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(take(x0, 2nd(z0))) → c37(TAKE(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(take(x0, take(z0, z1))) → c37(TAKE(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(take(x0, sel(z0, z1))) → c37(TAKE(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(take(from(z0), x1)) → c37(TAKE(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(cons(z0, z1), x1)) → c37(TAKE(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(s(z0), x1)) → c37(TAKE(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(head(z0), x1)) → c37(TAKE(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(2nd(z0), x1)) → c37(TAKE(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(take(z0, z1), x1)) → c37(TAKE(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(sel(z0, z1), x1)) → c37(TAKE(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(x0, 0)) → c37(TAKE(proper(x0), ok(0)), PROPER(x0)) 278.97/89.52
PROPER(take(x0, nil)) → c37(TAKE(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.52
PROPER(take(0, x1)) → c37(TAKE(ok(0), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(take(nil, x1)) → c37(TAKE(ok(nil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c40, c41, c42, c, c1, c7, c8, c9, c10, c11, c32, c32, c33, c33, c34, c34, c35, c35, c36, c36, c37, c37

278.97/89.52
278.97/89.52

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

Use narrowing to replace PROPER(sel(z0, z1)) → c40(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(sel(x0, from(z0))) → c40(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(sel(x0, cons(z0, z1))) → c40(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(sel(x0, s(z0))) → c40(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(sel(x0, head(z0))) → c40(SEL(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(sel(x0, 2nd(z0))) → c40(SEL(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(sel(x0, take(z0, z1))) → c40(SEL(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(sel(x0, 0)) → c40(SEL(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 278.97/89.52
PROPER(sel(x0, nil)) → c40(SEL(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 278.97/89.52
PROPER(sel(x0, sel(z0, z1))) → c40(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(sel(from(z0), x1)) → c40(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(cons(z0, z1), x1)) → c40(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(sel(s(z0), x1)) → c40(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(head(z0), x1)) → c40(SEL(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(2nd(z0), x1)) → c40(SEL(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(take(z0, z1), x1)) → c40(SEL(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(sel(0, x1)) → c40(SEL(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 278.97/89.52
PROPER(sel(nil, x1)) → c40(SEL(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 278.97/89.52
PROPER(sel(sel(z0, z1), x1)) → c40(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
278.97/89.52
278.97/89.52

(42) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.52
active(head(cons(z0, z1))) → mark(z0) 278.97/89.52
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.52
active(take(0, z0)) → mark(nil) 278.97/89.52
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.52
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.52
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.52
active(from(z0)) → from(active(z0)) 278.97/89.52
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.52
active(s(z0)) → s(active(z0)) 278.97/89.52
active(head(z0)) → head(active(z0)) 278.97/89.52
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.52
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.52
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.52
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.52
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.52
from(mark(z0)) → mark(from(z0)) 278.97/89.52
from(ok(z0)) → ok(from(z0)) 278.97/89.52
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.52
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.52
s(mark(z0)) → mark(s(z0)) 278.97/89.52
s(ok(z0)) → ok(s(z0)) 278.97/89.52
head(mark(z0)) → mark(head(z0)) 278.97/89.52
head(ok(z0)) → ok(head(z0)) 278.97/89.52
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.52
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.52
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.52
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.52
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.52
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.52
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.52
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.52
proper(from(z0)) → from(proper(z0)) 278.97/89.52
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.52
proper(s(z0)) → s(proper(z0)) 278.97/89.52
proper(head(z0)) → head(proper(z0)) 278.97/89.52
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.52
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.52
proper(0) → ok(0) 278.97/89.52
proper(nil) → ok(nil) 278.97/89.52
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.52
top(mark(z0)) → top(proper(z0)) 278.97/89.52
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.52
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.52
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.52
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.52
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.52
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.52
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.52
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.52
S(mark(z0)) → c20(S(z0)) 278.97/89.52
S(ok(z0)) → c21(S(z0)) 278.97/89.52
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.52
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.52
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.52
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.52
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.52
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.52
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.52
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.52
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.52
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.52
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.97/89.52
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.52
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.52
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.52
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.52
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.52
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.52
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.52
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.52
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.52
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.52
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.52
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.52
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(2nd(0)) → c36(2ND(ok(0))) 278.97/89.52
PROPER(2nd(nil)) → c36(2ND(ok(nil))) 278.97/89.52
PROPER(take(x0, from(z0))) → c37(TAKE(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(take(x0, cons(z0, z1))) → c37(TAKE(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(take(x0, s(z0))) → c37(TAKE(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(take(x0, head(z0))) → c37(TAKE(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(take(x0, 2nd(z0))) → c37(TAKE(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(take(x0, take(z0, z1))) → c37(TAKE(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(take(x0, sel(z0, z1))) → c37(TAKE(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(take(from(z0), x1)) → c37(TAKE(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(cons(z0, z1), x1)) → c37(TAKE(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(s(z0), x1)) → c37(TAKE(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(head(z0), x1)) → c37(TAKE(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(2nd(z0), x1)) → c37(TAKE(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(take(z0, z1), x1)) → c37(TAKE(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(sel(z0, z1), x1)) → c37(TAKE(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(x0, 0)) → c37(TAKE(proper(x0), ok(0)), PROPER(x0)) 278.97/89.52
PROPER(take(x0, nil)) → c37(TAKE(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.52
PROPER(take(0, x1)) → c37(TAKE(ok(0), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(take(nil, x1)) → c37(TAKE(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(sel(x0, from(z0))) → c40(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(sel(x0, cons(z0, z1))) → c40(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(sel(x0, s(z0))) → c40(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(sel(x0, head(z0))) → c40(SEL(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(sel(x0, 2nd(z0))) → c40(SEL(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(sel(x0, take(z0, z1))) → c40(SEL(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(sel(x0, 0)) → c40(SEL(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 278.97/89.52
PROPER(sel(x0, nil)) → c40(SEL(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 278.97/89.52
PROPER(sel(x0, sel(z0, z1))) → c40(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(sel(from(z0), x1)) → c40(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(cons(z0, z1), x1)) → c40(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(sel(s(z0), x1)) → c40(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(head(z0), x1)) → c40(SEL(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(2nd(z0), x1)) → c40(SEL(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(take(z0, z1), x1)) → c40(SEL(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(sel(0, x1)) → c40(SEL(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 278.97/89.52
PROPER(sel(nil, x1)) → c40(SEL(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 278.97/89.52
PROPER(sel(sel(z0, z1), x1)) → c40(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.52
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.52
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.52
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.52
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.52
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.52
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.52
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.52
S(mark(z0)) → c20(S(z0)) 278.97/89.52
S(ok(z0)) → c21(S(z0)) 278.97/89.52
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.52
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.52
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.52
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.52
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.52
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.52
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.52
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.52
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.52
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.52
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.97/89.52
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.52
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.52
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.52
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.52
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.52
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.52
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.52
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.52
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.52
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.52
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.52
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.52
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(2nd(0)) → c36(2ND(ok(0))) 278.97/89.52
PROPER(2nd(nil)) → c36(2ND(ok(nil))) 278.97/89.52
PROPER(take(x0, from(z0))) → c37(TAKE(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(take(x0, cons(z0, z1))) → c37(TAKE(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(take(x0, s(z0))) → c37(TAKE(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(take(x0, head(z0))) → c37(TAKE(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(take(x0, 2nd(z0))) → c37(TAKE(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(take(x0, take(z0, z1))) → c37(TAKE(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(take(x0, sel(z0, z1))) → c37(TAKE(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(take(from(z0), x1)) → c37(TAKE(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(cons(z0, z1), x1)) → c37(TAKE(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(s(z0), x1)) → c37(TAKE(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(head(z0), x1)) → c37(TAKE(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(2nd(z0), x1)) → c37(TAKE(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(take(z0, z1), x1)) → c37(TAKE(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(sel(z0, z1), x1)) → c37(TAKE(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(x0, 0)) → c37(TAKE(proper(x0), ok(0)), PROPER(x0)) 278.97/89.52
PROPER(take(x0, nil)) → c37(TAKE(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.52
PROPER(take(0, x1)) → c37(TAKE(ok(0), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(take(nil, x1)) → c37(TAKE(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(sel(x0, from(z0))) → c40(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(sel(x0, cons(z0, z1))) → c40(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(sel(x0, s(z0))) → c40(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(sel(x0, head(z0))) → c40(SEL(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(sel(x0, 2nd(z0))) → c40(SEL(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(sel(x0, take(z0, z1))) → c40(SEL(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(sel(x0, 0)) → c40(SEL(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 278.97/89.52
PROPER(sel(x0, nil)) → c40(SEL(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 278.97/89.52
PROPER(sel(x0, sel(z0, z1))) → c40(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(sel(from(z0), x1)) → c40(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(cons(z0, z1), x1)) → c40(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(sel(s(z0), x1)) → c40(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(head(z0), x1)) → c40(SEL(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(2nd(z0), x1)) → c40(SEL(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(take(z0, z1), x1)) → c40(SEL(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(sel(0, x1)) → c40(SEL(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 278.97/89.52
PROPER(sel(nil, x1)) → c40(SEL(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 278.97/89.52
PROPER(sel(sel(z0, z1), x1)) → c40(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, TOP, PROPER

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c41, c42, c, c1, c7, c8, c9, c10, c11, c32, c32, c33, c33, c34, c34, c35, c35, c36, c36, c37, c37, c40

