217.68/71.37 Runtime Complexity (innermost) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml.xml

217.68/71.37

217.68/71.37
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(n^3)).

0 CpxTRS

217.68/71.37

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

217.68/71.37

↳2 CdtProblem

217.68/71.37

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

217.68/71.37

↳4 CdtProblem

217.68/71.37

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

217.68/71.37

↳6 CdtProblem

217.68/71.37

↳7 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))

217.68/71.37

↳8 CdtProblem

217.68/71.37

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

217.68/71.37

↳10 CdtProblem

217.68/71.37

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

217.68/71.37

↳12 CdtProblem

217.68/71.37

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

217.68/71.37

↳14 CdtProblem

217.68/71.37

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

217.68/71.37

↳16 CdtProblem

217.68/71.37

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

217.68/71.37

↳18 CdtProblem

217.68/71.37

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

217.68/71.37

↳20 CdtProblem

217.68/71.37

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

217.68/71.37

↳22 CdtProblem

217.68/71.37

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

217.68/71.37

↳24 CdtProblem

217.68/71.37

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

217.68/71.37

↳26 CdtProblem

217.68/71.37

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

217.68/71.37

↳28 CdtProblem

217.68/71.37

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

217.68/71.37

↳30 CdtProblem

217.68/71.37

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

217.68/71.37

↳32 CdtProblem

217.68/71.37

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

217.68/71.37

↳34 CdtProblem

217.68/71.37

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

217.68/71.37

↳36 CdtProblem

217.68/71.37

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

217.68/71.37

↳38 CdtProblem

217.68/71.37

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

217.68/71.37

↳40 CdtProblem

217.68/71.37

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

217.68/71.37

↳42 CdtProblem

217.68/71.37

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

217.68/71.37

↳44 CdtProblem

217.68/71.37

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

217.68/71.37

↳46 CdtProblem

217.68/71.37

↳47 CdtUnreachableProof (⇔)

217.68/71.37

↳48 CdtProblem

217.68/71.37

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

217.68/71.37

↳50 CdtProblem

217.68/71.37

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

217.68/71.37

↳52 CdtProblem

217.68/71.37

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

217.68/71.37

↳54 CdtProblem

217.68/71.37

↳55 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^3))))

217.68/71.37

↳56 CdtProblem

217.68/71.37

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

217.68/71.37

↳58 CdtProblem

217.68/71.37

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

217.68/71.37

↳60 CdtProblem

217.68/71.37

↳61 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))

217.68/71.37

↳62 CdtProblem

217.68/71.37

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

217.68/71.37

↳64 CdtProblem

217.68/71.37

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

217.68/71.37

↳66 CdtProblem

217.68/71.37

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

217.68/71.37

↳68 BOUNDS(O(1), O(1))

217.68/71.37

217.68/71.37 217.68/71.37

217.68/71.37

(0) Obligation:

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

active(fst(0, Z)) → mark(nil) 218.05/71.41
active(fst(s(X), cons(Y, Z))) → mark(cons(Y, fst(X, Z))) 218.05/71.41
active(from(X)) → mark(cons(X, from(s(X)))) 218.05/71.41
active(add(0, X)) → mark(X) 218.05/71.41
active(add(s(X), Y)) → mark(s(add(X, Y))) 218.05/71.41
active(len(nil)) → mark(0) 218.05/71.41
active(len(cons(X, Z))) → mark(s(len(Z))) 218.05/71.41
active(cons(X1, X2)) → cons(active(X1), X2) 218.05/71.41
active(fst(X1, X2)) → fst(active(X1), X2) 218.05/71.41
active(fst(X1, X2)) → fst(X1, active(X2)) 218.05/71.41
active(from(X)) → from(active(X)) 218.05/71.41
active(add(X1, X2)) → add(active(X1), X2) 218.05/71.41
active(add(X1, X2)) → add(X1, active(X2)) 218.05/71.41
active(len(X)) → len(active(X)) 218.05/71.41
cons(mark(X1), X2) → mark(cons(X1, X2)) 218.05/71.41
fst(mark(X1), X2) → mark(fst(X1, X2)) 218.05/71.41
fst(X1, mark(X2)) → mark(fst(X1, X2)) 218.05/71.41
from(mark(X)) → mark(from(X)) 218.05/71.41
add(mark(X1), X2) → mark(add(X1, X2)) 218.05/71.41
add(X1, mark(X2)) → mark(add(X1, X2)) 218.05/71.41
len(mark(X)) → mark(len(X)) 218.05/71.41
proper(0) → ok(0) 218.05/71.41
proper(s(X)) → s(proper(X)) 218.05/71.41
proper(nil) → ok(nil) 218.05/71.41
proper(cons(X1, X2)) → cons(proper(X1), proper(X2)) 218.05/71.41
proper(fst(X1, X2)) → fst(proper(X1), proper(X2)) 218.05/71.41
proper(from(X)) → from(proper(X)) 218.05/71.41
proper(add(X1, X2)) → add(proper(X1), proper(X2)) 218.05/71.41
proper(len(X)) → len(proper(X)) 218.05/71.41
s(ok(X)) → ok(s(X)) 218.05/71.41
cons(ok(X1), ok(X2)) → ok(cons(X1, X2)) 218.05/71.41
fst(ok(X1), ok(X2)) → ok(fst(X1, X2)) 218.05/71.41
from(ok(X)) → ok(from(X)) 218.05/71.41
add(ok(X1), ok(X2)) → ok(add(X1, X2)) 218.05/71.41
len(ok(X)) → ok(len(X)) 218.05/71.41
top(mark(X)) → top(proper(X)) 218.05/71.41
top(ok(X)) → top(active(X))

Rewrite Strategy: INNERMOST

218.05/71.41

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

Converted CpxTRS to CDT

218.05/71.41

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.05/71.41
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.05/71.41
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.05/71.41
active(add(0, z0)) → mark(z0) 218.05/71.41
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.05/71.41
active(len(nil)) → mark(0) 218.05/71.41
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.05/71.41
active(cons(z0, z1)) → cons(active(z0), z1) 218.05/71.41
active(fst(z0, z1)) → fst(active(z0), z1) 218.05/71.41
active(fst(z0, z1)) → fst(z0, active(z1)) 218.05/71.41
active(from(z0)) → from(active(z0)) 218.05/71.41
active(add(z0, z1)) → add(active(z0), z1) 218.05/71.41
active(add(z0, z1)) → add(z0, active(z1)) 218.05/71.41
active(len(z0)) → len(active(z0)) 218.05/71.41
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.05/71.41
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.05/71.41
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.05/71.41
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.05/71.41
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.05/71.41
from(mark(z0)) → mark(from(z0)) 218.05/71.41
from(ok(z0)) → ok(from(z0)) 218.05/71.41
add(mark(z0), z1) → mark(add(z0, z1)) 218.05/71.41
add(z0, mark(z1)) → mark(add(z0, z1)) 218.05/71.41
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.05/71.41
len(mark(z0)) → mark(len(z0)) 218.05/71.41
len(ok(z0)) → ok(len(z0)) 218.05/71.41
proper(0) → ok(0) 218.05/71.41
proper(s(z0)) → s(proper(z0)) 218.05/71.41
proper(nil) → ok(nil) 218.05/71.41
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.05/71.41
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.05/71.41
proper(from(z0)) → from(proper(z0)) 218.05/71.41
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.05/71.41
proper(len(z0)) → len(proper(z0)) 218.05/71.41
s(ok(z0)) → ok(s(z0)) 218.05/71.41
top(mark(z0)) → top(proper(z0)) 218.05/71.41
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(s(z0), cons(z1, z2))) → c1(CONS(z1, fst(z0, z2)), FST(z0, z2)) 218.05/71.41
ACTIVE(from(z0)) → c2(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0)) 218.05/71.41
ACTIVE(add(s(z0), z1)) → c4(S(add(z0, z1)), ADD(z0, z1)) 218.05/71.41
ACTIVE(len(cons(z0, z1))) → c6(S(len(z1)), LEN(z1)) 218.05/71.41
ACTIVE(cons(z0, z1)) → c7(CONS(active(z0), z1), ACTIVE(z0)) 218.05/71.41
ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.05/71.41
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.05/71.41
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 218.05/71.41
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.05/71.41
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.05/71.41
ACTIVE(len(z0)) → c13(LEN(active(z0)), ACTIVE(z0)) 218.05/71.41
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.05/71.41
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.05/71.41
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.05/71.41
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.05/71.41
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.05/71.41
FROM(mark(z0)) → c19(FROM(z0)) 218.05/71.41
FROM(ok(z0)) → c20(FROM(z0)) 218.05/71.41
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.05/71.41
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.05/71.41
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.05/71.41
LEN(mark(z0)) → c24(LEN(z0)) 218.05/71.41
LEN(ok(z0)) → c25(LEN(z0)) 218.05/71.41
PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) 218.05/71.41
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.41
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.41
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.05/71.41
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.41
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.05/71.41
S(ok(z0)) → c34(S(z0)) 218.05/71.41
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.05/71.41
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0))

S tuples:

ACTIVE(fst(s(z0), cons(z1, z2))) → c1(CONS(z1, fst(z0, z2)), FST(z0, z2)) 218.05/71.41
ACTIVE(from(z0)) → c2(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0)) 218.05/71.41
ACTIVE(add(s(z0), z1)) → c4(S(add(z0, z1)), ADD(z0, z1)) 218.05/71.41
ACTIVE(len(cons(z0, z1))) → c6(S(len(z1)), LEN(z1)) 218.05/71.41
ACTIVE(cons(z0, z1)) → c7(CONS(active(z0), z1), ACTIVE(z0)) 218.05/71.41
ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.05/71.41
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.05/71.41
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 218.05/71.41
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.05/71.41
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.05/71.41
ACTIVE(len(z0)) → c13(LEN(active(z0)), ACTIVE(z0)) 218.05/71.41
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.05/71.41
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.05/71.41
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.05/71.41
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.05/71.41
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.05/71.41
FROM(mark(z0)) → c19(FROM(z0)) 218.05/71.41
FROM(ok(z0)) → c20(FROM(z0)) 218.05/71.41
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.05/71.41
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.05/71.41
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.05/71.41
LEN(mark(z0)) → c24(LEN(z0)) 218.05/71.41
LEN(ok(z0)) → c25(LEN(z0)) 218.05/71.41
PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) 218.05/71.41
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.41
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.41
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.05/71.41
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.41
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.05/71.41
S(ok(z0)) → c34(S(z0)) 218.05/71.41
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.05/71.41
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0))

K tuples:none
Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c1, c2, c4, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c27, c29, c30, c31, c32, c33, c34, c35, c36

218.05/71.41

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

Removed 1 trailing tuple parts

218.05/71.41

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.05/71.41
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.05/71.41
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.05/71.41
active(add(0, z0)) → mark(z0) 218.05/71.41
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.05/71.41
active(len(nil)) → mark(0) 218.05/71.41
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.05/71.41
active(cons(z0, z1)) → cons(active(z0), z1) 218.05/71.41
active(fst(z0, z1)) → fst(active(z0), z1) 218.05/71.41
active(fst(z0, z1)) → fst(z0, active(z1)) 218.05/71.41
active(from(z0)) → from(active(z0)) 218.05/71.41
active(add(z0, z1)) → add(active(z0), z1) 218.05/71.41
active(add(z0, z1)) → add(z0, active(z1)) 218.05/71.41
active(len(z0)) → len(active(z0)) 218.05/71.41
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.05/71.41
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.05/71.41
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.05/71.41
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.05/71.41
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.05/71.41
from(mark(z0)) → mark(from(z0)) 218.05/71.41
from(ok(z0)) → ok(from(z0)) 218.05/71.41
add(mark(z0), z1) → mark(add(z0, z1)) 218.05/71.41
add(z0, mark(z1)) → mark(add(z0, z1)) 218.05/71.41
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.05/71.41
len(mark(z0)) → mark(len(z0)) 218.05/71.41
len(ok(z0)) → ok(len(z0)) 218.05/71.41
proper(0) → ok(0) 218.05/71.41
proper(s(z0)) → s(proper(z0)) 218.05/71.41
proper(nil) → ok(nil) 218.05/71.41
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.05/71.41
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.05/71.41
proper(from(z0)) → from(proper(z0)) 218.05/71.41
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.05/71.41
proper(len(z0)) → len(proper(z0)) 218.05/71.41
s(ok(z0)) → ok(s(z0)) 218.05/71.41
top(mark(z0)) → top(proper(z0)) 218.05/71.41
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(s(z0), cons(z1, z2))) → c1(CONS(z1, fst(z0, z2)), FST(z0, z2)) 218.05/71.41
ACTIVE(add(s(z0), z1)) → c4(S(add(z0, z1)), ADD(z0, z1)) 218.05/71.41
ACTIVE(len(cons(z0, z1))) → c6(S(len(z1)), LEN(z1)) 218.05/71.41
ACTIVE(cons(z0, z1)) → c7(CONS(active(z0), z1), ACTIVE(z0)) 218.05/71.41
ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.05/71.41
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.05/71.41
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 218.05/71.41
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.05/71.41
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.05/71.41
ACTIVE(len(z0)) → c13(LEN(active(z0)), ACTIVE(z0)) 218.05/71.41
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.05/71.41
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.05/71.41
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.05/71.41
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.05/71.41
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.05/71.41
FROM(mark(z0)) → c19(FROM(z0)) 218.05/71.41
FROM(ok(z0)) → c20(FROM(z0)) 218.05/71.41
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.05/71.41
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.05/71.41
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.05/71.41
LEN(mark(z0)) → c24(LEN(z0)) 218.05/71.41
LEN(ok(z0)) → c25(LEN(z0)) 218.05/71.41
PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) 218.05/71.41
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.41
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.41
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.05/71.41
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.41
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.05/71.41
S(ok(z0)) → c34(S(z0)) 218.05/71.41
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.05/71.41
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.05/71.41
ACTIVE(from(z0)) → c2(CONS(z0, from(s(z0))), S(z0))

S tuples:

ACTIVE(fst(s(z0), cons(z1, z2))) → c1(CONS(z1, fst(z0, z2)), FST(z0, z2)) 218.05/71.41
ACTIVE(add(s(z0), z1)) → c4(S(add(z0, z1)), ADD(z0, z1)) 218.05/71.41
ACTIVE(len(cons(z0, z1))) → c6(S(len(z1)), LEN(z1)) 218.05/71.41
ACTIVE(cons(z0, z1)) → c7(CONS(active(z0), z1), ACTIVE(z0)) 218.05/71.49
ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.05/71.49
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.05/71.49
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 218.05/71.49
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.05/71.49
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.05/71.49
ACTIVE(len(z0)) → c13(LEN(active(z0)), ACTIVE(z0)) 218.05/71.49
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.05/71.49
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.05/71.49
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.05/71.49
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.05/71.49
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.05/71.49
FROM(mark(z0)) → c19(FROM(z0)) 218.05/71.49
FROM(ok(z0)) → c20(FROM(z0)) 218.05/71.49
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.05/71.49
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.05/71.49
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.05/71.49
LEN(mark(z0)) → c24(LEN(z0)) 218.05/71.49
LEN(ok(z0)) → c25(LEN(z0)) 218.05/71.49
PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) 218.05/71.49
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.49
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.49
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.05/71.49
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.49
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.05/71.49
S(ok(z0)) → c34(S(z0)) 218.05/71.49
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.05/71.49
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.05/71.49
ACTIVE(from(z0)) → c2(CONS(z0, from(s(z0))), S(z0))

K tuples:none
Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c1, c4, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c27, c29, c30, c31, c32, c33, c34, c35, c36, c2

218.05/71.49

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

Split RHS of tuples not part of any SCC

218.05/71.49

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.05/71.49
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.05/71.49
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.05/71.49
active(add(0, z0)) → mark(z0) 218.05/71.49
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.05/71.49
active(len(nil)) → mark(0) 218.05/71.49
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.05/71.49
active(cons(z0, z1)) → cons(active(z0), z1) 218.05/71.49
active(fst(z0, z1)) → fst(active(z0), z1) 218.05/71.49
active(fst(z0, z1)) → fst(z0, active(z1)) 218.05/71.49
active(from(z0)) → from(active(z0)) 218.05/71.49
active(add(z0, z1)) → add(active(z0), z1) 218.05/71.49
active(add(z0, z1)) → add(z0, active(z1)) 218.05/71.49
active(len(z0)) → len(active(z0)) 218.05/71.49
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.05/71.49
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.05/71.49
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.05/71.49
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.05/71.49
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.05/71.49
from(mark(z0)) → mark(from(z0)) 218.05/71.49
from(ok(z0)) → ok(from(z0)) 218.05/71.49
add(mark(z0), z1) → mark(add(z0, z1)) 218.05/71.49
add(z0, mark(z1)) → mark(add(z0, z1)) 218.05/71.49
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.05/71.49
len(mark(z0)) → mark(len(z0)) 218.05/71.49
len(ok(z0)) → ok(len(z0)) 218.05/71.49
proper(0) → ok(0) 218.05/71.49
proper(s(z0)) → s(proper(z0)) 218.05/71.49
proper(nil) → ok(nil) 218.05/71.49
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.05/71.49
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.05/71.49
proper(from(z0)) → from(proper(z0)) 218.05/71.49
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.05/71.49
proper(len(z0)) → len(proper(z0)) 218.05/71.49
s(ok(z0)) → ok(s(z0)) 218.05/71.49
top(mark(z0)) → top(proper(z0)) 218.05/71.49
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(cons(z0, z1)) → c7(CONS(active(z0), z1), ACTIVE(z0)) 218.05/71.49
ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.05/71.49
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.05/71.49
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 218.05/71.49
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.05/71.49
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.05/71.49
ACTIVE(len(z0)) → c13(LEN(active(z0)), ACTIVE(z0)) 218.05/71.49
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.05/71.49
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.05/71.49
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.05/71.49
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.05/71.49
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.05/71.49
FROM(mark(z0)) → c19(FROM(z0)) 218.05/71.49
FROM(ok(z0)) → c20(FROM(z0)) 218.05/71.49
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.05/71.49
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.05/71.49
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.05/71.49
LEN(mark(z0)) → c24(LEN(z0)) 218.05/71.49
LEN(ok(z0)) → c25(LEN(z0)) 218.05/71.49
PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) 218.05/71.49
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.49
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.49
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.05/71.49
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.49
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.05/71.49
S(ok(z0)) → c34(S(z0)) 218.05/71.49
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.05/71.49
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.05/71.49
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.05/71.49
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.05/71.49
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.05/71.49
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.05/71.49
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.05/71.49
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.05/71.49
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.05/71.49
ACTIVE(from(z0)) → c(S(z0))

S tuples:

ACTIVE(cons(z0, z1)) → c7(CONS(active(z0), z1), ACTIVE(z0)) 218.05/71.50
ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.05/71.50
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.05/71.50
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 218.05/71.50
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.05/71.50
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.05/71.50
ACTIVE(len(z0)) → c13(LEN(active(z0)), ACTIVE(z0)) 218.05/71.50
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.05/71.50
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.05/71.50
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.05/71.50
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.05/71.50
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.05/71.50
FROM(mark(z0)) → c19(FROM(z0)) 218.05/71.50
FROM(ok(z0)) → c20(FROM(z0)) 218.05/71.50
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.05/71.50
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.05/71.50
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.05/71.50
LEN(mark(z0)) → c24(LEN(z0)) 218.05/71.50
LEN(ok(z0)) → c25(LEN(z0)) 218.05/71.50
PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) 218.05/71.50
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.50
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.50
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.05/71.50
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.50
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.05/71.50
S(ok(z0)) → c34(S(z0)) 218.05/71.50
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.05/71.50
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.05/71.50
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.05/71.50
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.05/71.50
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.05/71.50
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.05/71.50
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.05/71.50
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.05/71.50
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.05/71.50
ACTIVE(from(z0)) → c(S(z0))

K tuples:none
Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c27, c29, c30, c31, c32, c33, c34, c35, c36, c

218.05/71.50

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

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

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

We considered the (Usable) Rules:

len(mark(z0)) → mark(len(z0)) 218.05/71.50
len(ok(z0)) → ok(len(z0)) 218.05/71.50
add(mark(z0), z1) → mark(add(z0, z1)) 218.05/71.50
add(z0, mark(z1)) → mark(add(z0, z1)) 218.05/71.50
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.05/71.50
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.05/71.50
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.05/71.50
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.05/71.50
active(fst(0, z0)) → mark(nil) 218.05/71.50
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.05/71.50
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.05/71.50
active(add(0, z0)) → mark(z0) 218.05/71.50
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.05/71.50
active(len(nil)) → mark(0) 218.05/71.50
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.05/71.50
active(cons(z0, z1)) → cons(active(z0), z1) 218.05/71.50
active(fst(z0, z1)) → fst(active(z0), z1) 218.05/71.50
active(fst(z0, z1)) → fst(z0, active(z1)) 218.05/71.50
active(from(z0)) → from(active(z0)) 218.05/71.50
active(add(z0, z1)) → add(active(z0), z1) 218.05/71.50
active(add(z0, z1)) → add(z0, active(z1)) 218.05/71.50
active(len(z0)) → len(active(z0)) 218.05/71.50
from(mark(z0)) → mark(from(z0)) 218.05/71.50
from(ok(z0)) → ok(from(z0)) 218.05/71.50
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.05/71.50
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.05/71.50
s(ok(z0)) → ok(s(z0)) 218.05/71.50
proper(0) → ok(0) 218.05/71.50
proper(s(z0)) → s(proper(z0)) 218.05/71.50
proper(nil) → ok(nil) 218.05/71.50
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.05/71.50
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.05/71.50
proper(from(z0)) → from(proper(z0)) 218.05/71.50
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.05/71.50
proper(len(z0)) → len(proper(z0))

And the Tuples:

ACTIVE(cons(z0, z1)) → c7(CONS(active(z0), z1), ACTIVE(z0)) 218.05/71.50
ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.05/71.50
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.05/71.50
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 218.05/71.50
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.05/71.50
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.05/71.50
ACTIVE(len(z0)) → c13(LEN(active(z0)), ACTIVE(z0)) 218.05/71.50
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.05/71.50
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.05/71.50
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.05/71.50
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.05/71.50
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.05/71.50
FROM(mark(z0)) → c19(FROM(z0)) 218.05/71.50
FROM(ok(z0)) → c20(FROM(z0)) 218.05/71.50
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.05/71.50
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.05/71.50
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.05/71.50
LEN(mark(z0)) → c24(LEN(z0)) 218.05/71.50
LEN(ok(z0)) → c25(LEN(z0)) 218.05/71.50
PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) 218.05/71.50
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.50
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.50
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.05/71.50
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.50
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.05/71.50
S(ok(z0)) → c34(S(z0)) 218.05/71.50
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.05/71.50
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.05/71.50
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.05/71.50
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.05/71.50
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.05/71.50
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.05/71.50
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.05/71.50
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.05/71.50
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.05/71.50
ACTIVE(from(z0)) → c(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 218.05/71.50

POL(0) = [1] 218.05/71.50
POL(ACTIVE(x₁)) = 0 218.05/71.50
POL(ADD(x₁, x₂)) = 0 218.05/71.50
POL(CONS(x₁, x₂)) = 0 218.05/71.50
POL(FROM(x₁)) = 0 218.05/71.50
POL(FST(x₁, x₂)) = 0 218.05/71.50
POL(LEN(x₁)) = 0 218.05/71.50
POL(PROPER(x₁)) = 0 218.05/71.50
POL(S(x₁)) = 0 218.05/71.50
POL(TOP(x₁)) = [2]x₁ 218.05/71.50
POL(active(x₁)) = x₁ 218.05/71.50
POL(add(x₁, x₂)) = [4] + [2]x₁ + [4]x₂ 218.05/71.50
POL(c(x₁)) = x₁ 218.05/71.50
POL(c10(x₁, x₂)) = x₁ + x₂ 218.05/71.50
POL(c11(x₁, x₂)) = x₁ + x₂ 218.05/71.50
POL(c12(x₁, x₂)) = x₁ + x₂ 218.05/71.50
POL(c13(x₁, x₂)) = x₁ + x₂ 218.05/71.50
POL(c14(x₁)) = x₁ 218.05/71.50
POL(c15(x₁)) = x₁ 218.05/71.50
POL(c16(x₁)) = x₁ 218.05/71.50
POL(c17(x₁)) = x₁ 218.05/71.50
POL(c18(x₁)) = x₁ 218.05/71.50
POL(c19(x₁)) = x₁ 218.05/71.50
POL(c20(x₁)) = x₁ 218.05/71.50
POL(c21(x₁)) = x₁ 218.05/71.50
POL(c22(x₁)) = x₁ 218.05/71.50
POL(c23(x₁)) = x₁ 218.05/71.50
POL(c24(x₁)) = x₁ 218.05/71.50
POL(c25(x₁)) = x₁ 218.05/71.50
POL(c27(x₁, x₂)) = x₁ + x₂ 218.05/71.50
POL(c29(x₁, x₂, x₃)) = x₁ + x₂ + x₃ 218.05/71.50
POL(c30(x₁, x₂, x₃)) = x₁ + x₂ + x₃ 218.05/71.50
POL(c31(x₁, x₂)) = x₁ + x₂ 218.05/71.50
POL(c32(x₁, x₂, x₃)) = x₁ + x₂ + x₃ 218.05/71.50
POL(c33(x₁, x₂)) = x₁ + x₂ 218.05/71.50
POL(c34(x₁)) = x₁ 218.05/71.50
POL(c35(x₁, x₂)) = x₁ + x₂ 218.05/71.50
POL(c36(x₁, x₂)) = x₁ + x₂ 218.05/71.50
POL(c7(x₁, x₂)) = x₁ + x₂ 218.05/71.50
POL(c8(x₁, x₂)) = x₁ + x₂ 218.05/71.50
POL(c9(x₁, x₂)) = x₁ + x₂ 218.05/71.50
POL(cons(x₁, x₂)) = [1] + x₁ 218.05/71.50
POL(from(x₁)) = [3] + x₁ 218.05/71.50
POL(fst(x₁, x₂)) = [4]x₁ + [4]x₂ 218.05/71.50
POL(len(x₁)) = [4]x₁ 218.05/71.50
POL(mark(x₁)) = [2] + x₁ 218.05/71.50
POL(nil) = [1] 218.05/71.50
POL(ok(x₁)) = x₁ 218.05/71.50
POL(proper(x₁)) = x₁ 218.05/71.50
POL(s(x₁)) = 0

218.05/71.50

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.05/71.50
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.05/71.50
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.05/71.50
active(add(0, z0)) → mark(z0) 218.05/71.50
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.05/71.50
active(len(nil)) → mark(0) 218.05/71.50
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.05/71.50
active(cons(z0, z1)) → cons(active(z0), z1) 218.05/71.50
active(fst(z0, z1)) → fst(active(z0), z1) 218.05/71.50
active(fst(z0, z1)) → fst(z0, active(z1)) 218.05/71.50
active(from(z0)) → from(active(z0)) 218.05/71.50
active(add(z0, z1)) → add(active(z0), z1) 218.05/71.50
active(add(z0, z1)) → add(z0, active(z1)) 218.05/71.50
active(len(z0)) → len(active(z0)) 218.05/71.50
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.05/71.50
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.05/71.50
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.05/71.50
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.05/71.50
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.05/71.50
from(mark(z0)) → mark(from(z0)) 218.05/71.50
from(ok(z0)) → ok(from(z0)) 218.05/71.50
add(mark(z0), z1) → mark(add(z0, z1)) 218.05/71.50
add(z0, mark(z1)) → mark(add(z0, z1)) 218.05/71.50
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.05/71.50
len(mark(z0)) → mark(len(z0)) 218.05/71.50
len(ok(z0)) → ok(len(z0)) 218.05/71.50
proper(0) → ok(0) 218.05/71.50
proper(s(z0)) → s(proper(z0)) 218.05/71.50
proper(nil) → ok(nil) 218.05/71.50
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.05/71.50
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.05/71.50
proper(from(z0)) → from(proper(z0)) 218.05/71.50
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.05/71.50
proper(len(z0)) → len(proper(z0)) 218.05/71.50
s(ok(z0)) → ok(s(z0)) 218.05/71.50
top(mark(z0)) → top(proper(z0)) 218.05/71.50
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(cons(z0, z1)) → c7(CONS(active(z0), z1), ACTIVE(z0)) 218.05/71.50
ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.05/71.50
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.05/71.50
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 218.05/71.50
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.05/71.50
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.05/71.50
ACTIVE(len(z0)) → c13(LEN(active(z0)), ACTIVE(z0)) 218.05/71.50
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.05/71.50
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.05/71.50
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.05/71.50
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.05/71.50
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.05/71.50
FROM(mark(z0)) → c19(FROM(z0)) 218.05/71.50
FROM(ok(z0)) → c20(FROM(z0)) 218.05/71.50
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.05/71.50
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.05/71.50
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.05/71.50
LEN(mark(z0)) → c24(LEN(z0)) 218.05/71.50
LEN(ok(z0)) → c25(LEN(z0)) 218.05/71.50
PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) 218.05/71.50
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.50
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.50
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.05/71.50
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.05/71.50
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.05/71.50
S(ok(z0)) → c34(S(z0)) 218.05/71.50
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.05/71.50
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.05/71.50
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.05/71.50
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.05/71.50
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.05/71.50
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.05/71.50
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.05/71.50
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.05/71.50
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.05/71.50
ACTIVE(from(z0)) → c(S(z0))

S tuples:

ACTIVE(cons(z0, z1)) → c7(CONS(active(z0), z1), ACTIVE(z0)) 218.05/71.50
ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.05/71.50
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.05/71.50
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 218.05/71.50
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.05/71.50
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.05/71.50
ACTIVE(len(z0)) → c13(LEN(active(z0)), ACTIVE(z0)) 218.05/71.50
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.05/71.50
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.05/71.50
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.05/71.50
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.05/71.50
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.05/71.50
FROM(mark(z0)) → c19(FROM(z0)) 218.05/71.50
FROM(ok(z0)) → c20(FROM(z0)) 218.05/71.50
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.05/71.50
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.05/71.50
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.05/71.50
LEN(mark(z0)) → c24(LEN(z0)) 218.05/71.50
LEN(ok(z0)) → c25(LEN(z0)) 218.05/71.50
PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) 218.05/71.50
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.51
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.51
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.51
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.51
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.51
S(ok(z0)) → c34(S(z0)) 218.44/71.51
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.51
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.51
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.51
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.51
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.51
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.51
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.51
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.51
ACTIVE(from(z0)) → c(S(z0))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c27, c29, c30, c31, c32, c33, c34, c35, c36, c

218.44/71.51

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

Use narrowing to replace ACTIVE(cons(z0, z1)) → c7(CONS(active(z0), z1), ACTIVE(z0)) by

ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.51
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.51
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.51
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.51
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.51
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1), ACTIVE(len(nil))) 218.44/71.51
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.51
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.51
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.51
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.51
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.51
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.51
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.51
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0)))

218.44/71.51

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.44/71.51
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.44/71.51
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.44/71.51
active(add(0, z0)) → mark(z0) 218.44/71.51
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.44/71.51
active(len(nil)) → mark(0) 218.44/71.51
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.44/71.51
active(cons(z0, z1)) → cons(active(z0), z1) 218.44/71.51
active(fst(z0, z1)) → fst(active(z0), z1) 218.44/71.51
active(fst(z0, z1)) → fst(z0, active(z1)) 218.44/71.51
active(from(z0)) → from(active(z0)) 218.44/71.51
active(add(z0, z1)) → add(active(z0), z1) 218.44/71.51
active(add(z0, z1)) → add(z0, active(z1)) 218.44/71.51
active(len(z0)) → len(active(z0)) 218.44/71.51
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.44/71.51
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.44/71.51
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.44/71.51
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.44/71.51
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.44/71.51
from(mark(z0)) → mark(from(z0)) 218.44/71.51
from(ok(z0)) → ok(from(z0)) 218.44/71.51
add(mark(z0), z1) → mark(add(z0, z1)) 218.44/71.51
add(z0, mark(z1)) → mark(add(z0, z1)) 218.44/71.51
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.44/71.51
len(mark(z0)) → mark(len(z0)) 218.44/71.51
len(ok(z0)) → ok(len(z0)) 218.44/71.51
proper(0) → ok(0) 218.44/71.51
proper(s(z0)) → s(proper(z0)) 218.44/71.51
proper(nil) → ok(nil) 218.44/71.51
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.44/71.51
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.44/71.51
proper(from(z0)) → from(proper(z0)) 218.44/71.51
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.44/71.51
proper(len(z0)) → len(proper(z0)) 218.44/71.51
s(ok(z0)) → ok(s(z0)) 218.44/71.51
top(mark(z0)) → top(proper(z0)) 218.44/71.51
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.51
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.51
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 218.44/71.51
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.51
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.51
ACTIVE(len(z0)) → c13(LEN(active(z0)), ACTIVE(z0)) 218.44/71.51
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.51
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.51
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.51
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.51
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.51
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.51
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.51
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.51
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.51
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.51
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.51
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.51
PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) 218.44/71.51
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.51
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.51
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.51
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.51
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.51
S(ok(z0)) → c34(S(z0)) 218.44/71.51
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.44/71.51
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.51
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.51
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.51
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.51
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.51
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.51
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.51
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.51
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.51
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.51
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.51
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.51
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.51
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.51
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1), ACTIVE(len(nil))) 218.44/71.51
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.51
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.51
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.51
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.51
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.51
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.51
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.51
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0)))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.51
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.51
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0)) 218.44/71.51
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.51
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.51
ACTIVE(len(z0)) → c13(LEN(active(z0)), ACTIVE(z0)) 218.44/71.51
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.51
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.51
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.51
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.51
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.51
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.51
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.51
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.51
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.51
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.51
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.51
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.51
PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) 218.44/71.51
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.51
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.51
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.51
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.51
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.51
S(ok(z0)) → c34(S(z0)) 218.44/71.51
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.51
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.51
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.51
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.51
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.51
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.51
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.51
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.51
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.51
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.51
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.51
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.51
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.51
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.51
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1), ACTIVE(len(nil))) 218.44/71.51
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.51
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.51
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.51
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.51
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.51
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.51
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.51
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0)))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c27, c29, c30, c31, c32, c33, c34, c35, c36, c, c7

218.44/71.51

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

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

ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.51
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.51
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.51
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.51
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.51
ACTIVE(from(len(nil))) → c10(FROM(mark(0)), ACTIVE(len(nil))) 218.44/71.51
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.51
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.51
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.51
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.51
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.51
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.51
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.51
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0)))

218.44/71.51

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.44/71.51
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.44/71.51
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.44/71.51
active(add(0, z0)) → mark(z0) 218.44/71.51
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.44/71.51
active(len(nil)) → mark(0) 218.44/71.51
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.44/71.51
active(cons(z0, z1)) → cons(active(z0), z1) 218.44/71.51
active(fst(z0, z1)) → fst(active(z0), z1) 218.44/71.51
active(fst(z0, z1)) → fst(z0, active(z1)) 218.44/71.51
active(from(z0)) → from(active(z0)) 218.44/71.51
active(add(z0, z1)) → add(active(z0), z1) 218.44/71.51
active(add(z0, z1)) → add(z0, active(z1)) 218.44/71.51
active(len(z0)) → len(active(z0)) 218.44/71.51
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.44/71.51
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.44/71.51
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.44/71.51
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.44/71.51
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.44/71.51
from(mark(z0)) → mark(from(z0)) 218.44/71.51
from(ok(z0)) → ok(from(z0)) 218.44/71.51
add(mark(z0), z1) → mark(add(z0, z1)) 218.44/71.51
add(z0, mark(z1)) → mark(add(z0, z1)) 218.44/71.51
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.44/71.51
len(mark(z0)) → mark(len(z0)) 218.44/71.51
len(ok(z0)) → ok(len(z0)) 218.44/71.51
proper(0) → ok(0) 218.44/71.51
proper(s(z0)) → s(proper(z0)) 218.44/71.51
proper(nil) → ok(nil) 218.44/71.51
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.44/71.51
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.44/71.51
proper(from(z0)) → from(proper(z0)) 218.44/71.51
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.44/71.51
proper(len(z0)) → len(proper(z0)) 218.44/71.51
s(ok(z0)) → ok(s(z0)) 218.44/71.51
top(mark(z0)) → top(proper(z0)) 218.44/71.51
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.51
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.51
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.51
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.51
ACTIVE(len(z0)) → c13(LEN(active(z0)), ACTIVE(z0)) 218.44/71.51
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.51
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.51
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.51
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.51
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.51
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.51
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.51
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.51
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.51
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.51
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.51
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.51
PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) 218.44/71.51
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.51
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.51
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.51
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.51
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.51
S(ok(z0)) → c34(S(z0)) 218.44/71.51
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.44/71.51
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.51
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.51
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.51
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.51
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.51
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.51
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.51
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.51
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.51
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.51
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.51
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.51
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.51
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.51
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1), ACTIVE(len(nil))) 218.44/71.51
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.51
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.51
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.51
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.51
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.51
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.51
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.51
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.51
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.51
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.51
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.51
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.51
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.51
ACTIVE(from(len(nil))) → c10(FROM(mark(0)), ACTIVE(len(nil))) 218.44/71.51
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.51
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.51
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.51
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.51
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.51
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.51
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.51
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0)))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.51
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.51
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.51
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.51
ACTIVE(len(z0)) → c13(LEN(active(z0)), ACTIVE(z0)) 218.44/71.51
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.51
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.51
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.51
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.51
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.51
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.51
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.51
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.51
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.51
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.51
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.51
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.51
PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) 218.44/71.51
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.51
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.51
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.51
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.51
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.51
S(ok(z0)) → c34(S(z0)) 218.44/71.51
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.51
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.51
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.51
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.51
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.51
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.51
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.51
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.51
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.51
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.51
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.51
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.51
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.51
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.51
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1), ACTIVE(len(nil))) 218.44/71.51
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.51
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.51
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.51
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.51
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.51
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.51
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.51
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.51
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.51
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.51
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.51
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.51
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.51
ACTIVE(from(len(nil))) → c10(FROM(mark(0)), ACTIVE(len(nil))) 218.44/71.51
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.51
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.51
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.51
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.51
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.57
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.57
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.57
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0)))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c8, c9, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c27, c29, c30, c31, c32, c33, c34, c35, c36, c, c7, c10

218.44/71.57

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

Use narrowing to replace ACTIVE(len(z0)) → c13(LEN(active(z0)), ACTIVE(z0)) by

ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.57
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.57
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.57
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.57
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.57
ACTIVE(len(len(nil))) → c13(LEN(mark(0)), ACTIVE(len(nil))) 218.44/71.57
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.57
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.57
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.57
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.57
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.57
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.57
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.57
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0)))

218.44/71.57

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.44/71.57
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.44/71.57
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.44/71.57
active(add(0, z0)) → mark(z0) 218.44/71.57
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.44/71.57
active(len(nil)) → mark(0) 218.44/71.57
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.44/71.57
active(cons(z0, z1)) → cons(active(z0), z1) 218.44/71.57
active(fst(z0, z1)) → fst(active(z0), z1) 218.44/71.57
active(fst(z0, z1)) → fst(z0, active(z1)) 218.44/71.57
active(from(z0)) → from(active(z0)) 218.44/71.57
active(add(z0, z1)) → add(active(z0), z1) 218.44/71.57
active(add(z0, z1)) → add(z0, active(z1)) 218.44/71.57
active(len(z0)) → len(active(z0)) 218.44/71.57
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.44/71.57
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.44/71.57
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.44/71.57
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.44/71.57
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.44/71.57
from(mark(z0)) → mark(from(z0)) 218.44/71.57
from(ok(z0)) → ok(from(z0)) 218.44/71.57
add(mark(z0), z1) → mark(add(z0, z1)) 218.44/71.57
add(z0, mark(z1)) → mark(add(z0, z1)) 218.44/71.57
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.44/71.57
len(mark(z0)) → mark(len(z0)) 218.44/71.57
len(ok(z0)) → ok(len(z0)) 218.44/71.57
proper(0) → ok(0) 218.44/71.57
proper(s(z0)) → s(proper(z0)) 218.44/71.57
proper(nil) → ok(nil) 218.44/71.57
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.44/71.57
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.44/71.57
proper(from(z0)) → from(proper(z0)) 218.44/71.57
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.44/71.57
proper(len(z0)) → len(proper(z0)) 218.44/71.57
s(ok(z0)) → ok(s(z0)) 218.44/71.57
top(mark(z0)) → top(proper(z0)) 218.44/71.57
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.57
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.57
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.57
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.57
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.57
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.57
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.57
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.57
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.57
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.57
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.57
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.57
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.57
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.57
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.57
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.57
PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) 218.44/71.57
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.57
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.57
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.57
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.57
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.57
S(ok(z0)) → c34(S(z0)) 218.44/71.57
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.44/71.57
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.57
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.57
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.57
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.57
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.57
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.57
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.57
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.57
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.57
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.57
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.57
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.57
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.57
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.57
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1), ACTIVE(len(nil))) 218.44/71.57
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.57
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.57
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.57
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.57
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.57
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.57
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.57
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.57
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.57
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.57
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.57
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.57
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.57
ACTIVE(from(len(nil))) → c10(FROM(mark(0)), ACTIVE(len(nil))) 218.44/71.57
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.57
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.57
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.57
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.57
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.57
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.57
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.57
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.57
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.57
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.57
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.57
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.57
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.57
ACTIVE(len(len(nil))) → c13(LEN(mark(0)), ACTIVE(len(nil))) 218.44/71.57
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.57
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.57
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.57
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.57
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.57
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.57
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.57
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0)))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.57
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.57
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.57
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.57
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.57
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.57
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.57
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.57
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.57
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.57
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.57
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.57
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.57
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.57
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.57
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.57
PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) 218.44/71.57
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.57
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.57
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.57
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.57
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.57
S(ok(z0)) → c34(S(z0)) 218.44/71.57
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.57
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.57
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.57
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.57
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.57
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.57
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.57
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.57
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.57
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.57
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.57
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.57
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.57
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.57
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1), ACTIVE(len(nil))) 218.44/71.57
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.57
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.57
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.57
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.57
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.57
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.57
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.57
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.57
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.57
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.57
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.57
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.57
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.57
ACTIVE(from(len(nil))) → c10(FROM(mark(0)), ACTIVE(len(nil))) 218.44/71.57
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.57
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.57
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.57
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.57
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.57
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.57
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.57
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.57
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.57
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.57
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.57
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.57
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.57
ACTIVE(len(len(nil))) → c13(LEN(mark(0)), ACTIVE(len(nil))) 218.44/71.57
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.57
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.57
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.57
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.57
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.57
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.57
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.57
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0)))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c8, c9, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c27, c29, c30, c31, c32, c33, c34, c35, c36, c, c7, c10, c13