278.97/89.52
278.97/89.52

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

Removed 4 trailing tuple parts
278.97/89.52
278.97/89.52

(44) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.52
active(head(cons(z0, z1))) → mark(z0) 278.97/89.52
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.52
active(take(0, z0)) → mark(nil) 278.97/89.52
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.52
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.52
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.52
active(from(z0)) → from(active(z0)) 278.97/89.52
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.52
active(s(z0)) → s(active(z0)) 278.97/89.52
active(head(z0)) → head(active(z0)) 278.97/89.52
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.52
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.52
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.52
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.52
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.52
from(mark(z0)) → mark(from(z0)) 278.97/89.52
from(ok(z0)) → ok(from(z0)) 278.97/89.52
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.52
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.52
s(mark(z0)) → mark(s(z0)) 278.97/89.52
s(ok(z0)) → ok(s(z0)) 278.97/89.52
head(mark(z0)) → mark(head(z0)) 278.97/89.52
head(ok(z0)) → ok(head(z0)) 278.97/89.52
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.52
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.52
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.52
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.52
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.52
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.52
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.52
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.52
proper(from(z0)) → from(proper(z0)) 278.97/89.52
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.52
proper(s(z0)) → s(proper(z0)) 278.97/89.52
proper(head(z0)) → head(proper(z0)) 278.97/89.52
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.52
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.52
proper(0) → ok(0) 278.97/89.52
proper(nil) → ok(nil) 278.97/89.52
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.52
top(mark(z0)) → top(proper(z0)) 278.97/89.52
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.52
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.52
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.52
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.52
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.52
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.52
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.52
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.52
S(mark(z0)) → c20(S(z0)) 278.97/89.52
S(ok(z0)) → c21(S(z0)) 278.97/89.52
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.52
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.52
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.52
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.52
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.52
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.52
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.52
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.52
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.52
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.52
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.97/89.52
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.52
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.52
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.52
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.52
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.52
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.52
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.52
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.52
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.52
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.52
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.52
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.52
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(2nd(0)) → c36(2ND(ok(0))) 278.97/89.52
PROPER(2nd(nil)) → c36(2ND(ok(nil))) 278.97/89.52
PROPER(take(x0, from(z0))) → c37(TAKE(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(take(x0, cons(z0, z1))) → c37(TAKE(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(take(x0, s(z0))) → c37(TAKE(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(take(x0, head(z0))) → c37(TAKE(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(take(x0, 2nd(z0))) → c37(TAKE(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(take(x0, take(z0, z1))) → c37(TAKE(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(take(x0, sel(z0, z1))) → c37(TAKE(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(take(from(z0), x1)) → c37(TAKE(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(cons(z0, z1), x1)) → c37(TAKE(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(s(z0), x1)) → c37(TAKE(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(head(z0), x1)) → c37(TAKE(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(2nd(z0), x1)) → c37(TAKE(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(take(z0, z1), x1)) → c37(TAKE(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(sel(z0, z1), x1)) → c37(TAKE(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(x0, 0)) → c37(TAKE(proper(x0), ok(0)), PROPER(x0)) 278.97/89.52
PROPER(take(x0, nil)) → c37(TAKE(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.52
PROPER(take(0, x1)) → c37(TAKE(ok(0), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(take(nil, x1)) → c37(TAKE(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(sel(x0, from(z0))) → c40(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(sel(x0, cons(z0, z1))) → c40(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(sel(x0, s(z0))) → c40(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(sel(x0, head(z0))) → c40(SEL(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(sel(x0, 2nd(z0))) → c40(SEL(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(sel(x0, take(z0, z1))) → c40(SEL(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(sel(x0, sel(z0, z1))) → c40(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(sel(from(z0), x1)) → c40(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(cons(z0, z1), x1)) → c40(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(sel(s(z0), x1)) → c40(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(head(z0), x1)) → c40(SEL(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(2nd(z0), x1)) → c40(SEL(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(take(z0, z1), x1)) → c40(SEL(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(sel(sel(z0, z1), x1)) → c40(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(sel(x0, 0)) → c40(SEL(proper(x0), ok(0)), PROPER(x0)) 278.97/89.52
PROPER(sel(x0, nil)) → c40(SEL(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.52
PROPER(sel(0, x1)) → c40(SEL(ok(0), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(sel(nil, x1)) → c40(SEL(ok(nil), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.52
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.52
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.52
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.52
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.52
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.52
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.52
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.52
S(mark(z0)) → c20(S(z0)) 278.97/89.52
S(ok(z0)) → c21(S(z0)) 278.97/89.52
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.52
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.52
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.52
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.52
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.52
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.52
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.52
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.52
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.52
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.52
TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) 278.97/89.52
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.52
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.52
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.52
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.52
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.52
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.52
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.52
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.52
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.52
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.52
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.52
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.52
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(2nd(0)) → c36(2ND(ok(0))) 278.97/89.52
PROPER(2nd(nil)) → c36(2ND(ok(nil))) 278.97/89.52
PROPER(take(x0, from(z0))) → c37(TAKE(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(take(x0, cons(z0, z1))) → c37(TAKE(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(take(x0, s(z0))) → c37(TAKE(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(take(x0, head(z0))) → c37(TAKE(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(take(x0, 2nd(z0))) → c37(TAKE(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(take(x0, take(z0, z1))) → c37(TAKE(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(take(x0, sel(z0, z1))) → c37(TAKE(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(take(from(z0), x1)) → c37(TAKE(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(cons(z0, z1), x1)) → c37(TAKE(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(s(z0), x1)) → c37(TAKE(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(head(z0), x1)) → c37(TAKE(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(2nd(z0), x1)) → c37(TAKE(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(take(take(z0, z1), x1)) → c37(TAKE(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(sel(z0, z1), x1)) → c37(TAKE(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(take(x0, 0)) → c37(TAKE(proper(x0), ok(0)), PROPER(x0)) 278.97/89.52
PROPER(take(x0, nil)) → c37(TAKE(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.52
PROPER(take(0, x1)) → c37(TAKE(ok(0), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(take(nil, x1)) → c37(TAKE(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(sel(x0, from(z0))) → c40(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(sel(x0, cons(z0, z1))) → c40(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(sel(x0, s(z0))) → c40(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(sel(x0, head(z0))) → c40(SEL(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(sel(x0, 2nd(z0))) → c40(SEL(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(sel(x0, take(z0, z1))) → c40(SEL(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(sel(x0, sel(z0, z1))) → c40(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(sel(from(z0), x1)) → c40(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(cons(z0, z1), x1)) → c40(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(sel(s(z0), x1)) → c40(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(head(z0), x1)) → c40(SEL(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(2nd(z0), x1)) → c40(SEL(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(sel(take(z0, z1), x1)) → c40(SEL(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(sel(sel(z0, z1), x1)) → c40(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(sel(x0, 0)) → c40(SEL(proper(x0), ok(0)), PROPER(x0)) 278.97/89.52
PROPER(sel(x0, nil)) → c40(SEL(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.52
PROPER(sel(0, x1)) → c40(SEL(ok(0), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(sel(nil, x1)) → c40(SEL(ok(nil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, TOP, PROPER

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c41, c42, c, c1, c7, c8, c9, c10, c11, c32, c32, c33, c33, c34, c34, c35, c35, c36, c36, c37, c37, c40, c40

278.97/89.52
278.97/89.52

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

Use narrowing to replace TOP(mark(z0)) → c41(TOP(proper(z0)), PROPER(z0)) by

TOP(mark(from(z0))) → c41(TOP(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
TOP(mark(cons(z0, z1))) → c41(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
TOP(mark(s(z0))) → c41(TOP(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
TOP(mark(head(z0))) → c41(TOP(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
TOP(mark(2nd(z0))) → c41(TOP(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
TOP(mark(take(z0, z1))) → c41(TOP(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
TOP(mark(0)) → c41(TOP(ok(0)), PROPER(0)) 278.97/89.52
TOP(mark(nil)) → c41(TOP(ok(nil)), PROPER(nil)) 278.97/89.52
TOP(mark(sel(z0, z1))) → c41(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
278.97/89.52
278.97/89.52

(46) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.52
active(head(cons(z0, z1))) → mark(z0) 278.97/89.52
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.52
active(take(0, z0)) → mark(nil) 278.97/89.52
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.52
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.52
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.52
active(from(z0)) → from(active(z0)) 278.97/89.52
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.52
active(s(z0)) → s(active(z0)) 278.97/89.52
active(head(z0)) → head(active(z0)) 278.97/89.52
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.52
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.52
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.52
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.52
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.52
from(mark(z0)) → mark(from(z0)) 278.97/89.52
from(ok(z0)) → ok(from(z0)) 278.97/89.52
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.52
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.52
s(mark(z0)) → mark(s(z0)) 278.97/89.52
s(ok(z0)) → ok(s(z0)) 278.97/89.52
head(mark(z0)) → mark(head(z0)) 278.97/89.52
head(ok(z0)) → ok(head(z0)) 278.97/89.52
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.52
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.52
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.52
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.52
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.52
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.52
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.52
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.52
proper(from(z0)) → from(proper(z0)) 278.97/89.52
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.52
proper(s(z0)) → s(proper(z0)) 278.97/89.52
proper(head(z0)) → head(proper(z0)) 278.97/89.52
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.52
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.52
proper(0) → ok(0) 278.97/89.52
proper(nil) → ok(nil) 278.97/89.52
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.52
top(mark(z0)) → top(proper(z0)) 278.97/89.52
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.52
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.52
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.52
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.52
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.52
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.52
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.52
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.52
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.52
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.52
S(mark(z0)) → c20(S(z0)) 278.97/89.52
S(ok(z0)) → c21(S(z0)) 278.97/89.52
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.52
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.52
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.52
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.52
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.52
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.52
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.52
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.52
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.52
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.52
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.52
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.52
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.52
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.52
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.52
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.52
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.52
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.52
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.52
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.52
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.52
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.52
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.52
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.52
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.52
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.52
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.52
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.52
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.52
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.52
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.52
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.52
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.52
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.52
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.52
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.52
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.52
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.52
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.52
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.52
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.52
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.52
PROPER(2nd(0)) → c36(2ND(ok(0))) 278.97/89.52
PROPER(2nd(nil)) → c36(2ND(ok(nil))) 278.97/89.52
PROPER(take(x0, from(z0))) → c37(TAKE(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.52
PROPER(take(x0, cons(z0, z1))) → c37(TAKE(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.52
PROPER(take(x0, s(z0))) → c37(TAKE(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.52
PROPER(take(x0, head(z0))) → c37(TAKE(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.52
PROPER(take(x0, 2nd(z0))) → c37(TAKE(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.52
PROPER(take(x0, take(z0, z1))) → c37(TAKE(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.52
PROPER(take(x0, sel(z0, z1))) → c37(TAKE(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(take(from(z0), x1)) → c37(TAKE(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(cons(z0, z1), x1)) → c37(TAKE(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(s(z0), x1)) → c37(TAKE(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(head(z0), x1)) → c37(TAKE(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(2nd(z0), x1)) → c37(TAKE(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(take(z0, z1), x1)) → c37(TAKE(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(sel(z0, z1), x1)) → c37(TAKE(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(x0, 0)) → c37(TAKE(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(take(x0, nil)) → c37(TAKE(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(take(0, x1)) → c37(TAKE(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(take(nil, x1)) → c37(TAKE(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(sel(x0, from(z0))) → c40(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(sel(x0, cons(z0, z1))) → c40(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(sel(x0, s(z0))) → c40(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(sel(x0, head(z0))) → c40(SEL(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(sel(x0, 2nd(z0))) → c40(SEL(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(sel(x0, take(z0, z1))) → c40(SEL(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(sel(x0, sel(z0, z1))) → c40(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(sel(from(z0), x1)) → c40(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(cons(z0, z1), x1)) → c40(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(s(z0), x1)) → c40(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(head(z0), x1)) → c40(SEL(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(2nd(z0), x1)) → c40(SEL(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(take(z0, z1), x1)) → c40(SEL(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(sel(z0, z1), x1)) → c40(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(x0, 0)) → c40(SEL(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(sel(x0, nil)) → c40(SEL(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(sel(0, x1)) → c40(SEL(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(sel(nil, x1)) → c40(SEL(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
TOP(mark(from(z0))) → c41(TOP(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
TOP(mark(cons(z0, z1))) → c41(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
TOP(mark(s(z0))) → c41(TOP(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
TOP(mark(head(z0))) → c41(TOP(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
TOP(mark(2nd(z0))) → c41(TOP(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
TOP(mark(take(z0, z1))) → c41(TOP(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
TOP(mark(0)) → c41(TOP(ok(0)), PROPER(0)) 278.97/89.53
TOP(mark(nil)) → c41(TOP(ok(nil)), PROPER(nil)) 278.97/89.53
TOP(mark(sel(z0, z1))) → c41(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.53
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.53
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.53
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.53
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.53
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.53
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.53
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.53
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.53
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.53
S(mark(z0)) → c20(S(z0)) 278.97/89.53
S(ok(z0)) → c21(S(z0)) 278.97/89.53
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.53
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.53
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.53
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.53
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.53
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.53
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.53
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.53
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.53
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.53
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.53
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.53
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.53
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.53
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.53
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.53
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.53
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.53
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.53
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.53
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(2nd(0)) → c36(2ND(ok(0))) 278.97/89.53
PROPER(2nd(nil)) → c36(2ND(ok(nil))) 278.97/89.53
PROPER(take(x0, from(z0))) → c37(TAKE(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(take(x0, cons(z0, z1))) → c37(TAKE(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(take(x0, s(z0))) → c37(TAKE(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(take(x0, head(z0))) → c37(TAKE(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(take(x0, 2nd(z0))) → c37(TAKE(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(take(x0, take(z0, z1))) → c37(TAKE(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(take(x0, sel(z0, z1))) → c37(TAKE(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(take(from(z0), x1)) → c37(TAKE(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(cons(z0, z1), x1)) → c37(TAKE(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(s(z0), x1)) → c37(TAKE(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(head(z0), x1)) → c37(TAKE(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(2nd(z0), x1)) → c37(TAKE(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(take(z0, z1), x1)) → c37(TAKE(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(sel(z0, z1), x1)) → c37(TAKE(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(x0, 0)) → c37(TAKE(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(take(x0, nil)) → c37(TAKE(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(take(0, x1)) → c37(TAKE(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(take(nil, x1)) → c37(TAKE(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(sel(x0, from(z0))) → c40(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(sel(x0, cons(z0, z1))) → c40(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(sel(x0, s(z0))) → c40(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(sel(x0, head(z0))) → c40(SEL(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(sel(x0, 2nd(z0))) → c40(SEL(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(sel(x0, take(z0, z1))) → c40(SEL(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(sel(x0, sel(z0, z1))) → c40(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(sel(from(z0), x1)) → c40(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(cons(z0, z1), x1)) → c40(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(s(z0), x1)) → c40(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(head(z0), x1)) → c40(SEL(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(2nd(z0), x1)) → c40(SEL(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(take(z0, z1), x1)) → c40(SEL(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(sel(z0, z1), x1)) → c40(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(x0, 0)) → c40(SEL(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(sel(x0, nil)) → c40(SEL(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(sel(0, x1)) → c40(SEL(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(sel(nil, x1)) → c40(SEL(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
TOP(mark(from(z0))) → c41(TOP(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
TOP(mark(cons(z0, z1))) → c41(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
TOP(mark(s(z0))) → c41(TOP(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
TOP(mark(head(z0))) → c41(TOP(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
TOP(mark(2nd(z0))) → c41(TOP(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
TOP(mark(take(z0, z1))) → c41(TOP(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
TOP(mark(0)) → c41(TOP(ok(0)), PROPER(0)) 278.97/89.53
TOP(mark(nil)) → c41(TOP(ok(nil)), PROPER(nil)) 278.97/89.53
TOP(mark(sel(z0, z1))) → c41(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, TOP, PROPER