218.44/71.57

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

Removed 3 trailing tuple parts

218.44/71.57

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.44/71.57
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.44/71.57
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.44/71.57
active(add(0, z0)) → mark(z0) 218.44/71.57
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.44/71.57
active(len(nil)) → mark(0) 218.44/71.57
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.44/71.57
active(cons(z0, z1)) → cons(active(z0), z1) 218.44/71.57
active(fst(z0, z1)) → fst(active(z0), z1) 218.44/71.57
active(fst(z0, z1)) → fst(z0, active(z1)) 218.44/71.57
active(from(z0)) → from(active(z0)) 218.44/71.57
active(add(z0, z1)) → add(active(z0), z1) 218.44/71.57
active(add(z0, z1)) → add(z0, active(z1)) 218.44/71.57
active(len(z0)) → len(active(z0)) 218.44/71.57
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.44/71.57
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.44/71.57
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.44/71.57
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.44/71.57
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.44/71.57
from(mark(z0)) → mark(from(z0)) 218.44/71.57
from(ok(z0)) → ok(from(z0)) 218.44/71.57
add(mark(z0), z1) → mark(add(z0, z1)) 218.44/71.57
add(z0, mark(z1)) → mark(add(z0, z1)) 218.44/71.57
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.44/71.57
len(mark(z0)) → mark(len(z0)) 218.44/71.57
len(ok(z0)) → ok(len(z0)) 218.44/71.57
proper(0) → ok(0) 218.44/71.57
proper(s(z0)) → s(proper(z0)) 218.44/71.57
proper(nil) → ok(nil) 218.44/71.57
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.44/71.57
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.44/71.57
proper(from(z0)) → from(proper(z0)) 218.44/71.57
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.44/71.57
proper(len(z0)) → len(proper(z0)) 218.44/71.57
s(ok(z0)) → ok(s(z0)) 218.44/71.57
top(mark(z0)) → top(proper(z0)) 218.44/71.57
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.57
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.57
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.57
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.57
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.57
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.57
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.57
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.57
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.57
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.57
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.57
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.57
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.57
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.57
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.57
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.57
PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) 218.44/71.57
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.58
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.58
S(ok(z0)) → c34(S(z0)) 218.44/71.58
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.44/71.58
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.58
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.58
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.58
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.58
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.58
ACTIVE(len(len(nil))) → c13(LEN(mark(0)))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.58
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.58
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.58
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.58
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.58
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.58
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.58
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.58
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.58
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.58
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.58
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.58
PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) 218.44/71.58
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.58
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.58
S(ok(z0)) → c34(S(z0)) 218.44/71.58
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.58
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.58
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.58
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.58
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.58
ACTIVE(len(len(nil))) → c13(LEN(mark(0)))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c8, c9, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c27, c29, c30, c31, c32, c33, c34, c35, c36, c, c7, c10, c13, c7, c10, c13

218.44/71.58

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

Use narrowing to replace PROPER(s(z0)) → c27(S(proper(z0)), PROPER(z0)) by

PROPER(s(0)) → c27(S(ok(0)), PROPER(0)) 218.44/71.58
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.58
PROPER(s(nil)) → c27(S(ok(nil)), PROPER(nil)) 218.44/71.58
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.58
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.58
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0)))

218.44/71.58

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.44/71.58
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.44/71.58
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.44/71.58
active(add(0, z0)) → mark(z0) 218.44/71.58
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.44/71.58
active(len(nil)) → mark(0) 218.44/71.58
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.44/71.58
active(cons(z0, z1)) → cons(active(z0), z1) 218.44/71.58
active(fst(z0, z1)) → fst(active(z0), z1) 218.44/71.58
active(fst(z0, z1)) → fst(z0, active(z1)) 218.44/71.58
active(from(z0)) → from(active(z0)) 218.44/71.58
active(add(z0, z1)) → add(active(z0), z1) 218.44/71.58
active(add(z0, z1)) → add(z0, active(z1)) 218.44/71.58
active(len(z0)) → len(active(z0)) 218.44/71.58
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.44/71.58
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.44/71.58
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.44/71.58
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.44/71.58
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.44/71.58
from(mark(z0)) → mark(from(z0)) 218.44/71.58
from(ok(z0)) → ok(from(z0)) 218.44/71.58
add(mark(z0), z1) → mark(add(z0, z1)) 218.44/71.58
add(z0, mark(z1)) → mark(add(z0, z1)) 218.44/71.58
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.44/71.58
len(mark(z0)) → mark(len(z0)) 218.44/71.58
len(ok(z0)) → ok(len(z0)) 218.44/71.58
proper(0) → ok(0) 218.44/71.58
proper(s(z0)) → s(proper(z0)) 218.44/71.58
proper(nil) → ok(nil) 218.44/71.58
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.44/71.58
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.44/71.58
proper(from(z0)) → from(proper(z0)) 218.44/71.58
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.44/71.58
proper(len(z0)) → len(proper(z0)) 218.44/71.58
s(ok(z0)) → ok(s(z0)) 218.44/71.58
top(mark(z0)) → top(proper(z0)) 218.44/71.58
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.58
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.58
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.58
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.58
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.58
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.58
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.58
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.58
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.58
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.58
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.58
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.58
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.58
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.58
S(ok(z0)) → c34(S(z0)) 218.44/71.58
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.44/71.58
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.58
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.58
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.58
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.58
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.58
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.58
PROPER(s(0)) → c27(S(ok(0)), PROPER(0)) 218.44/71.58
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.58
PROPER(s(nil)) → c27(S(ok(nil)), PROPER(nil)) 218.44/71.58
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.58
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.58
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0)))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.58
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.58
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.58
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.58
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.58
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.58
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.58
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.58
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.58
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.58
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.58
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.58
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.58
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.58
S(ok(z0)) → c34(S(z0)) 218.44/71.58
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.58
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.58
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.58
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.58
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.58
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.58
PROPER(s(0)) → c27(S(ok(0)), PROPER(0)) 218.44/71.58
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.58
PROPER(s(nil)) → c27(S(ok(nil)), PROPER(nil)) 218.44/71.58
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.58
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.58
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0)))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c8, c9, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c29, c30, c31, c32, c33, c34, c35, c36, c, c7, c10, c13, c7, c10, c13, c27

218.44/71.58

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

Removed 2 trailing tuple parts

218.44/71.58

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.44/71.58
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.44/71.58
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.44/71.58
active(add(0, z0)) → mark(z0) 218.44/71.58
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.44/71.58
active(len(nil)) → mark(0) 218.44/71.58
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.44/71.58
active(cons(z0, z1)) → cons(active(z0), z1) 218.44/71.58
active(fst(z0, z1)) → fst(active(z0), z1) 218.44/71.58
active(fst(z0, z1)) → fst(z0, active(z1)) 218.44/71.58
active(from(z0)) → from(active(z0)) 218.44/71.58
active(add(z0, z1)) → add(active(z0), z1) 218.44/71.58
active(add(z0, z1)) → add(z0, active(z1)) 218.44/71.58
active(len(z0)) → len(active(z0)) 218.44/71.58
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.44/71.58
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.44/71.58
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.44/71.58
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.44/71.58
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.44/71.58
from(mark(z0)) → mark(from(z0)) 218.44/71.58
from(ok(z0)) → ok(from(z0)) 218.44/71.58
add(mark(z0), z1) → mark(add(z0, z1)) 218.44/71.58
add(z0, mark(z1)) → mark(add(z0, z1)) 218.44/71.58
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.44/71.58
len(mark(z0)) → mark(len(z0)) 218.44/71.58
len(ok(z0)) → ok(len(z0)) 218.44/71.58
proper(0) → ok(0) 218.44/71.58
proper(s(z0)) → s(proper(z0)) 218.44/71.58
proper(nil) → ok(nil) 218.44/71.58
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.44/71.58
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.44/71.58
proper(from(z0)) → from(proper(z0)) 218.44/71.58
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.44/71.58
proper(len(z0)) → len(proper(z0)) 218.44/71.58
s(ok(z0)) → ok(s(z0)) 218.44/71.58
top(mark(z0)) → top(proper(z0)) 218.44/71.58
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.58
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.58
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.58
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.58
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.58
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.58
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.58
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.58
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.58
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.58
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.58
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.58
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.58
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.58
S(ok(z0)) → c34(S(z0)) 218.44/71.58
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.44/71.58
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.58
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.58
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.58
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.58
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.58
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.58
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.58
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.58
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.58
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.44/71.58
PROPER(s(0)) → c27(S(ok(0))) 218.44/71.58
PROPER(s(nil)) → c27(S(ok(nil)))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.58
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.58
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.58
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.58
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.58
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.58
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.58
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.58
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.58
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.58
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.58
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.58
PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.58
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.58
S(ok(z0)) → c34(S(z0)) 218.44/71.58
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.58
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.58
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.58
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.58
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.58
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.58
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.58
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.58
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.58
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.44/71.58
PROPER(s(0)) → c27(S(ok(0))) 218.44/71.58
PROPER(s(nil)) → c27(S(ok(nil)))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c8, c9, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c29, c30, c31, c32, c33, c34, c35, c36, c, c7, c10, c13, c7, c10, c13, c27, c27

218.44/71.58

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

Use narrowing to replace PROPER(cons(z0, z1)) → c29(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 218.44/71.58
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.58
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 218.44/71.58
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.58
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.58
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.58
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 218.44/71.58
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.58
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 218.44/71.58
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.58
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1))

218.44/71.58

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.44/71.58
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.44/71.58
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.44/71.58
active(add(0, z0)) → mark(z0) 218.44/71.58
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.44/71.58
active(len(nil)) → mark(0) 218.44/71.58
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.44/71.58
active(cons(z0, z1)) → cons(active(z0), z1) 218.44/71.58
active(fst(z0, z1)) → fst(active(z0), z1) 218.44/71.58
active(fst(z0, z1)) → fst(z0, active(z1)) 218.44/71.58
active(from(z0)) → from(active(z0)) 218.44/71.58
active(add(z0, z1)) → add(active(z0), z1) 218.44/71.58
active(add(z0, z1)) → add(z0, active(z1)) 218.44/71.58
active(len(z0)) → len(active(z0)) 218.44/71.58
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.44/71.58
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.44/71.58
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.44/71.58
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.44/71.58
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.44/71.58
from(mark(z0)) → mark(from(z0)) 218.44/71.58
from(ok(z0)) → ok(from(z0)) 218.44/71.58
add(mark(z0), z1) → mark(add(z0, z1)) 218.44/71.58
add(z0, mark(z1)) → mark(add(z0, z1)) 218.44/71.58
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.44/71.58
len(mark(z0)) → mark(len(z0)) 218.44/71.58
len(ok(z0)) → ok(len(z0)) 218.44/71.58
proper(0) → ok(0) 218.44/71.58
proper(s(z0)) → s(proper(z0)) 218.44/71.58
proper(nil) → ok(nil) 218.44/71.58
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.44/71.58
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.44/71.58
proper(from(z0)) → from(proper(z0)) 218.44/71.58
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.44/71.58
proper(len(z0)) → len(proper(z0)) 218.44/71.58
s(ok(z0)) → ok(s(z0)) 218.44/71.58
top(mark(z0)) → top(proper(z0)) 218.44/71.58
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.58
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.58
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.58
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.58
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.58
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.58
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.58
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.58
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.58
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.58
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.58
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.58
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.58
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.58
S(ok(z0)) → c34(S(z0)) 218.44/71.58
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.44/71.58
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.58
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.58
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.58
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.58
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.58
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.58
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.58
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.58
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.58
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.44/71.58
PROPER(s(0)) → c27(S(ok(0))) 218.44/71.58
PROPER(s(nil)) → c27(S(ok(nil))) 218.44/71.58
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 218.44/71.58
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.58
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 218.44/71.58
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.58
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.58
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.58
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 218.44/71.58
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.58
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 218.44/71.58
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.58
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.58
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.58
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.58
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.58
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.58
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.58
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.58
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.58
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.58
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.58
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.58
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.58
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.58
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.58
S(ok(z0)) → c34(S(z0)) 218.44/71.58
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.58
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.58
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.58
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.58
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.58
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.58
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.58
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.58
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.58
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.44/71.58
PROPER(s(0)) → c27(S(ok(0))) 218.44/71.58
PROPER(s(nil)) → c27(S(ok(nil))) 218.44/71.58
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 218.44/71.58
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.58
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 218.44/71.58
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.58
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.58
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.58
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 218.44/71.58
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.58
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 218.44/71.58
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.58
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c8, c9, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c30, c31, c32, c33, c34, c35, c36, c, c7, c10, c13, c7, c10, c13, c27, c27, c29

218.44/71.58

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

Removed 4 trailing tuple parts

218.44/71.58

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.44/71.58
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.44/71.58
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.44/71.58
active(add(0, z0)) → mark(z0) 218.44/71.58
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.44/71.58
active(len(nil)) → mark(0) 218.44/71.58
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.44/71.58
active(cons(z0, z1)) → cons(active(z0), z1) 218.44/71.58
active(fst(z0, z1)) → fst(active(z0), z1) 218.44/71.58
active(fst(z0, z1)) → fst(z0, active(z1)) 218.44/71.58
active(from(z0)) → from(active(z0)) 218.44/71.58
active(add(z0, z1)) → add(active(z0), z1) 218.44/71.58
active(add(z0, z1)) → add(z0, active(z1)) 218.44/71.58
active(len(z0)) → len(active(z0)) 218.44/71.58
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.44/71.58
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.44/71.58
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.44/71.58
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.44/71.58
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.44/71.58
from(mark(z0)) → mark(from(z0)) 218.44/71.58
from(ok(z0)) → ok(from(z0)) 218.44/71.58
add(mark(z0), z1) → mark(add(z0, z1)) 218.44/71.58
add(z0, mark(z1)) → mark(add(z0, z1)) 218.44/71.58
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.44/71.58
len(mark(z0)) → mark(len(z0)) 218.44/71.58
len(ok(z0)) → ok(len(z0)) 218.44/71.58
proper(0) → ok(0) 218.44/71.58
proper(s(z0)) → s(proper(z0)) 218.44/71.58
proper(nil) → ok(nil) 218.44/71.58
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.44/71.58
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.44/71.58
proper(from(z0)) → from(proper(z0)) 218.44/71.58
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.44/71.58
proper(len(z0)) → len(proper(z0)) 218.44/71.58
s(ok(z0)) → ok(s(z0)) 218.44/71.58
top(mark(z0)) → top(proper(z0)) 218.44/71.58
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.58
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.58
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.58
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.58
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.58
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.58
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.58
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.58
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.58
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.58
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.58
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.58
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.58
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.58
S(ok(z0)) → c34(S(z0)) 218.44/71.58
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.44/71.58
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.58
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.58
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.58
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.58
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.58
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.58
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.58
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.58
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.58
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.44/71.58
PROPER(s(0)) → c27(S(ok(0))) 218.44/71.58
PROPER(s(nil)) → c27(S(ok(nil))) 218.44/71.58
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.58
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.58
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.58
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.58
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.58
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.58
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.58
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.44/71.58
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.58
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.44/71.58
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.58
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.58
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.58
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.58
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.58
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.58
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.58
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.58
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.58
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.58
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.58
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.58
PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.58
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.58
S(ok(z0)) → c34(S(z0)) 218.44/71.58
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.58
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.58
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.58
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.58
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.58
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.58
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.58
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.58
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.58
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.44/71.58
PROPER(s(0)) → c27(S(ok(0))) 218.44/71.58
PROPER(s(nil)) → c27(S(ok(nil))) 218.44/71.58
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.58
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.58
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.58
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.58
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.58
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.58
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.58
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.44/71.58
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.58
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.44/71.58
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c8, c9, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c30, c31, c32, c33, c34, c35, c36, c, c7, c10, c13, c7, c10, c13, c27, c27, c29, c29

218.44/71.58

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

Use narrowing to replace PROPER(fst(z0, z1)) → c30(FST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 218.44/71.58
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.58
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 218.44/71.58
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.58
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.58
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.58
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 218.44/71.58
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.58
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 218.44/71.58
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.58
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1))

218.44/71.58

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.44/71.58
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.44/71.58
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.44/71.58
active(add(0, z0)) → mark(z0) 218.44/71.58
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.44/71.58
active(len(nil)) → mark(0) 218.44/71.58
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.44/71.58
active(cons(z0, z1)) → cons(active(z0), z1) 218.44/71.58
active(fst(z0, z1)) → fst(active(z0), z1) 218.44/71.58
active(fst(z0, z1)) → fst(z0, active(z1)) 218.44/71.58
active(from(z0)) → from(active(z0)) 218.44/71.58
active(add(z0, z1)) → add(active(z0), z1) 218.44/71.58
active(add(z0, z1)) → add(z0, active(z1)) 218.44/71.58
active(len(z0)) → len(active(z0)) 218.44/71.58
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.44/71.58
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.44/71.58
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.44/71.58
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.44/71.58
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.44/71.58
from(mark(z0)) → mark(from(z0)) 218.44/71.58
from(ok(z0)) → ok(from(z0)) 218.44/71.58
add(mark(z0), z1) → mark(add(z0, z1)) 218.44/71.58
add(z0, mark(z1)) → mark(add(z0, z1)) 218.44/71.58
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.44/71.58
len(mark(z0)) → mark(len(z0)) 218.44/71.58
len(ok(z0)) → ok(len(z0)) 218.44/71.58
proper(0) → ok(0) 218.44/71.58
proper(s(z0)) → s(proper(z0)) 218.44/71.58
proper(nil) → ok(nil) 218.44/71.58
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.44/71.58
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.44/71.58
proper(from(z0)) → from(proper(z0)) 218.44/71.58
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.44/71.58
proper(len(z0)) → len(proper(z0)) 218.44/71.58
s(ok(z0)) → ok(s(z0)) 218.44/71.58
top(mark(z0)) → top(proper(z0)) 218.44/71.58
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.58
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.58
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.58
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.58
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.58
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.58
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.58
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.58
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.58
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.58
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.58
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.58
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.58
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.58
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.58
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.58
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.58
S(ok(z0)) → c34(S(z0)) 218.44/71.58
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.44/71.58
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.58
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.58
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.58
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.58
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.58
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.58
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.58
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.58
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.58
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.58
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.58
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.58
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.58
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.58
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.58
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.58
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.58
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.58
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.44/71.58
PROPER(s(0)) → c27(S(ok(0))) 218.44/71.58
PROPER(s(nil)) → c27(S(ok(nil))) 218.44/71.58
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.58
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.58
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.58
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.58
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.58
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.58
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.58
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.58
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.44/71.58
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.58
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.44/71.58
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.58
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 218.44/71.58
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.58
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 218.44/71.58
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.58
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.58
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.58
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.58
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.58
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 218.44/71.58
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.58
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 218.44/71.58
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.59
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.59
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.59
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.59
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.59
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.59
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.59
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.59
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.59
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.59
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.59
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.59
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.59
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.59
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.59
S(ok(z0)) → c34(S(z0)) 218.44/71.59
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.59
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.59
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.59
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.59
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.59
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.59
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.59
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.59
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.59
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.44/71.59
PROPER(s(0)) → c27(S(ok(0))) 218.44/71.59
PROPER(s(nil)) → c27(S(ok(nil))) 218.44/71.59
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.44/71.59
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.59
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 218.44/71.59
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 218.44/71.59
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 218.44/71.59
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 218.44/71.59
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c8, c9, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c31, c32, c33, c34, c35, c36, c, c7, c10, c13, c7, c10, c13, c27, c27, c29, c29, c30

218.44/71.59

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

Removed 4 trailing tuple parts

218.44/71.59

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.44/71.59
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.44/71.59
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.44/71.59
active(add(0, z0)) → mark(z0) 218.44/71.59
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.44/71.59
active(len(nil)) → mark(0) 218.44/71.59
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.44/71.59
active(cons(z0, z1)) → cons(active(z0), z1) 218.44/71.59
active(fst(z0, z1)) → fst(active(z0), z1) 218.44/71.59
active(fst(z0, z1)) → fst(z0, active(z1)) 218.44/71.59
active(from(z0)) → from(active(z0)) 218.44/71.59
active(add(z0, z1)) → add(active(z0), z1) 218.44/71.59
active(add(z0, z1)) → add(z0, active(z1)) 218.44/71.59
active(len(z0)) → len(active(z0)) 218.44/71.59
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.44/71.59
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.44/71.59
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.44/71.59
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.44/71.59
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.44/71.59
from(mark(z0)) → mark(from(z0)) 218.44/71.59
from(ok(z0)) → ok(from(z0)) 218.44/71.59
add(mark(z0), z1) → mark(add(z0, z1)) 218.44/71.59
add(z0, mark(z1)) → mark(add(z0, z1)) 218.44/71.59
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.44/71.59
len(mark(z0)) → mark(len(z0)) 218.44/71.59
len(ok(z0)) → ok(len(z0)) 218.44/71.59
proper(0) → ok(0) 218.44/71.59
proper(s(z0)) → s(proper(z0)) 218.44/71.59
proper(nil) → ok(nil) 218.44/71.59
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.44/71.59
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.44/71.59
proper(from(z0)) → from(proper(z0)) 218.44/71.59
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.44/71.59
proper(len(z0)) → len(proper(z0)) 218.44/71.59
s(ok(z0)) → ok(s(z0)) 218.44/71.59
top(mark(z0)) → top(proper(z0)) 218.44/71.59
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.59
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.59
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.59
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.59
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.59
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.59
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.59
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.59
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.59
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.59
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.59
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.59
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.59
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.59
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.59
S(ok(z0)) → c34(S(z0)) 218.44/71.59
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.44/71.59
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.59
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.59
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.59
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.59
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.59
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.59
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.59
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.59
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.59
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.44/71.59
PROPER(s(0)) → c27(S(ok(0))) 218.44/71.59
PROPER(s(nil)) → c27(S(ok(nil))) 218.44/71.59
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.44/71.59
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.59
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.44/71.59
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.59
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.59
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.59
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.59
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.59
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.59
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.59
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.59
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.59
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.59
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.59
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.59
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.59
PROPER(from(z0)) → c31(FROM(proper(z0)), PROPER(z0)) 218.44/71.59
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.59
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.59
S(ok(z0)) → c34(S(z0)) 218.44/71.59
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.59
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.59
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.59
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.59
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.59
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.59
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.59
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.59
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.59
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.44/71.59
PROPER(s(0)) → c27(S(ok(0))) 218.44/71.59
PROPER(s(nil)) → c27(S(ok(nil))) 218.44/71.59
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.44/71.59
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.59
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.44/71.59
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.59
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c8, c9, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c31, c32, c33, c34, c35, c36, c, c7, c10, c13, c7, c10, c13, c27, c27, c29, c29, c30, c30

218.44/71.59

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

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

PROPER(from(0)) → c31(FROM(ok(0)), PROPER(0)) 218.44/71.59
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.44/71.59
PROPER(from(nil)) → c31(FROM(ok(nil)), PROPER(nil)) 218.44/71.59
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.44/71.59
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.59
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0)))

218.44/71.59

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.44/71.59
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.44/71.59
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.44/71.59
active(add(0, z0)) → mark(z0) 218.44/71.59
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.44/71.59
active(len(nil)) → mark(0) 218.44/71.59
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.44/71.59
active(cons(z0, z1)) → cons(active(z0), z1) 218.44/71.59
active(fst(z0, z1)) → fst(active(z0), z1) 218.44/71.59
active(fst(z0, z1)) → fst(z0, active(z1)) 218.44/71.59
active(from(z0)) → from(active(z0)) 218.44/71.59
active(add(z0, z1)) → add(active(z0), z1) 218.44/71.59
active(add(z0, z1)) → add(z0, active(z1)) 218.44/71.59
active(len(z0)) → len(active(z0)) 218.44/71.59
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.44/71.59
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.44/71.59
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.44/71.59
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.44/71.59
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.44/71.59
from(mark(z0)) → mark(from(z0)) 218.44/71.59
from(ok(z0)) → ok(from(z0)) 218.44/71.59
add(mark(z0), z1) → mark(add(z0, z1)) 218.44/71.59
add(z0, mark(z1)) → mark(add(z0, z1)) 218.44/71.59
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.44/71.59
len(mark(z0)) → mark(len(z0)) 218.44/71.59
len(ok(z0)) → ok(len(z0)) 218.44/71.59
proper(0) → ok(0) 218.44/71.59
proper(s(z0)) → s(proper(z0)) 218.44/71.59
proper(nil) → ok(nil) 218.44/71.59
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.44/71.59
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.44/71.59
proper(from(z0)) → from(proper(z0)) 218.44/71.59
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.44/71.59
proper(len(z0)) → len(proper(z0)) 218.44/71.59
s(ok(z0)) → ok(s(z0)) 218.44/71.59
top(mark(z0)) → top(proper(z0)) 218.44/71.59
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.59
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.59
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.59
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.59
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.59
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.59
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.59
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.59
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.59
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.59
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.59
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.59
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.59
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.59
S(ok(z0)) → c34(S(z0)) 218.44/71.59
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.44/71.59
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.59
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.59
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.59
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.59
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.59
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.59
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.59
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.59
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.59
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.44/71.59
PROPER(s(0)) → c27(S(ok(0))) 218.44/71.59
PROPER(s(nil)) → c27(S(ok(nil))) 218.44/71.59
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.44/71.59
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.59
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.44/71.59
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.59
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(from(0)) → c31(FROM(ok(0)), PROPER(0)) 218.44/71.59
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.44/71.59
PROPER(from(nil)) → c31(FROM(ok(nil)), PROPER(nil)) 218.44/71.59
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.44/71.59
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.59
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0)))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.59
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.59
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.59
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.59
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.59
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.59
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.59
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.59
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.59
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.59
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.59
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.59
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.59
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.59
S(ok(z0)) → c34(S(z0)) 218.44/71.59
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.59
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.59
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.59
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.59
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.59
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.59
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.59
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.59
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.59
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.44/71.59
PROPER(s(0)) → c27(S(ok(0))) 218.44/71.59
PROPER(s(nil)) → c27(S(ok(nil))) 218.44/71.59
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.44/71.59
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.59
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.44/71.59
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.59
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(from(0)) → c31(FROM(ok(0)), PROPER(0)) 218.44/71.59
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.44/71.59
PROPER(from(nil)) → c31(FROM(ok(nil)), PROPER(nil)) 218.44/71.59
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.44/71.59
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.59
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0)))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c8, c9, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c32, c33, c34, c35, c36, c, c7, c10, c13, c7, c10, c13, c27, c27, c29, c29, c30, c30, c31