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c42, c, c1, c7, c8, c9, c10, c11, c32, c32, c33, c33, c34, c34, c35, c35, c36, c36, c37, c37, c40, c40, c41

278.97/89.53
278.97/89.53

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

Removed 2 trailing tuple parts
278.97/89.53
278.97/89.53

(48) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.53
active(head(cons(z0, z1))) → mark(z0) 278.97/89.53
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.53
active(take(0, z0)) → mark(nil) 278.97/89.53
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.53
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.53
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.53
active(from(z0)) → from(active(z0)) 278.97/89.53
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.53
active(s(z0)) → s(active(z0)) 278.97/89.53
active(head(z0)) → head(active(z0)) 278.97/89.53
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.53
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.53
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.53
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.53
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.53
from(mark(z0)) → mark(from(z0)) 278.97/89.53
from(ok(z0)) → ok(from(z0)) 278.97/89.53
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.53
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.53
s(mark(z0)) → mark(s(z0)) 278.97/89.53
s(ok(z0)) → ok(s(z0)) 278.97/89.53
head(mark(z0)) → mark(head(z0)) 278.97/89.53
head(ok(z0)) → ok(head(z0)) 278.97/89.53
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.53
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.53
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.53
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.53
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.53
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.53
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.53
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.53
proper(from(z0)) → from(proper(z0)) 278.97/89.53
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.53
proper(s(z0)) → s(proper(z0)) 278.97/89.53
proper(head(z0)) → head(proper(z0)) 278.97/89.53
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.53
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.53
proper(0) → ok(0) 278.97/89.53
proper(nil) → ok(nil) 278.97/89.53
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.53
top(mark(z0)) → top(proper(z0)) 278.97/89.53
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.53
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.53
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.53
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.53
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.53
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.53
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.53
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.53
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.53
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.53
S(mark(z0)) → c20(S(z0)) 278.97/89.53
S(ok(z0)) → c21(S(z0)) 278.97/89.53
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.53
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.53
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.53
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.53
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.53
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.53
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.53
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.53
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.53
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.53
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.53
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.53
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.53
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.53
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.53
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.53
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.53
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.53
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.53
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.53
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(2nd(0)) → c36(2ND(ok(0))) 278.97/89.53
PROPER(2nd(nil)) → c36(2ND(ok(nil))) 278.97/89.53
PROPER(take(x0, from(z0))) → c37(TAKE(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(take(x0, cons(z0, z1))) → c37(TAKE(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(take(x0, s(z0))) → c37(TAKE(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(take(x0, head(z0))) → c37(TAKE(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(take(x0, 2nd(z0))) → c37(TAKE(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(take(x0, take(z0, z1))) → c37(TAKE(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(take(x0, sel(z0, z1))) → c37(TAKE(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(take(from(z0), x1)) → c37(TAKE(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(cons(z0, z1), x1)) → c37(TAKE(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(s(z0), x1)) → c37(TAKE(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(head(z0), x1)) → c37(TAKE(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(2nd(z0), x1)) → c37(TAKE(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(take(z0, z1), x1)) → c37(TAKE(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(sel(z0, z1), x1)) → c37(TAKE(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(x0, 0)) → c37(TAKE(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(take(x0, nil)) → c37(TAKE(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(take(0, x1)) → c37(TAKE(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(take(nil, x1)) → c37(TAKE(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(sel(x0, from(z0))) → c40(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(sel(x0, cons(z0, z1))) → c40(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(sel(x0, s(z0))) → c40(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(sel(x0, head(z0))) → c40(SEL(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(sel(x0, 2nd(z0))) → c40(SEL(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(sel(x0, take(z0, z1))) → c40(SEL(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(sel(x0, sel(z0, z1))) → c40(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(sel(from(z0), x1)) → c40(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(cons(z0, z1), x1)) → c40(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(s(z0), x1)) → c40(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(head(z0), x1)) → c40(SEL(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(2nd(z0), x1)) → c40(SEL(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(take(z0, z1), x1)) → c40(SEL(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(sel(z0, z1), x1)) → c40(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(x0, 0)) → c40(SEL(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(sel(x0, nil)) → c40(SEL(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(sel(0, x1)) → c40(SEL(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(sel(nil, x1)) → c40(SEL(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
TOP(mark(from(z0))) → c41(TOP(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
TOP(mark(cons(z0, z1))) → c41(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
TOP(mark(s(z0))) → c41(TOP(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
TOP(mark(head(z0))) → c41(TOP(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
TOP(mark(2nd(z0))) → c41(TOP(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
TOP(mark(take(z0, z1))) → c41(TOP(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
TOP(mark(sel(z0, z1))) → c41(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
TOP(mark(0)) → c41(TOP(ok(0))) 278.97/89.53
TOP(mark(nil)) → c41(TOP(ok(nil)))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.53
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.53
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.53
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.53
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.53
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.53
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.53
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.53
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.53
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.53
S(mark(z0)) → c20(S(z0)) 278.97/89.53
S(ok(z0)) → c21(S(z0)) 278.97/89.53
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.53
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.53
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.53
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.53
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.53
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.53
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.53
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.53
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.53
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.53
TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) 278.97/89.53
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.53
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.53
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.53
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.53
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.53
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.53
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.53
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.53
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.53
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(2nd(0)) → c36(2ND(ok(0))) 278.97/89.53
PROPER(2nd(nil)) → c36(2ND(ok(nil))) 278.97/89.53
PROPER(take(x0, from(z0))) → c37(TAKE(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(take(x0, cons(z0, z1))) → c37(TAKE(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(take(x0, s(z0))) → c37(TAKE(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(take(x0, head(z0))) → c37(TAKE(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(take(x0, 2nd(z0))) → c37(TAKE(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(take(x0, take(z0, z1))) → c37(TAKE(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(take(x0, sel(z0, z1))) → c37(TAKE(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(take(from(z0), x1)) → c37(TAKE(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(cons(z0, z1), x1)) → c37(TAKE(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(s(z0), x1)) → c37(TAKE(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(head(z0), x1)) → c37(TAKE(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(2nd(z0), x1)) → c37(TAKE(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(take(z0, z1), x1)) → c37(TAKE(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(sel(z0, z1), x1)) → c37(TAKE(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(x0, 0)) → c37(TAKE(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(take(x0, nil)) → c37(TAKE(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(take(0, x1)) → c37(TAKE(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(take(nil, x1)) → c37(TAKE(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(sel(x0, from(z0))) → c40(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(sel(x0, cons(z0, z1))) → c40(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(sel(x0, s(z0))) → c40(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(sel(x0, head(z0))) → c40(SEL(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(sel(x0, 2nd(z0))) → c40(SEL(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(sel(x0, take(z0, z1))) → c40(SEL(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(sel(x0, sel(z0, z1))) → c40(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(sel(from(z0), x1)) → c40(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(cons(z0, z1), x1)) → c40(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(s(z0), x1)) → c40(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(head(z0), x1)) → c40(SEL(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(2nd(z0), x1)) → c40(SEL(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(take(z0, z1), x1)) → c40(SEL(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(sel(z0, z1), x1)) → c40(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(x0, 0)) → c40(SEL(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(sel(x0, nil)) → c40(SEL(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(sel(0, x1)) → c40(SEL(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(sel(nil, x1)) → c40(SEL(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
TOP(mark(from(z0))) → c41(TOP(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
TOP(mark(cons(z0, z1))) → c41(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
TOP(mark(s(z0))) → c41(TOP(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
TOP(mark(head(z0))) → c41(TOP(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
TOP(mark(2nd(z0))) → c41(TOP(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
TOP(mark(take(z0, z1))) → c41(TOP(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
TOP(mark(sel(z0, z1))) → c41(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
TOP(mark(0)) → c41(TOP(ok(0))) 278.97/89.53
TOP(mark(nil)) → c41(TOP(ok(nil)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, TOP, PROPER

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c42, c, c1, c7, c8, c9, c10, c11, c32, c32, c33, c33, c34, c34, c35, c35, c36, c36, c37, c37, c40, c40, c41, c41

278.97/89.53
278.97/89.53

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

Use narrowing to replace TOP(ok(z0)) → c42(TOP(active(z0)), ACTIVE(z0)) by

TOP(ok(from(z0))) → c42(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
TOP(ok(head(cons(z0, z1)))) → c42(TOP(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
TOP(ok(2nd(cons(z0, z1)))) → c42(TOP(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
TOP(ok(take(0, z0))) → c42(TOP(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
TOP(ok(take(s(z0), cons(z1, z2)))) → c42(TOP(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
TOP(ok(sel(0, cons(z0, z1)))) → c42(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
TOP(ok(sel(s(z0), cons(z1, z2)))) → c42(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
TOP(ok(from(z0))) → c42(TOP(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
TOP(ok(cons(z0, z1))) → c42(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
TOP(ok(s(z0))) → c42(TOP(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
TOP(ok(head(z0))) → c42(TOP(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
TOP(ok(2nd(z0))) → c42(TOP(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
TOP(ok(take(z0, z1))) → c42(TOP(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
TOP(ok(take(z0, z1))) → c42(TOP(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
TOP(ok(sel(z0, z1))) → c42(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
TOP(ok(sel(z0, z1))) → c42(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
278.97/89.53
278.97/89.53

(50) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.53
active(head(cons(z0, z1))) → mark(z0) 278.97/89.53
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.53
active(take(0, z0)) → mark(nil) 278.97/89.53
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.53
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.53
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.53
active(from(z0)) → from(active(z0)) 278.97/89.53
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.53
active(s(z0)) → s(active(z0)) 278.97/89.53
active(head(z0)) → head(active(z0)) 278.97/89.53
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.53
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.53
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.53
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.53
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.53
from(mark(z0)) → mark(from(z0)) 278.97/89.53
from(ok(z0)) → ok(from(z0)) 278.97/89.53
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.53
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.53
s(mark(z0)) → mark(s(z0)) 278.97/89.53
s(ok(z0)) → ok(s(z0)) 278.97/89.53
head(mark(z0)) → mark(head(z0)) 278.97/89.53
head(ok(z0)) → ok(head(z0)) 278.97/89.53
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.53
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.53
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.53
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.53
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.53
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.53
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.53
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.53
proper(from(z0)) → from(proper(z0)) 278.97/89.53
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.53
proper(s(z0)) → s(proper(z0)) 278.97/89.53
proper(head(z0)) → head(proper(z0)) 278.97/89.53
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.53
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.53
proper(0) → ok(0) 278.97/89.53
proper(nil) → ok(nil) 278.97/89.53
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.53
top(mark(z0)) → top(proper(z0)) 278.97/89.53
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.53
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.53
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.53
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.53
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.53
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.53
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.53
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.53
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.53
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.53
S(mark(z0)) → c20(S(z0)) 278.97/89.53
S(ok(z0)) → c21(S(z0)) 278.97/89.53
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.53
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.53
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.53
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.53
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.53
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.53
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.53
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.53
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.53
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.53
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.53
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.53
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.53
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.53
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.53
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.53
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.53
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.53
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.53
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(2nd(0)) → c36(2ND(ok(0))) 278.97/89.53
PROPER(2nd(nil)) → c36(2ND(ok(nil))) 278.97/89.53
PROPER(take(x0, from(z0))) → c37(TAKE(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(take(x0, cons(z0, z1))) → c37(TAKE(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(take(x0, s(z0))) → c37(TAKE(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(take(x0, head(z0))) → c37(TAKE(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(take(x0, 2nd(z0))) → c37(TAKE(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(take(x0, take(z0, z1))) → c37(TAKE(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(take(x0, sel(z0, z1))) → c37(TAKE(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(take(from(z0), x1)) → c37(TAKE(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(cons(z0, z1), x1)) → c37(TAKE(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(s(z0), x1)) → c37(TAKE(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(head(z0), x1)) → c37(TAKE(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(2nd(z0), x1)) → c37(TAKE(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(take(z0, z1), x1)) → c37(TAKE(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(sel(z0, z1), x1)) → c37(TAKE(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(x0, 0)) → c37(TAKE(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(take(x0, nil)) → c37(TAKE(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(take(0, x1)) → c37(TAKE(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(take(nil, x1)) → c37(TAKE(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(sel(x0, from(z0))) → c40(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(sel(x0, cons(z0, z1))) → c40(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(sel(x0, s(z0))) → c40(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(sel(x0, head(z0))) → c40(SEL(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(sel(x0, 2nd(z0))) → c40(SEL(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(sel(x0, take(z0, z1))) → c40(SEL(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(sel(x0, sel(z0, z1))) → c40(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(sel(from(z0), x1)) → c40(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(cons(z0, z1), x1)) → c40(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(s(z0), x1)) → c40(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(head(z0), x1)) → c40(SEL(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(2nd(z0), x1)) → c40(SEL(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(take(z0, z1), x1)) → c40(SEL(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(sel(z0, z1), x1)) → c40(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(x0, 0)) → c40(SEL(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(sel(x0, nil)) → c40(SEL(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(sel(0, x1)) → c40(SEL(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(sel(nil, x1)) → c40(SEL(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
TOP(mark(from(z0))) → c41(TOP(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
TOP(mark(cons(z0, z1))) → c41(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
TOP(mark(s(z0))) → c41(TOP(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
TOP(mark(head(z0))) → c41(TOP(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
TOP(mark(2nd(z0))) → c41(TOP(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
TOP(mark(take(z0, z1))) → c41(TOP(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
TOP(mark(sel(z0, z1))) → c41(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
TOP(mark(0)) → c41(TOP(ok(0))) 278.97/89.53
TOP(mark(nil)) → c41(TOP(ok(nil))) 278.97/89.53
TOP(ok(from(z0))) → c42(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
TOP(ok(head(cons(z0, z1)))) → c42(TOP(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
TOP(ok(2nd(cons(z0, z1)))) → c42(TOP(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
TOP(ok(take(0, z0))) → c42(TOP(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
TOP(ok(take(s(z0), cons(z1, z2)))) → c42(TOP(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
TOP(ok(sel(0, cons(z0, z1)))) → c42(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
TOP(ok(sel(s(z0), cons(z1, z2)))) → c42(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
TOP(ok(from(z0))) → c42(TOP(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
TOP(ok(cons(z0, z1))) → c42(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
TOP(ok(s(z0))) → c42(TOP(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
TOP(ok(head(z0))) → c42(TOP(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
TOP(ok(2nd(z0))) → c42(TOP(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
TOP(ok(take(z0, z1))) → c42(TOP(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
TOP(ok(take(z0, z1))) → c42(TOP(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
TOP(ok(sel(z0, z1))) → c42(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
TOP(ok(sel(z0, z1))) → c42(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
S tuples:

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.53
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.53
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.53
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.53
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.53
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.53
FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.53
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.53
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.53
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.53
S(mark(z0)) → c20(S(z0)) 278.97/89.53
S(ok(z0)) → c21(S(z0)) 278.97/89.53
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.53
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.53
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.53
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.53
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.53
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.53
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.53
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.53
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.53
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.53
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.53
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.53
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.53
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.53
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.53
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.53
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.53
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.53
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.53
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(2nd(0)) → c36(2ND(ok(0))) 278.97/89.53
PROPER(2nd(nil)) → c36(2ND(ok(nil))) 278.97/89.53
PROPER(take(x0, from(z0))) → c37(TAKE(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(take(x0, cons(z0, z1))) → c37(TAKE(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(take(x0, s(z0))) → c37(TAKE(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(take(x0, head(z0))) → c37(TAKE(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(take(x0, 2nd(z0))) → c37(TAKE(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(take(x0, take(z0, z1))) → c37(TAKE(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(take(x0, sel(z0, z1))) → c37(TAKE(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(take(from(z0), x1)) → c37(TAKE(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(cons(z0, z1), x1)) → c37(TAKE(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(s(z0), x1)) → c37(TAKE(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(head(z0), x1)) → c37(TAKE(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(2nd(z0), x1)) → c37(TAKE(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(take(z0, z1), x1)) → c37(TAKE(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(sel(z0, z1), x1)) → c37(TAKE(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(x0, 0)) → c37(TAKE(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(take(x0, nil)) → c37(TAKE(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(take(0, x1)) → c37(TAKE(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(take(nil, x1)) → c37(TAKE(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(sel(x0, from(z0))) → c40(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(sel(x0, cons(z0, z1))) → c40(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(sel(x0, s(z0))) → c40(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(sel(x0, head(z0))) → c40(SEL(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(sel(x0, 2nd(z0))) → c40(SEL(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(sel(x0, take(z0, z1))) → c40(SEL(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(sel(x0, sel(z0, z1))) → c40(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(sel(from(z0), x1)) → c40(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(cons(z0, z1), x1)) → c40(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(s(z0), x1)) → c40(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(head(z0), x1)) → c40(SEL(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(2nd(z0), x1)) → c40(SEL(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(take(z0, z1), x1)) → c40(SEL(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(sel(z0, z1), x1)) → c40(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(x0, 0)) → c40(SEL(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(sel(x0, nil)) → c40(SEL(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(sel(0, x1)) → c40(SEL(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(sel(nil, x1)) → c40(SEL(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
TOP(mark(from(z0))) → c41(TOP(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
TOP(mark(cons(z0, z1))) → c41(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
TOP(mark(s(z0))) → c41(TOP(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
TOP(mark(head(z0))) → c41(TOP(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
TOP(mark(2nd(z0))) → c41(TOP(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
TOP(mark(take(z0, z1))) → c41(TOP(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
TOP(mark(sel(z0, z1))) → c41(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
TOP(mark(0)) → c41(TOP(ok(0))) 278.97/89.53
TOP(mark(nil)) → c41(TOP(ok(nil))) 278.97/89.53
TOP(ok(from(z0))) → c42(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
TOP(ok(head(cons(z0, z1)))) → c42(TOP(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
TOP(ok(2nd(cons(z0, z1)))) → c42(TOP(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
TOP(ok(take(0, z0))) → c42(TOP(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
TOP(ok(take(s(z0), cons(z1, z2)))) → c42(TOP(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
TOP(ok(sel(0, cons(z0, z1)))) → c42(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
TOP(ok(sel(s(z0), cons(z1, z2)))) → c42(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
TOP(ok(from(z0))) → c42(TOP(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
TOP(ok(cons(z0, z1))) → c42(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
TOP(ok(s(z0))) → c42(TOP(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
TOP(ok(head(z0))) → c42(TOP(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
TOP(ok(2nd(z0))) → c42(TOP(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
TOP(ok(take(z0, z1))) → c42(TOP(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
TOP(ok(take(z0, z1))) → c42(TOP(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
TOP(ok(sel(z0, z1))) → c42(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
TOP(ok(sel(z0, z1))) → c42(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, HEAD, 2ND, TAKE, SEL, PROPER, TOP

Compound Symbols:

c2, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c, c1, c7, c8, c9, c10, c11, c32, c32, c33, c33, c34, c34, c35, c35, c36, c36, c37, c37, c40, c40, c41, c41, c42

278.97/89.53
278.97/89.53

(51) CdtUnreachableProof (EQUIVALENT transformation)