218.44/71.59

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

Removed 2 trailing tuple parts

218.44/71.59

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.44/71.59
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.44/71.59
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.44/71.59
active(add(0, z0)) → mark(z0) 218.44/71.59
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.44/71.59
active(len(nil)) → mark(0) 218.44/71.59
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.44/71.59
active(cons(z0, z1)) → cons(active(z0), z1) 218.44/71.59
active(fst(z0, z1)) → fst(active(z0), z1) 218.44/71.59
active(fst(z0, z1)) → fst(z0, active(z1)) 218.44/71.59
active(from(z0)) → from(active(z0)) 218.44/71.59
active(add(z0, z1)) → add(active(z0), z1) 218.44/71.59
active(add(z0, z1)) → add(z0, active(z1)) 218.44/71.59
active(len(z0)) → len(active(z0)) 218.44/71.59
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.44/71.59
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.44/71.59
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.44/71.59
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.44/71.59
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.44/71.59
from(mark(z0)) → mark(from(z0)) 218.44/71.59
from(ok(z0)) → ok(from(z0)) 218.44/71.59
add(mark(z0), z1) → mark(add(z0, z1)) 218.44/71.59
add(z0, mark(z1)) → mark(add(z0, z1)) 218.44/71.59
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.44/71.59
len(mark(z0)) → mark(len(z0)) 218.44/71.59
len(ok(z0)) → ok(len(z0)) 218.44/71.59
proper(0) → ok(0) 218.44/71.59
proper(s(z0)) → s(proper(z0)) 218.44/71.59
proper(nil) → ok(nil) 218.44/71.59
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.44/71.59
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.44/71.59
proper(from(z0)) → from(proper(z0)) 218.44/71.59
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.44/71.59
proper(len(z0)) → len(proper(z0)) 218.44/71.59
s(ok(z0)) → ok(s(z0)) 218.44/71.59
top(mark(z0)) → top(proper(z0)) 218.44/71.59
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.59
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.59
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.59
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.59
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.59
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.59
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.59
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.59
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.59
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.59
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.59
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.59
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.59
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.59
S(ok(z0)) → c34(S(z0)) 218.44/71.59
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.44/71.59
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.59
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.59
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.59
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.59
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.59
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.59
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.59
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.59
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.59
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.44/71.59
PROPER(s(0)) → c27(S(ok(0))) 218.44/71.59
PROPER(s(nil)) → c27(S(ok(nil))) 218.44/71.59
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.44/71.59
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.59
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.44/71.59
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.59
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.44/71.59
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.44/71.59
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.59
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0))) 218.44/71.59
PROPER(from(0)) → c31(FROM(ok(0))) 218.44/71.59
PROPER(from(nil)) → c31(FROM(ok(nil)))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.59
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.59
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.59
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.59
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.59
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.59
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.59
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.59
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.59
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.59
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.59
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.59
PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 218.44/71.59
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.59
S(ok(z0)) → c34(S(z0)) 218.44/71.59
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.59
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.59
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.59
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.59
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.59
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.59
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.59
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.59
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.59
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.44/71.59
PROPER(s(0)) → c27(S(ok(0))) 218.44/71.59
PROPER(s(nil)) → c27(S(ok(nil))) 218.44/71.59
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.44/71.59
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.59
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.44/71.59
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.59
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.44/71.59
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.44/71.59
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.59
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0))) 218.44/71.59
PROPER(from(0)) → c31(FROM(ok(0))) 218.44/71.59
PROPER(from(nil)) → c31(FROM(ok(nil)))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c8, c9, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c32, c33, c34, c35, c36, c, c7, c10, c13, c7, c10, c13, c27, c27, c29, c29, c30, c30, c31, c31

218.44/71.59

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

Use narrowing to replace PROPER(add(z0, z1)) → c32(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(add(x0, 0)) → c32(ADD(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 218.44/71.59
PROPER(add(x0, s(z0))) → c32(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(add(x0, nil)) → c32(ADD(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 218.44/71.59
PROPER(add(x0, cons(z0, z1))) → c32(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(add(x0, fst(z0, z1))) → c32(ADD(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(add(x0, from(z0))) → c32(ADD(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(add(x0, add(z0, z1))) → c32(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(add(x0, len(z0))) → c32(ADD(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(add(0, x1)) → c32(ADD(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 218.44/71.59
PROPER(add(s(z0), x1)) → c32(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(add(nil, x1)) → c32(ADD(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 218.44/71.59
PROPER(add(cons(z0, z1), x1)) → c32(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(add(fst(z0, z1), x1)) → c32(ADD(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(add(from(z0), x1)) → c32(ADD(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(add(add(z0, z1), x1)) → c32(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(add(len(z0), x1)) → c32(ADD(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1))

218.44/71.59

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.44/71.59
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.44/71.59
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.44/71.59
active(add(0, z0)) → mark(z0) 218.44/71.59
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.44/71.59
active(len(nil)) → mark(0) 218.44/71.59
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.44/71.59
active(cons(z0, z1)) → cons(active(z0), z1) 218.44/71.59
active(fst(z0, z1)) → fst(active(z0), z1) 218.44/71.59
active(fst(z0, z1)) → fst(z0, active(z1)) 218.44/71.59
active(from(z0)) → from(active(z0)) 218.44/71.59
active(add(z0, z1)) → add(active(z0), z1) 218.44/71.59
active(add(z0, z1)) → add(z0, active(z1)) 218.44/71.59
active(len(z0)) → len(active(z0)) 218.44/71.59
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.44/71.59
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.44/71.59
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.44/71.59
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.44/71.59
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.44/71.59
from(mark(z0)) → mark(from(z0)) 218.44/71.59
from(ok(z0)) → ok(from(z0)) 218.44/71.59
add(mark(z0), z1) → mark(add(z0, z1)) 218.44/71.59
add(z0, mark(z1)) → mark(add(z0, z1)) 218.44/71.59
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.44/71.59
len(mark(z0)) → mark(len(z0)) 218.44/71.59
len(ok(z0)) → ok(len(z0)) 218.44/71.59
proper(0) → ok(0) 218.44/71.59
proper(s(z0)) → s(proper(z0)) 218.44/71.59
proper(nil) → ok(nil) 218.44/71.59
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.44/71.59
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.44/71.59
proper(from(z0)) → from(proper(z0)) 218.44/71.59
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.44/71.59
proper(len(z0)) → len(proper(z0)) 218.44/71.59
s(ok(z0)) → ok(s(z0)) 218.44/71.59
top(mark(z0)) → top(proper(z0)) 218.44/71.59
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.59
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.59
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.59
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.59
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.59
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.59
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.59
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.59
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.59
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.59
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.59
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.59
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.59
S(ok(z0)) → c34(S(z0)) 218.44/71.59
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.44/71.59
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.59
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.59
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.59
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.59
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.59
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.59
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.59
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.59
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.59
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.44/71.59
PROPER(s(0)) → c27(S(ok(0))) 218.44/71.59
PROPER(s(nil)) → c27(S(ok(nil))) 218.44/71.59
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.59
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.44/71.59
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.59
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.59
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.44/71.59
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.59
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.59
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.44/71.59
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.44/71.59
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.59
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0))) 218.44/71.59
PROPER(from(0)) → c31(FROM(ok(0))) 218.44/71.59
PROPER(from(nil)) → c31(FROM(ok(nil))) 218.44/71.59
PROPER(add(x0, 0)) → c32(ADD(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 218.44/71.59
PROPER(add(x0, s(z0))) → c32(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.59
PROPER(add(x0, nil)) → c32(ADD(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 218.44/71.59
PROPER(add(x0, cons(z0, z1))) → c32(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.59
PROPER(add(x0, fst(z0, z1))) → c32(ADD(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.59
PROPER(add(x0, from(z0))) → c32(ADD(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.59
PROPER(add(x0, add(z0, z1))) → c32(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.59
PROPER(add(x0, len(z0))) → c32(ADD(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.59
PROPER(add(0, x1)) → c32(ADD(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 218.44/71.59
PROPER(add(s(z0), x1)) → c32(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.59
PROPER(add(nil, x1)) → c32(ADD(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 218.44/71.59
PROPER(add(cons(z0, z1), x1)) → c32(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(add(fst(z0, z1), x1)) → c32(ADD(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(add(from(z0), x1)) → c32(ADD(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.59
PROPER(add(add(z0, z1), x1)) → c32(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.59
PROPER(add(len(z0), x1)) → c32(ADD(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.59
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.59
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.59
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.59
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.59
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.59
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.59
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.59
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.59
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.59
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.59
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.59
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.59
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.59
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.59
S(ok(z0)) → c34(S(z0)) 218.44/71.59
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.59
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.59
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.59
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.59
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.59
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.59
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.59
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.59
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.59
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.59
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.59
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.59
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.59
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.60
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.60
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.60
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.60
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.60
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.60
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.60
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.60
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.60
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.60
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.60
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.60
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.60
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.60
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.60
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.60
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.60
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.60
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.60
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.60
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.60
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.60
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.60
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.60
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.60
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.60
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.60
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.60
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.60
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.60
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.60
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.60
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.60
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.44/71.60
PROPER(s(0)) → c27(S(ok(0))) 218.44/71.60
PROPER(s(nil)) → c27(S(ok(nil))) 218.44/71.60
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.60
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.60
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.60
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.60
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.60
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.60
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.60
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.60
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.60
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.44/71.60
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.60
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.44/71.60
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.60
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.60
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.60
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.60
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.60
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.60
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.60
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.60
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.60
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.60
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.44/71.60
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.60
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.44/71.60
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.60
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.44/71.60
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.60
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.60
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.44/71.60
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.60
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0))) 218.44/71.60
PROPER(from(0)) → c31(FROM(ok(0))) 218.44/71.60
PROPER(from(nil)) → c31(FROM(ok(nil))) 218.44/71.60
PROPER(add(x0, 0)) → c32(ADD(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 218.44/71.60
PROPER(add(x0, s(z0))) → c32(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.60
PROPER(add(x0, nil)) → c32(ADD(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 218.44/71.60
PROPER(add(x0, cons(z0, z1))) → c32(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.60
PROPER(add(x0, fst(z0, z1))) → c32(ADD(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.60
PROPER(add(x0, from(z0))) → c32(ADD(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.60
PROPER(add(x0, add(z0, z1))) → c32(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.60
PROPER(add(x0, len(z0))) → c32(ADD(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.60
PROPER(add(0, x1)) → c32(ADD(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 218.44/71.60
PROPER(add(s(z0), x1)) → c32(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.60
PROPER(add(nil, x1)) → c32(ADD(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 218.44/71.60
PROPER(add(cons(z0, z1), x1)) → c32(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(add(fst(z0, z1), x1)) → c32(ADD(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(add(from(z0), x1)) → c32(ADD(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.60
PROPER(add(add(z0, z1), x1)) → c32(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(add(len(z0), x1)) → c32(ADD(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c8, c9, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c33, c34, c35, c36, c, c7, c10, c13, c7, c10, c13, c27, c27, c29, c29, c30, c30, c31, c31, c32

218.44/71.60

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

Removed 4 trailing tuple parts

218.44/71.60

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.44/71.60
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.44/71.60
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.44/71.60
active(add(0, z0)) → mark(z0) 218.44/71.60
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.44/71.60
active(len(nil)) → mark(0) 218.44/71.60
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.44/71.60
active(cons(z0, z1)) → cons(active(z0), z1) 218.44/71.60
active(fst(z0, z1)) → fst(active(z0), z1) 218.44/71.60
active(fst(z0, z1)) → fst(z0, active(z1)) 218.44/71.60
active(from(z0)) → from(active(z0)) 218.44/71.60
active(add(z0, z1)) → add(active(z0), z1) 218.44/71.60
active(add(z0, z1)) → add(z0, active(z1)) 218.44/71.60
active(len(z0)) → len(active(z0)) 218.44/71.60
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.44/71.60
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.44/71.60
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.44/71.60
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.44/71.60
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.44/71.60
from(mark(z0)) → mark(from(z0)) 218.44/71.60
from(ok(z0)) → ok(from(z0)) 218.44/71.60
add(mark(z0), z1) → mark(add(z0, z1)) 218.44/71.60
add(z0, mark(z1)) → mark(add(z0, z1)) 218.44/71.60
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.44/71.60
len(mark(z0)) → mark(len(z0)) 218.44/71.60
len(ok(z0)) → ok(len(z0)) 218.44/71.60
proper(0) → ok(0) 218.44/71.60
proper(s(z0)) → s(proper(z0)) 218.44/71.60
proper(nil) → ok(nil) 218.44/71.60
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.44/71.60
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.44/71.60
proper(from(z0)) → from(proper(z0)) 218.44/71.60
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.44/71.60
proper(len(z0)) → len(proper(z0)) 218.44/71.60
s(ok(z0)) → ok(s(z0)) 218.44/71.60
top(mark(z0)) → top(proper(z0)) 218.44/71.60
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.60
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.60
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.60
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.60
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.60
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.60
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.60
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.60
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.60
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.60
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.60
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.60
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.60
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.60
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.60
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.60
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.60
S(ok(z0)) → c34(S(z0)) 218.44/71.60
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.44/71.60
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.60
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.60
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.60
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.60
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.60
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.60
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.60
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.60
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.60
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.60
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.60
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.60
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.60
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.60
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.60
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.60
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.60
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.60
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.60
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.60
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.60
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.60
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.60
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.60
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.60
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.60
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.60
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.60
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.60
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.60
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.60
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.44/71.60
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.60
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.60
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.44/71.60
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.60
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.60
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.60
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.60
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.60
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.60
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.60
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.60
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.44/71.60
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.44/71.60
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.44/71.60
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.44/71.60
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.44/71.60
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.44/71.60
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.44/71.60
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.44/71.60
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.44/71.60
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.60
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.60
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.44/71.60
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.60
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.44/71.60
PROPER(s(0)) → c27(S(ok(0))) 218.44/71.60
PROPER(s(nil)) → c27(S(ok(nil))) 218.44/71.60
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.60
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.60
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.60
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.60
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.60
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.60
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.60
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.60
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.60
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.44/71.60
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.60
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.44/71.60
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.60
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.60
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.60
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.60
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.60
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.60
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.60
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.60
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.60
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.60
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.44/71.60
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.60
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.44/71.60
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.44/71.60
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.44/71.60
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.44/71.60
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.44/71.60
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.44/71.60
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.44/71.60
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0))) 218.44/71.60
PROPER(from(0)) → c31(FROM(ok(0))) 218.44/71.60
PROPER(from(nil)) → c31(FROM(ok(nil))) 218.44/71.60
PROPER(add(x0, s(z0))) → c32(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.44/71.60
PROPER(add(x0, cons(z0, z1))) → c32(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.44/71.60
PROPER(add(x0, fst(z0, z1))) → c32(ADD(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.44/71.60
PROPER(add(x0, from(z0))) → c32(ADD(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.44/71.60
PROPER(add(x0, add(z0, z1))) → c32(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.44/71.60
PROPER(add(x0, len(z0))) → c32(ADD(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.44/71.60
PROPER(add(s(z0), x1)) → c32(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.44/71.60
PROPER(add(cons(z0, z1), x1)) → c32(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(add(fst(z0, z1), x1)) → c32(ADD(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(add(from(z0), x1)) → c32(ADD(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.44/71.60
PROPER(add(add(z0, z1), x1)) → c32(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.44/71.60
PROPER(add(len(z0), x1)) → c32(ADD(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.44/71.60
PROPER(add(x0, 0)) → c32(ADD(proper(x0), ok(0)), PROPER(x0)) 218.44/71.60
PROPER(add(x0, nil)) → c32(ADD(proper(x0), ok(nil)), PROPER(x0)) 218.44/71.60
PROPER(add(0, x1)) → c32(ADD(ok(0), proper(x1)), PROPER(x1)) 218.44/71.60
PROPER(add(nil, x1)) → c32(ADD(ok(nil), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.44/71.60
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.44/71.60
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.44/71.60
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.44/71.60
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.44/71.60
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.44/71.60
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.44/71.60
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.44/71.60
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.44/71.60
FROM(mark(z0)) → c19(FROM(z0)) 218.44/71.60
FROM(ok(z0)) → c20(FROM(z0)) 218.44/71.60
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.44/71.60
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.44/71.60
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.44/71.60
LEN(mark(z0)) → c24(LEN(z0)) 218.44/71.60
LEN(ok(z0)) → c25(LEN(z0)) 218.44/71.60
PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) 218.44/71.60
S(ok(z0)) → c34(S(z0)) 218.44/71.60
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.44/71.60
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.44/71.60
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.44/71.60
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.44/71.60
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.44/71.60
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.44/71.60
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.44/71.60
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.44/71.60
ACTIVE(from(z0)) → c(S(z0)) 218.44/71.60
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.44/71.60
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.60
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.44/71.60
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.44/71.60
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.44/71.60
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.44/71.60
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.44/71.60
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.44/71.60
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.44/71.60
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.44/71.60
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.44/71.60
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.44/71.60
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.44/71.60
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.44/71.60
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.44/71.60
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.44/71.60
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.44/71.60
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.44/71.60
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.44/71.60
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.44/71.60
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.44/71.60
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.77/71.60
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.60
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.60
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.60
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.60
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.60
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.60
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.77/71.60
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.77/71.60
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.77/71.60
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.77/71.60
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.77/71.60
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.77/71.60
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.60
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.77/71.60
PROPER(s(0)) → c27(S(ok(0))) 218.77/71.60
PROPER(s(nil)) → c27(S(ok(nil))) 218.77/71.60
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.60
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.60
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.60
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.60
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.60
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.60
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.60
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.77/71.60
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.60
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.60
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.60
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.60
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.60
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.60
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.60
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.60
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.77/71.60
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.60
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.77/71.60
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.77/71.60
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.60
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0))) 218.77/71.60
PROPER(from(0)) → c31(FROM(ok(0))) 218.77/71.60
PROPER(from(nil)) → c31(FROM(ok(nil))) 218.77/71.60
PROPER(add(x0, s(z0))) → c32(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.60
PROPER(add(x0, cons(z0, z1))) → c32(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(add(x0, fst(z0, z1))) → c32(ADD(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(add(x0, from(z0))) → c32(ADD(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.60
PROPER(add(x0, add(z0, z1))) → c32(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.60
PROPER(add(x0, len(z0))) → c32(ADD(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.60
PROPER(add(s(z0), x1)) → c32(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.60
PROPER(add(cons(z0, z1), x1)) → c32(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(add(fst(z0, z1), x1)) → c32(ADD(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(add(from(z0), x1)) → c32(ADD(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.60
PROPER(add(add(z0, z1), x1)) → c32(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(add(len(z0), x1)) → c32(ADD(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.60
PROPER(add(x0, 0)) → c32(ADD(proper(x0), ok(0)), PROPER(x0)) 218.77/71.60
PROPER(add(x0, nil)) → c32(ADD(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.60
PROPER(add(0, x1)) → c32(ADD(ok(0), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(add(nil, x1)) → c32(ADD(ok(nil), proper(x1)), PROPER(x1))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, PROPER, S, TOP

Compound Symbols:

c8, c9, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c33, c34, c35, c36, c, c7, c10, c13, c7, c10, c13, c27, c27, c29, c29, c30, c30, c31, c31, c32, c32

218.77/71.60

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

Use narrowing to replace PROPER(len(z0)) → c33(LEN(proper(z0)), PROPER(z0)) by

PROPER(len(0)) → c33(LEN(ok(0)), PROPER(0)) 218.77/71.60
PROPER(len(s(z0))) → c33(LEN(s(proper(z0))), PROPER(s(z0))) 218.77/71.60
PROPER(len(nil)) → c33(LEN(ok(nil)), PROPER(nil)) 218.77/71.60
PROPER(len(cons(z0, z1))) → c33(LEN(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(len(fst(z0, z1))) → c33(LEN(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(len(from(z0))) → c33(LEN(from(proper(z0))), PROPER(from(z0))) 218.77/71.60
PROPER(len(add(z0, z1))) → c33(LEN(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.60
PROPER(len(len(z0))) → c33(LEN(len(proper(z0))), PROPER(len(z0)))

218.77/71.60

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.77/71.60
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.77/71.60
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.77/71.60
active(add(0, z0)) → mark(z0) 218.77/71.60
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.77/71.60
active(len(nil)) → mark(0) 218.77/71.60
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.77/71.60
active(cons(z0, z1)) → cons(active(z0), z1) 218.77/71.60
active(fst(z0, z1)) → fst(active(z0), z1) 218.77/71.60
active(fst(z0, z1)) → fst(z0, active(z1)) 218.77/71.60
active(from(z0)) → from(active(z0)) 218.77/71.60
active(add(z0, z1)) → add(active(z0), z1) 218.77/71.60
active(add(z0, z1)) → add(z0, active(z1)) 218.77/71.60
active(len(z0)) → len(active(z0)) 218.77/71.60
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.77/71.60
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.77/71.60
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.77/71.60
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.77/71.60
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.77/71.60
from(mark(z0)) → mark(from(z0)) 218.77/71.60
from(ok(z0)) → ok(from(z0)) 218.77/71.60
add(mark(z0), z1) → mark(add(z0, z1)) 218.77/71.60
add(z0, mark(z1)) → mark(add(z0, z1)) 218.77/71.60
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.77/71.60
len(mark(z0)) → mark(len(z0)) 218.77/71.60
len(ok(z0)) → ok(len(z0)) 218.77/71.60
proper(0) → ok(0) 218.77/71.60
proper(s(z0)) → s(proper(z0)) 218.77/71.60
proper(nil) → ok(nil) 218.77/71.60
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.77/71.60
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.77/71.60
proper(from(z0)) → from(proper(z0)) 218.77/71.60
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.77/71.60
proper(len(z0)) → len(proper(z0)) 218.77/71.60
s(ok(z0)) → ok(s(z0)) 218.77/71.60
top(mark(z0)) → top(proper(z0)) 218.77/71.60
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.77/71.60
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.77/71.60
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.77/71.60
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.77/71.60
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.60
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.60
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.60
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.60
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.60
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.60
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.60
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.60
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.60
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.60
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.60
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.60
S(ok(z0)) → c34(S(z0)) 218.77/71.60
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.77/71.60
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.77/71.60
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.77/71.60
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.77/71.60
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.77/71.60
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.77/71.60
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.77/71.60
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.77/71.60
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.77/71.60
ACTIVE(from(z0)) → c(S(z0)) 218.77/71.60
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.77/71.60
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.60
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.77/71.60
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.77/71.60
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.77/71.60
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.77/71.60
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.77/71.60
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.60
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.60
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.60
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.60
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.60
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.60
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.77/71.60
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.60
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.60
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.60
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.60
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.60
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.60
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.77/71.60
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.77/71.60
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.77/71.60
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.77/71.60
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.77/71.60
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.77/71.60
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.60
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.77/71.60
PROPER(s(0)) → c27(S(ok(0))) 218.77/71.60
PROPER(s(nil)) → c27(S(ok(nil))) 218.77/71.60
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.60
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.60
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.60
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.60
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.60
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.60
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.60
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.77/71.60
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.60
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.60
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.60
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.60
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.60
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.60
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.60
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.60
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.77/71.60
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.60
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.77/71.60
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.77/71.60
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.60
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0))) 218.77/71.60
PROPER(from(0)) → c31(FROM(ok(0))) 218.77/71.60
PROPER(from(nil)) → c31(FROM(ok(nil))) 218.77/71.60
PROPER(add(x0, s(z0))) → c32(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.60
PROPER(add(x0, cons(z0, z1))) → c32(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(add(x0, fst(z0, z1))) → c32(ADD(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(add(x0, from(z0))) → c32(ADD(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.60
PROPER(add(x0, add(z0, z1))) → c32(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.60
PROPER(add(x0, len(z0))) → c32(ADD(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.60
PROPER(add(s(z0), x1)) → c32(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.60
PROPER(add(cons(z0, z1), x1)) → c32(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(add(fst(z0, z1), x1)) → c32(ADD(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(add(from(z0), x1)) → c32(ADD(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.60
PROPER(add(add(z0, z1), x1)) → c32(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(add(len(z0), x1)) → c32(ADD(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.60
PROPER(add(x0, 0)) → c32(ADD(proper(x0), ok(0)), PROPER(x0)) 218.77/71.60
PROPER(add(x0, nil)) → c32(ADD(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.60
PROPER(add(0, x1)) → c32(ADD(ok(0), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(add(nil, x1)) → c32(ADD(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(len(0)) → c33(LEN(ok(0)), PROPER(0)) 218.77/71.60
PROPER(len(s(z0))) → c33(LEN(s(proper(z0))), PROPER(s(z0))) 218.77/71.60
PROPER(len(nil)) → c33(LEN(ok(nil)), PROPER(nil)) 218.77/71.60
PROPER(len(cons(z0, z1))) → c33(LEN(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(len(fst(z0, z1))) → c33(LEN(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(len(from(z0))) → c33(LEN(from(proper(z0))), PROPER(from(z0))) 218.77/71.60
PROPER(len(add(z0, z1))) → c33(LEN(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.60
PROPER(len(len(z0))) → c33(LEN(len(proper(z0))), PROPER(len(z0)))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.77/71.60
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.77/71.60
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.77/71.60
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.77/71.60
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.60
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.60
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.60
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.60
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.60
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.60
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.60
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.60
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.60
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.60
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.60
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.60
S(ok(z0)) → c34(S(z0)) 218.77/71.60
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.77/71.60
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.77/71.60
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.77/71.60
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.77/71.60
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.77/71.60
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.77/71.60
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.77/71.60
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.77/71.60
ACTIVE(from(z0)) → c(S(z0)) 218.77/71.60
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.77/71.60
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.60
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.77/71.60
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.77/71.60
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.77/71.60
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.77/71.60
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.77/71.60
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.60
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.60
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.60
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.60
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.60
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.60
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.77/71.60
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.60
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.60
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.60
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.60
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.60
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.60
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.77/71.60
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.77/71.60
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.77/71.60
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.77/71.60
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.77/71.60
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.77/71.60
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.60
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.77/71.60
PROPER(s(0)) → c27(S(ok(0))) 218.77/71.60
PROPER(s(nil)) → c27(S(ok(nil))) 218.77/71.60
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.60
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.60
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.60
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.60
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.60
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.60
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.60
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.77/71.60
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.60
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.60
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.60
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.60
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.60
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.60
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.60
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.60
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.77/71.60
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.60
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.77/71.60
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.77/71.60
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.60
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0))) 218.77/71.60
PROPER(from(0)) → c31(FROM(ok(0))) 218.77/71.60
PROPER(from(nil)) → c31(FROM(ok(nil))) 218.77/71.60
PROPER(add(x0, s(z0))) → c32(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.60
PROPER(add(x0, cons(z0, z1))) → c32(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(add(x0, fst(z0, z1))) → c32(ADD(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(add(x0, from(z0))) → c32(ADD(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.60
PROPER(add(x0, add(z0, z1))) → c32(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.60
PROPER(add(x0, len(z0))) → c32(ADD(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.60
PROPER(add(s(z0), x1)) → c32(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.60
PROPER(add(cons(z0, z1), x1)) → c32(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(add(fst(z0, z1), x1)) → c32(ADD(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(add(from(z0), x1)) → c32(ADD(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.60
PROPER(add(add(z0, z1), x1)) → c32(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(add(len(z0), x1)) → c32(ADD(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.60
PROPER(add(x0, 0)) → c32(ADD(proper(x0), ok(0)), PROPER(x0)) 218.77/71.60
PROPER(add(x0, nil)) → c32(ADD(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.60
PROPER(add(0, x1)) → c32(ADD(ok(0), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(add(nil, x1)) → c32(ADD(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(len(0)) → c33(LEN(ok(0)), PROPER(0)) 218.77/71.60
PROPER(len(s(z0))) → c33(LEN(s(proper(z0))), PROPER(s(z0))) 218.77/71.60
PROPER(len(nil)) → c33(LEN(ok(nil)), PROPER(nil)) 218.77/71.60
PROPER(len(cons(z0, z1))) → c33(LEN(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(len(fst(z0, z1))) → c33(LEN(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(len(from(z0))) → c33(LEN(from(proper(z0))), PROPER(from(z0))) 218.77/71.60
PROPER(len(add(z0, z1))) → c33(LEN(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.60
PROPER(len(len(z0))) → c33(LEN(len(proper(z0))), PROPER(len(z0)))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, S, TOP, PROPER

Compound Symbols:

c8, c9, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c34, c35, c36, c, c7, c10, c13, c7, c10, c13, c27, c27, c29, c29, c30, c30, c31, c31, c32, c32, c33