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

ACTIVE(2nd(cons(z0, z1))) → c2(HEAD(z1)) 278.97/89.53
ACTIVE(sel(s(z0), cons(z1, z2))) → c6(SEL(z0, z2)) 278.97/89.53
ACTIVE(take(z0, z1)) → c12(TAKE(active(z0), z1), ACTIVE(z0)) 278.97/89.53
ACTIVE(take(z0, z1)) → c13(TAKE(z0, active(z1)), ACTIVE(z1)) 278.97/89.53
ACTIVE(sel(z0, z1)) → c14(SEL(active(z0), z1), ACTIVE(z0)) 278.97/89.53
ACTIVE(sel(z0, z1)) → c15(SEL(z0, active(z1)), ACTIVE(z1)) 278.97/89.53
ACTIVE(from(z0)) → c(S(z0)) 278.97/89.53
ACTIVE(take(s(z0), cons(z1, z2))) → c1(CONS(z1, take(z0, z2))) 278.97/89.53
ACTIVE(take(s(z0), cons(z1, z2))) → c1(TAKE(z0, z2)) 278.97/89.53
ACTIVE(from(from(z0))) → c7(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(from(head(cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(from(2nd(cons(z0, z1)))) → c7(FROM(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(from(take(0, z0))) → c7(FROM(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(from(take(s(z0), cons(z1, z2)))) → c7(FROM(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(from(sel(0, cons(z0, z1)))) → c7(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c7(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(from(from(z0))) → c7(FROM(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(from(cons(z0, z1))) → c7(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(from(s(z0))) → c7(FROM(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(from(head(z0))) → c7(FROM(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(from(2nd(z0))) → c7(FROM(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(from(take(z0, z1))) → c7(FROM(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(from(take(z0, z1))) → c7(FROM(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(from(sel(z0, z1))) → c7(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(cons(from(z0), x1)) → c8(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(cons(head(cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(2nd(cons(z0, z1)), x1)) → c8(CONS(mark(head(z1)), x1), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(take(0, z0), x1)) → c8(CONS(mark(nil), x1), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(cons(take(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(cons(z1, take(z0, z2))), x1), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c8(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c8(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(cons(from(z0), x1)) → c8(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(cons(cons(z0, z1), x1)) → c8(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(cons(s(z0), x1)) → c8(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(cons(head(z0), x1)) → c8(CONS(head(active(z0)), x1), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(cons(2nd(z0), x1)) → c8(CONS(2nd(active(z0)), x1), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(active(z0), z1), x1), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(cons(take(z0, z1), x1)) → c8(CONS(take(z0, active(z1)), x1), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(cons(sel(z0, z1), x1)) → c8(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(s(from(z0))) → c9(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(s(head(cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(s(2nd(cons(z0, z1)))) → c9(S(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(s(take(0, z0))) → c9(S(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(s(take(s(z0), cons(z1, z2)))) → c9(S(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(s(sel(0, cons(z0, z1)))) → c9(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c9(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(s(from(z0))) → c9(S(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(s(cons(z0, z1))) → c9(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(s(s(z0))) → c9(S(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(s(head(z0))) → c9(S(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(s(2nd(z0))) → c9(S(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(s(take(z0, z1))) → c9(S(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(s(take(z0, z1))) → c9(S(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(s(sel(z0, z1))) → c9(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(s(sel(z0, z1))) → c9(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(head(from(z0))) → c10(HEAD(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(head(head(cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(head(2nd(cons(z0, z1)))) → c10(HEAD(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(head(take(0, z0))) → c10(HEAD(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(head(take(s(z0), cons(z1, z2)))) → c10(HEAD(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(head(sel(0, cons(z0, z1)))) → c10(HEAD(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(head(sel(s(z0), cons(z1, z2)))) → c10(HEAD(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(head(from(z0))) → c10(HEAD(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(head(cons(z0, z1))) → c10(HEAD(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(head(s(z0))) → c10(HEAD(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(head(head(z0))) → c10(HEAD(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(head(2nd(z0))) → c10(HEAD(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(head(take(z0, z1))) → c10(HEAD(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(head(sel(z0, z1))) → c10(HEAD(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(2nd(from(z0))) → c11(2ND(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(2nd(head(cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(2nd(cons(z0, z1)))) → c11(2ND(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(take(0, z0))) → c11(2ND(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
ACTIVE(2nd(take(s(z0), cons(z1, z2)))) → c11(2ND(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(2nd(sel(0, cons(z0, z1)))) → c11(2ND(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
ACTIVE(2nd(sel(s(z0), cons(z1, z2)))) → c11(2ND(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
ACTIVE(2nd(from(z0))) → c11(2ND(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
ACTIVE(2nd(cons(z0, z1))) → c11(2ND(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
ACTIVE(2nd(s(z0))) → c11(2ND(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
ACTIVE(2nd(head(z0))) → c11(2ND(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
ACTIVE(2nd(2nd(z0))) → c11(2ND(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(2nd(take(z0, z1))) → c11(2ND(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
ACTIVE(2nd(sel(z0, z1))) → c11(2ND(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 278.97/89.53
PROPER(from(from(z0))) → c32(FROM(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(from(cons(z0, z1))) → c32(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(from(s(z0))) → c32(FROM(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(from(head(z0))) → c32(FROM(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(from(2nd(z0))) → c32(FROM(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(from(take(z0, z1))) → c32(FROM(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(from(sel(z0, z1))) → c32(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(from(0)) → c32(FROM(ok(0))) 278.97/89.53
PROPER(from(nil)) → c32(FROM(ok(nil))) 278.97/89.53
PROPER(cons(x0, from(z0))) → c33(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(cons(x0, cons(z0, z1))) → c33(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(cons(x0, s(z0))) → c33(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(cons(x0, head(z0))) → c33(CONS(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(cons(x0, 2nd(z0))) → c33(CONS(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(cons(x0, take(z0, z1))) → c33(CONS(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(cons(x0, sel(z0, z1))) → c33(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(cons(from(z0), x1)) → c33(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(cons(z0, z1), x1)) → c33(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(s(z0), x1)) → c33(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(head(z0), x1)) → c33(CONS(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(2nd(z0), x1)) → c33(CONS(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(cons(take(z0, z1), x1)) → c33(CONS(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(sel(z0, z1), x1)) → c33(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(cons(x0, 0)) → c33(CONS(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(cons(x0, nil)) → c33(CONS(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(cons(0, x1)) → c33(CONS(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(cons(nil, x1)) → c33(CONS(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(s(from(z0))) → c34(S(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(s(cons(z0, z1))) → c34(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(s(s(z0))) → c34(S(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(s(head(z0))) → c34(S(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(s(2nd(z0))) → c34(S(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(s(take(z0, z1))) → c34(S(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(s(sel(z0, z1))) → c34(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(s(0)) → c34(S(ok(0))) 278.97/89.53
PROPER(s(nil)) → c34(S(ok(nil))) 278.97/89.53
PROPER(head(from(z0))) → c35(HEAD(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(head(cons(z0, z1))) → c35(HEAD(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(head(s(z0))) → c35(HEAD(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(head(head(z0))) → c35(HEAD(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(head(2nd(z0))) → c35(HEAD(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(head(take(z0, z1))) → c35(HEAD(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(head(sel(z0, z1))) → c35(HEAD(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(head(0)) → c35(HEAD(ok(0))) 278.97/89.53
PROPER(head(nil)) → c35(HEAD(ok(nil))) 278.97/89.53
PROPER(2nd(from(z0))) → c36(2ND(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
PROPER(2nd(cons(z0, z1))) → c36(2ND(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(2nd(s(z0))) → c36(2ND(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
PROPER(2nd(head(z0))) → c36(2ND(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
PROPER(2nd(2nd(z0))) → c36(2ND(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
PROPER(2nd(take(z0, z1))) → c36(2ND(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
PROPER(2nd(sel(z0, z1))) → c36(2ND(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(2nd(0)) → c36(2ND(ok(0))) 278.97/89.53
PROPER(2nd(nil)) → c36(2ND(ok(nil))) 278.97/89.53
PROPER(take(x0, from(z0))) → c37(TAKE(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(take(x0, cons(z0, z1))) → c37(TAKE(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(take(x0, s(z0))) → c37(TAKE(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(take(x0, head(z0))) → c37(TAKE(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(take(x0, 2nd(z0))) → c37(TAKE(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(take(x0, take(z0, z1))) → c37(TAKE(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(take(x0, sel(z0, z1))) → c37(TAKE(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(take(from(z0), x1)) → c37(TAKE(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(cons(z0, z1), x1)) → c37(TAKE(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(s(z0), x1)) → c37(TAKE(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(head(z0), x1)) → c37(TAKE(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(2nd(z0), x1)) → c37(TAKE(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(take(take(z0, z1), x1)) → c37(TAKE(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(sel(z0, z1), x1)) → c37(TAKE(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(take(x0, 0)) → c37(TAKE(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(take(x0, nil)) → c37(TAKE(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(take(0, x1)) → c37(TAKE(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(take(nil, x1)) → c37(TAKE(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(sel(x0, from(z0))) → c40(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 278.97/89.53
PROPER(sel(x0, cons(z0, z1))) → c40(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 278.97/89.53
PROPER(sel(x0, s(z0))) → c40(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 278.97/89.53
PROPER(sel(x0, head(z0))) → c40(SEL(proper(x0), head(proper(z0))), PROPER(x0), PROPER(head(z0))) 278.97/89.53
PROPER(sel(x0, 2nd(z0))) → c40(SEL(proper(x0), 2nd(proper(z0))), PROPER(x0), PROPER(2nd(z0))) 278.97/89.53
PROPER(sel(x0, take(z0, z1))) → c40(SEL(proper(x0), take(proper(z0), proper(z1))), PROPER(x0), PROPER(take(z0, z1))) 278.97/89.53
PROPER(sel(x0, sel(z0, z1))) → c40(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 278.97/89.53
PROPER(sel(from(z0), x1)) → c40(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(cons(z0, z1), x1)) → c40(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(s(z0), x1)) → c40(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(head(z0), x1)) → c40(SEL(head(proper(z0)), proper(x1)), PROPER(head(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(2nd(z0), x1)) → c40(SEL(2nd(proper(z0)), proper(x1)), PROPER(2nd(z0)), PROPER(x1)) 278.97/89.53
PROPER(sel(take(z0, z1), x1)) → c40(SEL(take(proper(z0), proper(z1)), proper(x1)), PROPER(take(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(sel(z0, z1), x1)) → c40(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 278.97/89.53
PROPER(sel(x0, 0)) → c40(SEL(proper(x0), ok(0)), PROPER(x0)) 278.97/89.53
PROPER(sel(x0, nil)) → c40(SEL(proper(x0), ok(nil)), PROPER(x0)) 278.97/89.53
PROPER(sel(0, x1)) → c40(SEL(ok(0), proper(x1)), PROPER(x1)) 278.97/89.53
PROPER(sel(nil, x1)) → c40(SEL(ok(nil), proper(x1)), PROPER(x1)) 278.97/89.53
TOP(mark(from(z0))) → c41(TOP(from(proper(z0))), PROPER(from(z0))) 278.97/89.53
TOP(mark(cons(z0, z1))) → c41(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 278.97/89.53
TOP(mark(s(z0))) → c41(TOP(s(proper(z0))), PROPER(s(z0))) 278.97/89.53
TOP(mark(head(z0))) → c41(TOP(head(proper(z0))), PROPER(head(z0))) 278.97/89.53
TOP(mark(2nd(z0))) → c41(TOP(2nd(proper(z0))), PROPER(2nd(z0))) 278.97/89.53
TOP(mark(take(z0, z1))) → c41(TOP(take(proper(z0), proper(z1))), PROPER(take(z0, z1))) 278.97/89.53
TOP(mark(sel(z0, z1))) → c41(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 278.97/89.53
TOP(ok(from(z0))) → c42(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 278.97/89.53
TOP(ok(head(cons(z0, z1)))) → c42(TOP(mark(z0)), ACTIVE(head(cons(z0, z1)))) 278.97/89.53
TOP(ok(2nd(cons(z0, z1)))) → c42(TOP(mark(head(z1))), ACTIVE(2nd(cons(z0, z1)))) 278.97/89.53
TOP(ok(take(0, z0))) → c42(TOP(mark(nil)), ACTIVE(take(0, z0))) 278.97/89.53
TOP(ok(take(s(z0), cons(z1, z2)))) → c42(TOP(mark(cons(z1, take(z0, z2)))), ACTIVE(take(s(z0), cons(z1, z2)))) 278.97/89.53
TOP(ok(sel(0, cons(z0, z1)))) → c42(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 278.97/89.53
TOP(ok(sel(s(z0), cons(z1, z2)))) → c42(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 278.97/89.53
TOP(ok(from(z0))) → c42(TOP(from(active(z0))), ACTIVE(from(z0))) 278.97/89.53
TOP(ok(cons(z0, z1))) → c42(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 278.97/89.53
TOP(ok(s(z0))) → c42(TOP(s(active(z0))), ACTIVE(s(z0))) 278.97/89.53
TOP(ok(head(z0))) → c42(TOP(head(active(z0))), ACTIVE(head(z0))) 278.97/89.53
TOP(ok(2nd(z0))) → c42(TOP(2nd(active(z0))), ACTIVE(2nd(z0))) 278.97/89.53
TOP(ok(take(z0, z1))) → c42(TOP(take(active(z0), z1)), ACTIVE(take(z0, z1))) 278.97/89.53
TOP(ok(take(z0, z1))) → c42(TOP(take(z0, active(z1))), ACTIVE(take(z0, z1))) 278.97/89.53
TOP(ok(sel(z0, z1))) → c42(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 278.97/89.53
TOP(ok(sel(z0, z1))) → c42(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
278.97/89.53
278.97/89.53

(52) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.53
active(head(cons(z0, z1))) → mark(z0) 278.97/89.53
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.53
active(take(0, z0)) → mark(nil) 278.97/89.53
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.53
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.53
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.53
active(from(z0)) → from(active(z0)) 278.97/89.53
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.53
active(s(z0)) → s(active(z0)) 278.97/89.53
active(head(z0)) → head(active(z0)) 278.97/89.53
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.53
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.53
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.53
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.53
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.53
from(mark(z0)) → mark(from(z0)) 278.97/89.53
from(ok(z0)) → ok(from(z0)) 278.97/89.53
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.53
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.53
s(mark(z0)) → mark(s(z0)) 278.97/89.53
s(ok(z0)) → ok(s(z0)) 278.97/89.53
head(mark(z0)) → mark(head(z0)) 278.97/89.53
head(ok(z0)) → ok(head(z0)) 278.97/89.53
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.53
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.53
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.53
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.53
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.53
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.53
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.53
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.53
proper(from(z0)) → from(proper(z0)) 278.97/89.53
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.53
proper(s(z0)) → s(proper(z0)) 278.97/89.53
proper(head(z0)) → head(proper(z0)) 278.97/89.53
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.53
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.53
proper(0) → ok(0) 278.97/89.53
proper(nil) → ok(nil) 278.97/89.53
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.53
top(mark(z0)) → top(proper(z0)) 278.97/89.53
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.53
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.53
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.53
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.53
S(mark(z0)) → c20(S(z0)) 278.97/89.53
S(ok(z0)) → c21(S(z0)) 278.97/89.53
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.53
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.53
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.53
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.53
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.53
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.53
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.53
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.53
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.53
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.53
TOP(mark(0)) → c41(TOP(ok(0))) 278.97/89.53
TOP(mark(nil)) → c41(TOP(ok(nil)))
S tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.53
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.53
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.53
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.53
S(mark(z0)) → c20(S(z0)) 278.97/89.53
S(ok(z0)) → c21(S(z0)) 278.97/89.53
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.53
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.53
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.53
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.53
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.53
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.53
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.53
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.53
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.53
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.53
TOP(mark(0)) → c41(TOP(ok(0))) 278.97/89.53
TOP(mark(nil)) → c41(TOP(ok(nil)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

FROM, CONS, S, HEAD, 2ND, TAKE, SEL, TOP

Compound Symbols:

c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c41

278.97/89.53
278.97/89.53

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

Removed 2 trailing tuple parts
278.97/89.53
278.97/89.53

(54) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.53
active(head(cons(z0, z1))) → mark(z0) 278.97/89.53
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.53
active(take(0, z0)) → mark(nil) 278.97/89.53
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.53
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.53
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.53
active(from(z0)) → from(active(z0)) 278.97/89.53
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.53
active(s(z0)) → s(active(z0)) 278.97/89.53
active(head(z0)) → head(active(z0)) 278.97/89.53
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.53
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.53
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.53
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.53
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.53
from(mark(z0)) → mark(from(z0)) 278.97/89.53
from(ok(z0)) → ok(from(z0)) 278.97/89.53
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.53
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.53
s(mark(z0)) → mark(s(z0)) 278.97/89.53
s(ok(z0)) → ok(s(z0)) 278.97/89.53
head(mark(z0)) → mark(head(z0)) 278.97/89.53
head(ok(z0)) → ok(head(z0)) 278.97/89.53
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.53
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.53
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.53
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.53
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.53
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.53
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.53
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.53
proper(from(z0)) → from(proper(z0)) 278.97/89.53
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.53
proper(s(z0)) → s(proper(z0)) 278.97/89.53
proper(head(z0)) → head(proper(z0)) 278.97/89.53
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.54
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.54
proper(0) → ok(0) 278.97/89.54
proper(nil) → ok(nil) 278.97/89.54
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.54
top(mark(z0)) → top(proper(z0)) 278.97/89.54
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.54
TOP(mark(0)) → c41 278.97/89.54
TOP(mark(nil)) → c41
S tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.54
TOP(mark(0)) → c41 278.97/89.54
TOP(mark(nil)) → c41
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

FROM, CONS, S, HEAD, 2ND, TAKE, SEL, TOP

Compound Symbols:

c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c41

278.97/89.54
278.97/89.54

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

Removed 2 trailing nodes:

TOP(mark(nil)) → c41 278.97/89.54
TOP(mark(0)) → c41
278.97/89.54
278.97/89.54

(56) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.54
active(head(cons(z0, z1))) → mark(z0) 278.97/89.54
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.54
active(take(0, z0)) → mark(nil) 278.97/89.54
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.54
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.54
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.54
active(from(z0)) → from(active(z0)) 278.97/89.54
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.54
active(s(z0)) → s(active(z0)) 278.97/89.54
active(head(z0)) → head(active(z0)) 278.97/89.54
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.54
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.54
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.54
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.54
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.54
from(mark(z0)) → mark(from(z0)) 278.97/89.54
from(ok(z0)) → ok(from(z0)) 278.97/89.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.54
s(mark(z0)) → mark(s(z0)) 278.97/89.54
s(ok(z0)) → ok(s(z0)) 278.97/89.54
head(mark(z0)) → mark(head(z0)) 278.97/89.54
head(ok(z0)) → ok(head(z0)) 278.97/89.54
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.54
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.54
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.54
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.54
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.54
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.54
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.54
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.54
proper(from(z0)) → from(proper(z0)) 278.97/89.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.54
proper(s(z0)) → s(proper(z0)) 278.97/89.54
proper(head(z0)) → head(proper(z0)) 278.97/89.54
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.54
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.54
proper(0) → ok(0) 278.97/89.54
proper(nil) → ok(nil) 278.97/89.54
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.54
top(mark(z0)) → top(proper(z0)) 278.97/89.54
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
S tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

FROM, CONS, S, HEAD, 2ND, TAKE, SEL

Compound Symbols:

c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31

278.97/89.54
278.97/89.54

(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.

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0))
We considered the (Usable) Rules:none
And the Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 278.97/89.54

POL(2ND(x1)) = 0    278.97/89.54
POL(CONS(x1, x2)) = 0    278.97/89.54
POL(FROM(x1)) = [2]x1    278.97/89.54
POL(HEAD(x1)) = 0    278.97/89.54
POL(S(x1)) = 0    278.97/89.54
POL(SEL(x1, x2)) = 0    278.97/89.54
POL(TAKE(x1, x2)) = 0    278.97/89.54
POL(c16(x1)) = x1    278.97/89.54
POL(c17(x1)) = x1    278.97/89.54
POL(c18(x1)) = x1    278.97/89.54
POL(c19(x1)) = x1    278.97/89.54
POL(c20(x1)) = x1    278.97/89.54
POL(c21(x1)) = x1    278.97/89.54
POL(c22(x1)) = x1    278.97/89.54
POL(c23(x1)) = x1    278.97/89.54
POL(c24(x1)) = x1    278.97/89.54
POL(c25(x1)) = x1    278.97/89.54
POL(c26(x1)) = x1    278.97/89.54
POL(c27(x1)) = x1    278.97/89.54
POL(c28(x1)) = x1    278.97/89.54
POL(c29(x1)) = x1    278.97/89.54
POL(c30(x1)) = x1    278.97/89.54
POL(c31(x1)) = x1    278.97/89.54
POL(mark(x1)) = [1] + x1    278.97/89.54
POL(ok(x1)) = [1] + x1   
278.97/89.54
278.97/89.54

(58) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.54
active(head(cons(z0, z1))) → mark(z0) 278.97/89.54
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.54
active(take(0, z0)) → mark(nil) 278.97/89.54
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.54
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.54
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.54
active(from(z0)) → from(active(z0)) 278.97/89.54
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.54
active(s(z0)) → s(active(z0)) 278.97/89.54
active(head(z0)) → head(active(z0)) 278.97/89.54
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.54
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.54
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.54
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.54
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.54
from(mark(z0)) → mark(from(z0)) 278.97/89.54
from(ok(z0)) → ok(from(z0)) 278.97/89.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.54
s(mark(z0)) → mark(s(z0)) 278.97/89.54
s(ok(z0)) → ok(s(z0)) 278.97/89.54
head(mark(z0)) → mark(head(z0)) 278.97/89.54
head(ok(z0)) → ok(head(z0)) 278.97/89.54
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.54
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.54
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.54
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.54
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.54
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.54
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.54
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.54
proper(from(z0)) → from(proper(z0)) 278.97/89.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.54
proper(s(z0)) → s(proper(z0)) 278.97/89.54
proper(head(z0)) → head(proper(z0)) 278.97/89.54
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.54
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.54
proper(0) → ok(0) 278.97/89.54
proper(nil) → ok(nil) 278.97/89.54
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.54
top(mark(z0)) → top(proper(z0)) 278.97/89.54
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
S tuples:

CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
K tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0))
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

FROM, CONS, S, HEAD, 2ND, TAKE, SEL

Compound Symbols:

c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31

278.97/89.54
278.97/89.54

(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.

S(mark(z0)) → c20(S(z0))
We considered the (Usable) Rules:none
And the Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 278.97/89.54

POL(2ND(x1)) = 0    278.97/89.54
POL(CONS(x1, x2)) = 0    278.97/89.54
POL(FROM(x1)) = [3]x1    278.97/89.54
POL(HEAD(x1)) = 0    278.97/89.54
POL(S(x1)) = [2]x1    278.97/89.54
POL(SEL(x1, x2)) = 0    278.97/89.54
POL(TAKE(x1, x2)) = 0    278.97/89.54
POL(c16(x1)) = x1    278.97/89.54
POL(c17(x1)) = x1    278.97/89.54
POL(c18(x1)) = x1    278.97/89.54
POL(c19(x1)) = x1    278.97/89.54
POL(c20(x1)) = x1    278.97/89.54
POL(c21(x1)) = x1    278.97/89.54
POL(c22(x1)) = x1    278.97/89.54
POL(c23(x1)) = x1    278.97/89.54
POL(c24(x1)) = x1    278.97/89.54
POL(c25(x1)) = x1    278.97/89.54
POL(c26(x1)) = x1    278.97/89.54
POL(c27(x1)) = x1    278.97/89.54
POL(c28(x1)) = x1    278.97/89.54
POL(c29(x1)) = x1    278.97/89.54
POL(c30(x1)) = x1    278.97/89.54
POL(c31(x1)) = x1    278.97/89.54
POL(mark(x1)) = [1] + x1    278.97/89.54
POL(ok(x1)) = x1   
278.97/89.54
278.97/89.54

(60) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.54
active(head(cons(z0, z1))) → mark(z0) 278.97/89.54
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.54
active(take(0, z0)) → mark(nil) 278.97/89.54
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.54
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.54
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.54
active(from(z0)) → from(active(z0)) 278.97/89.54
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.54
active(s(z0)) → s(active(z0)) 278.97/89.54
active(head(z0)) → head(active(z0)) 278.97/89.54
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.54
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.54
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.54
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.54
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.54
from(mark(z0)) → mark(from(z0)) 278.97/89.54
from(ok(z0)) → ok(from(z0)) 278.97/89.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.54
s(mark(z0)) → mark(s(z0)) 278.97/89.54
s(ok(z0)) → ok(s(z0)) 278.97/89.54
head(mark(z0)) → mark(head(z0)) 278.97/89.54
head(ok(z0)) → ok(head(z0)) 278.97/89.54
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.54
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.54
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.54
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.54
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.54
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.54
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.54
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.54
proper(from(z0)) → from(proper(z0)) 278.97/89.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.54
proper(s(z0)) → s(proper(z0)) 278.97/89.54
proper(head(z0)) → head(proper(z0)) 278.97/89.54
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.54
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.54
proper(0) → ok(0) 278.97/89.54
proper(nil) → ok(nil) 278.97/89.54
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.54
top(mark(z0)) → top(proper(z0)) 278.97/89.54
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
S tuples:

CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
K tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
S(mark(z0)) → c20(S(z0))
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

FROM, CONS, S, HEAD, 2ND, TAKE, SEL

Compound Symbols:

c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31

278.97/89.54
278.97/89.54

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

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

S(ok(z0)) → c21(S(z0))
We considered the (Usable) Rules:none
And the Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 278.97/89.54

POL(2ND(x1)) = 0    278.97/89.54
POL(CONS(x1, x2)) = 0    278.97/89.54
POL(FROM(x1)) = [3]x1    278.97/89.54
POL(HEAD(x1)) = 0    278.97/89.54
POL(S(x1)) = x1    278.97/89.54
POL(SEL(x1, x2)) = 0    278.97/89.54
POL(TAKE(x1, x2)) = 0    278.97/89.54
POL(c16(x1)) = x1    278.97/89.54
POL(c17(x1)) = x1    278.97/89.54
POL(c18(x1)) = x1    278.97/89.54
POL(c19(x1)) = x1    278.97/89.54
POL(c20(x1)) = x1    278.97/89.54
POL(c21(x1)) = x1    278.97/89.54
POL(c22(x1)) = x1    278.97/89.54
POL(c23(x1)) = x1    278.97/89.54
POL(c24(x1)) = x1    278.97/89.54
POL(c25(x1)) = x1    278.97/89.54
POL(c26(x1)) = x1    278.97/89.54
POL(c27(x1)) = x1    278.97/89.54
POL(c28(x1)) = x1    278.97/89.54
POL(c29(x1)) = x1    278.97/89.54
POL(c30(x1)) = x1    278.97/89.54
POL(c31(x1)) = x1    278.97/89.54
POL(mark(x1)) = x1    278.97/89.54
POL(ok(x1)) = [1] + x1   
278.97/89.54
278.97/89.54

(62) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.54
active(head(cons(z0, z1))) → mark(z0) 278.97/89.54
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.54
active(take(0, z0)) → mark(nil) 278.97/89.54
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.54
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.54
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.54
active(from(z0)) → from(active(z0)) 278.97/89.54
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.54
active(s(z0)) → s(active(z0)) 278.97/89.54
active(head(z0)) → head(active(z0)) 278.97/89.54
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.54
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.54
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.54
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.54
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.54
from(mark(z0)) → mark(from(z0)) 278.97/89.54
from(ok(z0)) → ok(from(z0)) 278.97/89.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.54
s(mark(z0)) → mark(s(z0)) 278.97/89.54
s(ok(z0)) → ok(s(z0)) 278.97/89.54
head(mark(z0)) → mark(head(z0)) 278.97/89.54
head(ok(z0)) → ok(head(z0)) 278.97/89.54
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.54
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.54
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.54
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.54
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.54
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.54
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.54
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.54
proper(from(z0)) → from(proper(z0)) 278.97/89.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.54
proper(s(z0)) → s(proper(z0)) 278.97/89.54
proper(head(z0)) → head(proper(z0)) 278.97/89.54
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.54
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.54
proper(0) → ok(0) 278.97/89.54
proper(nil) → ok(nil) 278.97/89.54
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.54
top(mark(z0)) → top(proper(z0)) 278.97/89.54
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
S tuples:

CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
K tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0))
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

FROM, CONS, S, HEAD, 2ND, TAKE, SEL

Compound Symbols:

c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31

278.97/89.54
278.97/89.54

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

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

TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 278.97/89.54

POL(2ND(x1)) = 0    278.97/89.54
POL(CONS(x1, x2)) = 0    278.97/89.54
POL(FROM(x1)) = [5]x1    278.97/89.54
POL(HEAD(x1)) = 0    278.97/89.54
POL(S(x1)) = [5]x1    278.97/89.54
POL(SEL(x1, x2)) = x1    278.97/89.54
POL(TAKE(x1, x2)) = x1    278.97/89.54
POL(c16(x1)) = x1    278.97/89.54
POL(c17(x1)) = x1    278.97/89.54
POL(c18(x1)) = x1    278.97/89.54
POL(c19(x1)) = x1    278.97/89.54
POL(c20(x1)) = x1    278.97/89.54
POL(c21(x1)) = x1    278.97/89.54
POL(c22(x1)) = x1    278.97/89.54
POL(c23(x1)) = x1    278.97/89.54
POL(c24(x1)) = x1    278.97/89.54
POL(c25(x1)) = x1    278.97/89.54
POL(c26(x1)) = x1    278.97/89.54
POL(c27(x1)) = x1    278.97/89.54
POL(c28(x1)) = x1    278.97/89.54
POL(c29(x1)) = x1    278.97/89.54
POL(c30(x1)) = x1    278.97/89.54
POL(c31(x1)) = x1    278.97/89.54
POL(mark(x1)) = [1] + x1    278.97/89.54
POL(ok(x1)) = [1] + x1   
278.97/89.54
278.97/89.54

(64) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.54
active(head(cons(z0, z1))) → mark(z0) 278.97/89.54
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.54
active(take(0, z0)) → mark(nil) 278.97/89.54
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.54
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.54
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.54
active(from(z0)) → from(active(z0)) 278.97/89.54
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.54
active(s(z0)) → s(active(z0)) 278.97/89.54
active(head(z0)) → head(active(z0)) 278.97/89.54
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.54
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.54
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.54
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.54
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.54
from(mark(z0)) → mark(from(z0)) 278.97/89.54
from(ok(z0)) → ok(from(z0)) 278.97/89.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.54
s(mark(z0)) → mark(s(z0)) 278.97/89.54
s(ok(z0)) → ok(s(z0)) 278.97/89.54
head(mark(z0)) → mark(head(z0)) 278.97/89.54
head(ok(z0)) → ok(head(z0)) 278.97/89.54
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.54
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.54
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.54
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.54
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.54
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.54
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.54
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.54
proper(from(z0)) → from(proper(z0)) 278.97/89.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.54
proper(s(z0)) → s(proper(z0)) 278.97/89.54
proper(head(z0)) → head(proper(z0)) 278.97/89.54
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.54
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.54
proper(0) → ok(0) 278.97/89.54
proper(nil) → ok(nil) 278.97/89.54
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.54
top(mark(z0)) → top(proper(z0)) 278.97/89.54
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
S tuples:

CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1))
K tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

FROM, CONS, S, HEAD, 2ND, TAKE, SEL

Compound Symbols:

c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31

278.97/89.54
278.97/89.54

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

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

CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 278.97/89.54

POL(2ND(x1)) = 0    278.97/89.54
POL(CONS(x1, x2)) = [2]x1    278.97/89.54
POL(FROM(x1)) = [3]x1    278.97/89.54
POL(HEAD(x1)) = 0    278.97/89.54
POL(S(x1)) = [5]x1    278.97/89.54
POL(SEL(x1, x2)) = [5]x1 + x2    278.97/89.54
POL(TAKE(x1, x2)) = [3]x1 + [2]x2    278.97/89.54
POL(c16(x1)) = x1    278.97/89.54
POL(c17(x1)) = x1    278.97/89.54
POL(c18(x1)) = x1    278.97/89.54
POL(c19(x1)) = x1    278.97/89.54
POL(c20(x1)) = x1    278.97/89.54
POL(c21(x1)) = x1    278.97/89.54
POL(c22(x1)) = x1    278.97/89.54
POL(c23(x1)) = x1    278.97/89.54
POL(c24(x1)) = x1    278.97/89.54
POL(c25(x1)) = x1    278.97/89.54
POL(c26(x1)) = x1    278.97/89.54
POL(c27(x1)) = x1    278.97/89.54
POL(c28(x1)) = x1    278.97/89.54
POL(c29(x1)) = x1    278.97/89.54
POL(c30(x1)) = x1    278.97/89.54
POL(c31(x1)) = x1    278.97/89.54
POL(mark(x1)) = [1] + x1    278.97/89.54
POL(ok(x1)) = [1] + x1   
278.97/89.54
278.97/89.54

(66) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.54
active(head(cons(z0, z1))) → mark(z0) 278.97/89.54
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.54
active(take(0, z0)) → mark(nil) 278.97/89.54
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.54
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.54
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.54
active(from(z0)) → from(active(z0)) 278.97/89.54
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.54
active(s(z0)) → s(active(z0)) 278.97/89.54
active(head(z0)) → head(active(z0)) 278.97/89.54
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.54
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.54
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.54
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.54
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.54
from(mark(z0)) → mark(from(z0)) 278.97/89.54
from(ok(z0)) → ok(from(z0)) 278.97/89.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.54
s(mark(z0)) → mark(s(z0)) 278.97/89.54
s(ok(z0)) → ok(s(z0)) 278.97/89.54
head(mark(z0)) → mark(head(z0)) 278.97/89.54
head(ok(z0)) → ok(head(z0)) 278.97/89.54
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.54
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.54
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.54
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.54
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.54
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.54
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.54
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.54
proper(from(z0)) → from(proper(z0)) 278.97/89.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.54
proper(s(z0)) → s(proper(z0)) 278.97/89.54
proper(head(z0)) → head(proper(z0)) 278.97/89.54
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.54
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.54
proper(0) → ok(0) 278.97/89.54
proper(nil) → ok(nil) 278.97/89.54
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.54
top(mark(z0)) → top(proper(z0)) 278.97/89.54
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
S tuples:

HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0))
K tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1))
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

FROM, CONS, S, HEAD, 2ND, TAKE, SEL

Compound Symbols:

c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31

278.97/89.54
278.97/89.54

(67) 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.

2ND(mark(z0)) → c24(2ND(z0))
We considered the (Usable) Rules:none
And the Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 278.97/89.54

POL(2ND(x1)) = x1    278.97/89.54
POL(CONS(x1, x2)) = [3]x1 + [5]x2    278.97/89.54
POL(FROM(x1)) = [3]x1    278.97/89.54
POL(HEAD(x1)) = 0    278.97/89.54
POL(S(x1)) = [3]x1    278.97/89.54
POL(SEL(x1, x2)) = [3]x1 + [3]x2    278.97/89.54
POL(TAKE(x1, x2)) = [3]x1 + [3]x2    278.97/89.54
POL(c16(x1)) = x1    278.97/89.54
POL(c17(x1)) = x1    278.97/89.54
POL(c18(x1)) = x1    278.97/89.54
POL(c19(x1)) = x1    278.97/89.54
POL(c20(x1)) = x1    278.97/89.54
POL(c21(x1)) = x1    278.97/89.54
POL(c22(x1)) = x1    278.97/89.54
POL(c23(x1)) = x1    278.97/89.54
POL(c24(x1)) = x1    278.97/89.54
POL(c25(x1)) = x1    278.97/89.54
POL(c26(x1)) = x1    278.97/89.54
POL(c27(x1)) = x1    278.97/89.54
POL(c28(x1)) = x1    278.97/89.54
POL(c29(x1)) = x1    278.97/89.54
POL(c30(x1)) = x1    278.97/89.54
POL(c31(x1)) = x1    278.97/89.54
POL(mark(x1)) = [1] + x1    278.97/89.54
POL(ok(x1)) = x1   
278.97/89.54
278.97/89.54

(68) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.54
active(head(cons(z0, z1))) → mark(z0) 278.97/89.54
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.54
active(take(0, z0)) → mark(nil) 278.97/89.54
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.54
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.54
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.54
active(from(z0)) → from(active(z0)) 278.97/89.54
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.54
active(s(z0)) → s(active(z0)) 278.97/89.54
active(head(z0)) → head(active(z0)) 278.97/89.54
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.54
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.54
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.54
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.54
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.54
from(mark(z0)) → mark(from(z0)) 278.97/89.54
from(ok(z0)) → ok(from(z0)) 278.97/89.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.54
s(mark(z0)) → mark(s(z0)) 278.97/89.54
s(ok(z0)) → ok(s(z0)) 278.97/89.54
head(mark(z0)) → mark(head(z0)) 278.97/89.54
head(ok(z0)) → ok(head(z0)) 278.97/89.54
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.54
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.54
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.54
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.54
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.54
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.54
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.54
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.54
proper(from(z0)) → from(proper(z0)) 278.97/89.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.54
proper(s(z0)) → s(proper(z0)) 278.97/89.54
proper(head(z0)) → head(proper(z0)) 278.97/89.54
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.54
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.54
proper(0) → ok(0) 278.97/89.54
proper(nil) → ok(nil) 278.97/89.54
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.54
top(mark(z0)) → top(proper(z0)) 278.97/89.54
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
S tuples:

HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0))
K tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0))
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

FROM, CONS, S, HEAD, 2ND, TAKE, SEL

Compound Symbols:

c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31

278.97/89.54
278.97/89.54

(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.

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

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 278.97/89.54

POL(2ND(x1)) = x1    278.97/89.54
POL(CONS(x1, x2)) = x1 + x2 + [3]x22 + [3]x1·x2 + [3]x12    278.97/89.54
POL(FROM(x1)) = [3]x1 + [3]x12    278.97/89.54
POL(HEAD(x1)) = x12    278.97/89.54
POL(S(x1)) = [3]x1 + [3]x12    278.97/89.54
POL(SEL(x1, x2)) = x1 + x2 + [3]x22 + [3]x1·x2 + [3]x12    278.97/89.54
POL(TAKE(x1, x2)) = x1 + x2 + [3]x22 + [3]x1·x2 + [3]x12    278.97/89.54
POL(c16(x1)) = x1    278.97/89.54
POL(c17(x1)) = x1    278.97/89.54
POL(c18(x1)) = x1    278.97/89.54
POL(c19(x1)) = x1    278.97/89.54
POL(c20(x1)) = x1    278.97/89.54
POL(c21(x1)) = x1    278.97/89.54
POL(c22(x1)) = x1    278.97/89.54
POL(c23(x1)) = x1    278.97/89.54
POL(c24(x1)) = x1    278.97/89.54
POL(c25(x1)) = x1    278.97/89.54
POL(c26(x1)) = x1    278.97/89.54
POL(c27(x1)) = x1    278.97/89.54
POL(c28(x1)) = x1    278.97/89.54
POL(c29(x1)) = x1    278.97/89.54
POL(c30(x1)) = x1    278.97/89.54
POL(c31(x1)) = x1    278.97/89.54
POL(mark(x1)) = [1] + x1    278.97/89.54
POL(ok(x1)) = x1   
278.97/89.54
278.97/89.54

(70) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.54
active(head(cons(z0, z1))) → mark(z0) 278.97/89.54
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.54
active(take(0, z0)) → mark(nil) 278.97/89.54
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.54
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.54
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.54
active(from(z0)) → from(active(z0)) 278.97/89.54
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.54
active(s(z0)) → s(active(z0)) 278.97/89.54
active(head(z0)) → head(active(z0)) 278.97/89.54
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.54
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.54
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.54
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.54
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.54
from(mark(z0)) → mark(from(z0)) 278.97/89.54
from(ok(z0)) → ok(from(z0)) 278.97/89.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.54
s(mark(z0)) → mark(s(z0)) 278.97/89.54
s(ok(z0)) → ok(s(z0)) 278.97/89.54
head(mark(z0)) → mark(head(z0)) 278.97/89.54
head(ok(z0)) → ok(head(z0)) 278.97/89.54
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.54
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.54
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.54
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.54
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.54
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.54
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.54
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.54
proper(from(z0)) → from(proper(z0)) 278.97/89.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.54
proper(s(z0)) → s(proper(z0)) 278.97/89.54
proper(head(z0)) → head(proper(z0)) 278.97/89.54
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.54
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.54
proper(0) → ok(0) 278.97/89.54
proper(nil) → ok(nil) 278.97/89.54
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.54
top(mark(z0)) → top(proper(z0)) 278.97/89.54
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
S tuples:

HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0))
K tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0))
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

FROM, CONS, S, HEAD, 2ND, TAKE, SEL

Compound Symbols:

c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31

278.97/89.54
278.97/89.54

(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.

2ND(ok(z0)) → c25(2ND(z0))
We considered the (Usable) Rules:none
And the Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 278.97/89.54

POL(2ND(x1)) = x1    278.97/89.54
POL(CONS(x1, x2)) = [5]x1 + [5]x2    278.97/89.54
POL(FROM(x1)) = [5]x1    278.97/89.54
POL(HEAD(x1)) = 0    278.97/89.54
POL(S(x1)) = [3]x1    278.97/89.54
POL(SEL(x1, x2)) = [5]x1 + [5]x2    278.97/89.54
POL(TAKE(x1, x2)) = [5]x1 + [5]x2    278.97/89.54
POL(c16(x1)) = x1    278.97/89.54
POL(c17(x1)) = x1    278.97/89.54
POL(c18(x1)) = x1    278.97/89.54
POL(c19(x1)) = x1    278.97/89.54
POL(c20(x1)) = x1    278.97/89.54
POL(c21(x1)) = x1    278.97/89.54
POL(c22(x1)) = x1    278.97/89.54
POL(c23(x1)) = x1    278.97/89.54
POL(c24(x1)) = x1    278.97/89.54
POL(c25(x1)) = x1    278.97/89.54
POL(c26(x1)) = x1    278.97/89.54
POL(c27(x1)) = x1    278.97/89.54
POL(c28(x1)) = x1    278.97/89.54
POL(c29(x1)) = x1    278.97/89.54
POL(c30(x1)) = x1    278.97/89.54
POL(c31(x1)) = x1    278.97/89.54
POL(mark(x1)) = x1    278.97/89.54
POL(ok(x1)) = [1] + x1   
278.97/89.54
278.97/89.54

(72) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.54
active(head(cons(z0, z1))) → mark(z0) 278.97/89.54
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.54
active(take(0, z0)) → mark(nil) 278.97/89.54
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.54
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.54
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.54
active(from(z0)) → from(active(z0)) 278.97/89.54
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.54
active(s(z0)) → s(active(z0)) 278.97/89.54
active(head(z0)) → head(active(z0)) 278.97/89.54
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.54
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.54
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.54
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.54
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.54
from(mark(z0)) → mark(from(z0)) 278.97/89.54
from(ok(z0)) → ok(from(z0)) 278.97/89.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.54
s(mark(z0)) → mark(s(z0)) 278.97/89.54
s(ok(z0)) → ok(s(z0)) 278.97/89.54
head(mark(z0)) → mark(head(z0)) 278.97/89.54
head(ok(z0)) → ok(head(z0)) 278.97/89.54
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.54
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.54
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.54
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.54
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.54
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.54
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.54
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.54
proper(from(z0)) → from(proper(z0)) 278.97/89.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.54
proper(s(z0)) → s(proper(z0)) 278.97/89.54
proper(head(z0)) → head(proper(z0)) 278.97/89.54
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.54
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.54
proper(0) → ok(0) 278.97/89.54
proper(nil) → ok(nil) 278.97/89.54
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.54
top(mark(z0)) → top(proper(z0)) 278.97/89.54
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
S tuples:

HEAD(ok(z0)) → c23(HEAD(z0))
K tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0))
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

FROM, CONS, S, HEAD, 2ND, TAKE, SEL

Compound Symbols:

c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31

278.97/89.54
278.97/89.54

(73) 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.

HEAD(ok(z0)) → c23(HEAD(z0))
We considered the (Usable) Rules:none
And the Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 278.97/89.54

POL(2ND(x1)) = [5]x1    278.97/89.54
POL(CONS(x1, x2)) = [3]x1 + [5]x2    278.97/89.54
POL(FROM(x1)) = [5]x1    278.97/89.54
POL(HEAD(x1)) = [3]x1    278.97/89.54
POL(S(x1)) = [5]x1    278.97/89.54
POL(SEL(x1, x2)) = [3]x1 + [5]x2    278.97/89.54
POL(TAKE(x1, x2)) = [3]x1 + [3]x2    278.97/89.54
POL(c16(x1)) = x1    278.97/89.54
POL(c17(x1)) = x1    278.97/89.54
POL(c18(x1)) = x1    278.97/89.54
POL(c19(x1)) = x1    278.97/89.54
POL(c20(x1)) = x1    278.97/89.54
POL(c21(x1)) = x1    278.97/89.54
POL(c22(x1)) = x1    278.97/89.54
POL(c23(x1)) = x1    278.97/89.54
POL(c24(x1)) = x1    278.97/89.54
POL(c25(x1)) = x1    278.97/89.54
POL(c26(x1)) = x1    278.97/89.54
POL(c27(x1)) = x1    278.97/89.54
POL(c28(x1)) = x1    278.97/89.54
POL(c29(x1)) = x1    278.97/89.54
POL(c30(x1)) = x1    278.97/89.54
POL(c31(x1)) = x1    278.97/89.54
POL(mark(x1)) = x1    278.97/89.54
POL(ok(x1)) = [1] + x1   
278.97/89.54
278.97/89.54

(74) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 278.97/89.54
active(head(cons(z0, z1))) → mark(z0) 278.97/89.54
active(2nd(cons(z0, z1))) → mark(head(z1)) 278.97/89.54
active(take(0, z0)) → mark(nil) 278.97/89.54
active(take(s(z0), cons(z1, z2))) → mark(cons(z1, take(z0, z2))) 278.97/89.54
active(sel(0, cons(z0, z1))) → mark(z0) 278.97/89.54
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 278.97/89.54
active(from(z0)) → from(active(z0)) 278.97/89.54
active(cons(z0, z1)) → cons(active(z0), z1) 278.97/89.54
active(s(z0)) → s(active(z0)) 278.97/89.54
active(head(z0)) → head(active(z0)) 278.97/89.54
active(2nd(z0)) → 2nd(active(z0)) 278.97/89.54
active(take(z0, z1)) → take(active(z0), z1) 278.97/89.54
active(take(z0, z1)) → take(z0, active(z1)) 278.97/89.54
active(sel(z0, z1)) → sel(active(z0), z1) 278.97/89.54
active(sel(z0, z1)) → sel(z0, active(z1)) 278.97/89.54
from(mark(z0)) → mark(from(z0)) 278.97/89.54
from(ok(z0)) → ok(from(z0)) 278.97/89.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 278.97/89.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 278.97/89.54
s(mark(z0)) → mark(s(z0)) 278.97/89.54
s(ok(z0)) → ok(s(z0)) 278.97/89.54
head(mark(z0)) → mark(head(z0)) 278.97/89.54
head(ok(z0)) → ok(head(z0)) 278.97/89.54
2nd(mark(z0)) → mark(2nd(z0)) 278.97/89.54
2nd(ok(z0)) → ok(2nd(z0)) 278.97/89.54
take(mark(z0), z1) → mark(take(z0, z1)) 278.97/89.54
take(z0, mark(z1)) → mark(take(z0, z1)) 278.97/89.54
take(ok(z0), ok(z1)) → ok(take(z0, z1)) 278.97/89.54
sel(mark(z0), z1) → mark(sel(z0, z1)) 278.97/89.54
sel(z0, mark(z1)) → mark(sel(z0, z1)) 278.97/89.54
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 278.97/89.54
proper(from(z0)) → from(proper(z0)) 278.97/89.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 278.97/89.54
proper(s(z0)) → s(proper(z0)) 278.97/89.54
proper(head(z0)) → head(proper(z0)) 278.97/89.54
proper(2nd(z0)) → 2nd(proper(z0)) 278.97/89.54
proper(take(z0, z1)) → take(proper(z0), proper(z1)) 278.97/89.54
proper(0) → ok(0) 278.97/89.54
proper(nil) → ok(nil) 278.97/89.54
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 278.97/89.54
top(mark(z0)) → top(proper(z0)) 278.97/89.54
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1))
S tuples:none
K tuples:

FROM(mark(z0)) → c16(FROM(z0)) 278.97/89.54
FROM(ok(z0)) → c17(FROM(z0)) 278.97/89.54
S(mark(z0)) → c20(S(z0)) 278.97/89.54
S(ok(z0)) → c21(S(z0)) 278.97/89.54
TAKE(mark(z0), z1) → c26(TAKE(z0, z1)) 278.97/89.54
TAKE(ok(z0), ok(z1)) → c28(TAKE(z0, z1)) 278.97/89.54
SEL(mark(z0), z1) → c29(SEL(z0, z1)) 278.97/89.54
SEL(ok(z0), ok(z1)) → c31(SEL(z0, z1)) 278.97/89.54
CONS(mark(z0), z1) → c18(CONS(z0, z1)) 278.97/89.54
CONS(ok(z0), ok(z1)) → c19(CONS(z0, z1)) 278.97/89.54
TAKE(z0, mark(z1)) → c27(TAKE(z0, z1)) 278.97/89.54
SEL(z0, mark(z1)) → c30(SEL(z0, z1)) 278.97/89.54
2ND(mark(z0)) → c24(2ND(z0)) 278.97/89.54
HEAD(mark(z0)) → c22(HEAD(z0)) 278.97/89.54
2ND(ok(z0)) → c25(2ND(z0)) 278.97/89.54
HEAD(ok(z0)) → c23(HEAD(z0))
Defined Rule Symbols:

active, from, cons, s, head, 2nd, take, sel, proper, top

Defined Pair Symbols:

FROM, CONS, S, HEAD, 2ND, TAKE, SEL

Compound Symbols:

c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31

278.97/89.54
278.97/89.54

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

The set S is empty
278.97/89.54
278.97/89.54

(76) BOUNDS(O(1), O(1))

278.97/89.54
278.97/89.54
279.14/89.62 EOF