218.77/71.60

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

Removed 2 trailing tuple parts

218.77/71.60

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.77/71.60
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.77/71.60
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.77/71.60
active(add(0, z0)) → mark(z0) 218.77/71.60
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.77/71.60
active(len(nil)) → mark(0) 218.77/71.60
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.77/71.60
active(cons(z0, z1)) → cons(active(z0), z1) 218.77/71.60
active(fst(z0, z1)) → fst(active(z0), z1) 218.77/71.60
active(fst(z0, z1)) → fst(z0, active(z1)) 218.77/71.60
active(from(z0)) → from(active(z0)) 218.77/71.60
active(add(z0, z1)) → add(active(z0), z1) 218.77/71.60
active(add(z0, z1)) → add(z0, active(z1)) 218.77/71.60
active(len(z0)) → len(active(z0)) 218.77/71.60
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.77/71.60
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.77/71.60
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.77/71.60
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.77/71.60
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.77/71.60
from(mark(z0)) → mark(from(z0)) 218.77/71.60
from(ok(z0)) → ok(from(z0)) 218.77/71.60
add(mark(z0), z1) → mark(add(z0, z1)) 218.77/71.60
add(z0, mark(z1)) → mark(add(z0, z1)) 218.77/71.60
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.77/71.60
len(mark(z0)) → mark(len(z0)) 218.77/71.60
len(ok(z0)) → ok(len(z0)) 218.77/71.60
proper(0) → ok(0) 218.77/71.60
proper(s(z0)) → s(proper(z0)) 218.77/71.60
proper(nil) → ok(nil) 218.77/71.60
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.77/71.60
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.77/71.60
proper(from(z0)) → from(proper(z0)) 218.77/71.60
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.77/71.60
proper(len(z0)) → len(proper(z0)) 218.77/71.60
s(ok(z0)) → ok(s(z0)) 218.77/71.60
top(mark(z0)) → top(proper(z0)) 218.77/71.60
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.77/71.60
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.77/71.60
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.77/71.60
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.77/71.60
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.60
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.60
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.60
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.60
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.60
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.60
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.60
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.60
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.60
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.60
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.60
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.60
S(ok(z0)) → c34(S(z0)) 218.77/71.60
TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0)) 218.77/71.60
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.77/71.60
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.77/71.60
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.77/71.60
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.77/71.60
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.77/71.60
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.77/71.60
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.77/71.60
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.77/71.60
ACTIVE(from(z0)) → c(S(z0)) 218.77/71.60
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.77/71.60
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.60
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.77/71.60
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.77/71.60
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.77/71.60
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.77/71.60
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.77/71.60
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.60
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.60
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.60
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.60
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.60
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.60
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.77/71.60
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.60
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.60
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.60
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.60
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.60
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.60
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.77/71.60
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.77/71.60
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.77/71.60
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.77/71.60
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.77/71.60
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.77/71.60
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.60
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.77/71.60
PROPER(s(0)) → c27(S(ok(0))) 218.77/71.60
PROPER(s(nil)) → c27(S(ok(nil))) 218.77/71.60
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.60
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.60
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.60
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.60
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.60
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.60
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.60
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.77/71.60
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.60
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.60
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.60
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.60
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.60
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.60
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.60
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.60
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.77/71.60
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.60
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.77/71.60
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.77/71.60
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.60
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0))) 218.77/71.60
PROPER(from(0)) → c31(FROM(ok(0))) 218.77/71.60
PROPER(from(nil)) → c31(FROM(ok(nil))) 218.77/71.60
PROPER(add(x0, s(z0))) → c32(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.60
PROPER(add(x0, cons(z0, z1))) → c32(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(add(x0, fst(z0, z1))) → c32(ADD(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(add(x0, from(z0))) → c32(ADD(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.60
PROPER(add(x0, add(z0, z1))) → c32(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.60
PROPER(add(x0, len(z0))) → c32(ADD(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.60
PROPER(add(s(z0), x1)) → c32(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.60
PROPER(add(cons(z0, z1), x1)) → c32(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(add(fst(z0, z1), x1)) → c32(ADD(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(add(from(z0), x1)) → c32(ADD(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.60
PROPER(add(add(z0, z1), x1)) → c32(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(add(len(z0), x1)) → c32(ADD(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.60
PROPER(add(x0, 0)) → c32(ADD(proper(x0), ok(0)), PROPER(x0)) 218.77/71.60
PROPER(add(x0, nil)) → c32(ADD(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.60
PROPER(add(0, x1)) → c32(ADD(ok(0), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(add(nil, x1)) → c32(ADD(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(len(s(z0))) → c33(LEN(s(proper(z0))), PROPER(s(z0))) 218.77/71.60
PROPER(len(cons(z0, z1))) → c33(LEN(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(len(fst(z0, z1))) → c33(LEN(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(len(from(z0))) → c33(LEN(from(proper(z0))), PROPER(from(z0))) 218.77/71.60
PROPER(len(add(z0, z1))) → c33(LEN(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.60
PROPER(len(len(z0))) → c33(LEN(len(proper(z0))), PROPER(len(z0))) 218.77/71.60
PROPER(len(0)) → c33(LEN(ok(0))) 218.77/71.60
PROPER(len(nil)) → c33(LEN(ok(nil)))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.77/71.60
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.77/71.60
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.77/71.60
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.77/71.60
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.60
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.60
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.60
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.60
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.60
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.60
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.60
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.60
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.60
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.60
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.60
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.60
S(ok(z0)) → c34(S(z0)) 218.77/71.60
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.77/71.60
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.77/71.60
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.77/71.60
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.77/71.60
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.77/71.60
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.77/71.60
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.77/71.60
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.77/71.60
ACTIVE(from(z0)) → c(S(z0)) 218.77/71.60
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.77/71.60
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.60
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.77/71.60
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.77/71.60
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.77/71.60
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.77/71.60
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.77/71.60
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.60
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.60
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.60
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.60
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.60
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.60
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.77/71.60
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.60
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.60
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.60
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.60
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.60
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.60
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.77/71.60
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.77/71.60
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.77/71.60
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.77/71.60
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.77/71.60
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.77/71.60
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.60
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.77/71.60
PROPER(s(0)) → c27(S(ok(0))) 218.77/71.60
PROPER(s(nil)) → c27(S(ok(nil))) 218.77/71.60
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.60
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.60
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.60
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.60
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.60
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.60
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.60
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.77/71.60
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.60
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.60
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.60
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.60
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.60
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.60
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.60
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.60
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.77/71.60
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.60
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.77/71.60
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.77/71.60
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.60
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0))) 218.77/71.60
PROPER(from(0)) → c31(FROM(ok(0))) 218.77/71.60
PROPER(from(nil)) → c31(FROM(ok(nil))) 218.77/71.60
PROPER(add(x0, s(z0))) → c32(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.60
PROPER(add(x0, cons(z0, z1))) → c32(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(add(x0, fst(z0, z1))) → c32(ADD(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(add(x0, from(z0))) → c32(ADD(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.60
PROPER(add(x0, add(z0, z1))) → c32(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.60
PROPER(add(x0, len(z0))) → c32(ADD(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.60
PROPER(add(s(z0), x1)) → c32(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.60
PROPER(add(cons(z0, z1), x1)) → c32(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(add(fst(z0, z1), x1)) → c32(ADD(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(add(from(z0), x1)) → c32(ADD(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.60
PROPER(add(add(z0, z1), x1)) → c32(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.60
PROPER(add(len(z0), x1)) → c32(ADD(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.60
PROPER(add(x0, 0)) → c32(ADD(proper(x0), ok(0)), PROPER(x0)) 218.77/71.60
PROPER(add(x0, nil)) → c32(ADD(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.60
PROPER(add(0, x1)) → c32(ADD(ok(0), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(add(nil, x1)) → c32(ADD(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.60
PROPER(len(s(z0))) → c33(LEN(s(proper(z0))), PROPER(s(z0))) 218.77/71.60
PROPER(len(cons(z0, z1))) → c33(LEN(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.60
PROPER(len(fst(z0, z1))) → c33(LEN(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.60
PROPER(len(from(z0))) → c33(LEN(from(proper(z0))), PROPER(from(z0))) 218.77/71.60
PROPER(len(add(z0, z1))) → c33(LEN(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.60
PROPER(len(len(z0))) → c33(LEN(len(proper(z0))), PROPER(len(z0))) 218.77/71.60
PROPER(len(0)) → c33(LEN(ok(0))) 218.77/71.60
PROPER(len(nil)) → c33(LEN(ok(nil)))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, S, TOP, PROPER

Compound Symbols:

c8, c9, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c34, c35, c36, c, c7, c10, c13, c7, c10, c13, c27, c27, c29, c29, c30, c30, c31, c31, c32, c32, c33, c33

218.77/71.60

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

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

TOP(mark(0)) → c35(TOP(ok(0)), PROPER(0)) 218.77/71.60
TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 218.77/71.60
TOP(mark(nil)) → c35(TOP(ok(nil)), PROPER(nil)) 218.77/71.60
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.60
TOP(mark(fst(z0, z1))) → c35(TOP(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.60
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0))) 218.77/71.60
TOP(mark(add(z0, z1))) → c35(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.60
TOP(mark(len(z0))) → c35(TOP(len(proper(z0))), PROPER(len(z0)))

218.77/71.60

(42) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.77/71.60
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.77/71.60
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.77/71.60
active(add(0, z0)) → mark(z0) 218.77/71.60
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.77/71.60
active(len(nil)) → mark(0) 218.77/71.60
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.77/71.60
active(cons(z0, z1)) → cons(active(z0), z1) 218.77/71.60
active(fst(z0, z1)) → fst(active(z0), z1) 218.77/71.60
active(fst(z0, z1)) → fst(z0, active(z1)) 218.77/71.60
active(from(z0)) → from(active(z0)) 218.77/71.60
active(add(z0, z1)) → add(active(z0), z1) 218.77/71.60
active(add(z0, z1)) → add(z0, active(z1)) 218.77/71.60
active(len(z0)) → len(active(z0)) 218.77/71.60
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.77/71.60
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.77/71.60
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.77/71.60
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.77/71.60
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.77/71.60
from(mark(z0)) → mark(from(z0)) 218.77/71.60
from(ok(z0)) → ok(from(z0)) 218.77/71.60
add(mark(z0), z1) → mark(add(z0, z1)) 218.77/71.60
add(z0, mark(z1)) → mark(add(z0, z1)) 218.77/71.60
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.77/71.60
len(mark(z0)) → mark(len(z0)) 218.77/71.60
len(ok(z0)) → ok(len(z0)) 218.77/71.60
proper(0) → ok(0) 218.77/71.60
proper(s(z0)) → s(proper(z0)) 218.77/71.60
proper(nil) → ok(nil) 218.77/71.60
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.77/71.60
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.77/71.60
proper(from(z0)) → from(proper(z0)) 218.77/71.60
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.77/71.60
proper(len(z0)) → len(proper(z0)) 218.77/71.60
s(ok(z0)) → ok(s(z0)) 218.77/71.60
top(mark(z0)) → top(proper(z0)) 218.77/71.60
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.77/71.60
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.77/71.60
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.77/71.60
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.77/71.60
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.60
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.60
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.60
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.60
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.60
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.60
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.60
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.60
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.60
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.60
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.60
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.60
S(ok(z0)) → c34(S(z0)) 218.77/71.60
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.77/71.60
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.77/71.60
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.77/71.60
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.77/71.60
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.77/71.60
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.77/71.60
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.77/71.60
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.77/71.60
ACTIVE(from(z0)) → c(S(z0)) 218.77/71.60
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.77/71.60
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.60
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.77/71.60
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.77/71.60
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.77/71.60
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.77/71.60
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.77/71.60
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.77/71.60
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.77/71.60
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.77/71.60
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.77/71.61
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.77/71.61
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.77/71.61
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(s(0)) → c27(S(ok(0))) 218.77/71.61
PROPER(s(nil)) → c27(S(ok(nil))) 218.77/71.61
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(from(0)) → c31(FROM(ok(0))) 218.77/71.61
PROPER(from(nil)) → c31(FROM(ok(nil))) 218.77/71.61
PROPER(add(x0, s(z0))) → c32(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(add(x0, cons(z0, z1))) → c32(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(add(x0, fst(z0, z1))) → c32(ADD(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(add(x0, from(z0))) → c32(ADD(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(add(x0, add(z0, z1))) → c32(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(add(x0, len(z0))) → c32(ADD(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(add(s(z0), x1)) → c32(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(cons(z0, z1), x1)) → c32(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(fst(z0, z1), x1)) → c32(ADD(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(from(z0), x1)) → c32(ADD(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(add(z0, z1), x1)) → c32(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(len(z0), x1)) → c32(ADD(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(x0, 0)) → c32(ADD(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(add(x0, nil)) → c32(ADD(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(add(0, x1)) → c32(ADD(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(add(nil, x1)) → c32(ADD(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(len(s(z0))) → c33(LEN(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(len(cons(z0, z1))) → c33(LEN(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(len(fst(z0, z1))) → c33(LEN(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(len(from(z0))) → c33(LEN(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(len(add(z0, z1))) → c33(LEN(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(len(len(z0))) → c33(LEN(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(len(0)) → c33(LEN(ok(0))) 218.77/71.61
PROPER(len(nil)) → c33(LEN(ok(nil))) 218.77/71.61
TOP(mark(0)) → c35(TOP(ok(0)), PROPER(0)) 218.77/71.61
TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
TOP(mark(nil)) → c35(TOP(ok(nil)), PROPER(nil)) 218.77/71.61
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
TOP(mark(fst(z0, z1))) → c35(TOP(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
TOP(mark(add(z0, z1))) → c35(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
TOP(mark(len(z0))) → c35(TOP(len(proper(z0))), PROPER(len(z0)))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.77/71.61
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.77/71.61
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.77/71.61
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.77/71.61
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.61
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.61
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.61
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.61
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.61
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.61
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.61
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.61
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.61
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.61
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.61
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.61
S(ok(z0)) → c34(S(z0)) 218.77/71.61
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.77/71.61
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.77/71.61
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.77/71.61
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.77/71.61
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.77/71.61
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.77/71.61
ACTIVE(from(z0)) → c(S(z0)) 218.77/71.61
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.77/71.61
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.77/71.61
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.77/71.61
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(s(0)) → c27(S(ok(0))) 218.77/71.61
PROPER(s(nil)) → c27(S(ok(nil))) 218.77/71.61
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(from(0)) → c31(FROM(ok(0))) 218.77/71.61
PROPER(from(nil)) → c31(FROM(ok(nil))) 218.77/71.61
PROPER(add(x0, s(z0))) → c32(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(add(x0, cons(z0, z1))) → c32(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(add(x0, fst(z0, z1))) → c32(ADD(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(add(x0, from(z0))) → c32(ADD(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(add(x0, add(z0, z1))) → c32(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(add(x0, len(z0))) → c32(ADD(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(add(s(z0), x1)) → c32(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(cons(z0, z1), x1)) → c32(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(fst(z0, z1), x1)) → c32(ADD(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(from(z0), x1)) → c32(ADD(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(add(z0, z1), x1)) → c32(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(len(z0), x1)) → c32(ADD(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(x0, 0)) → c32(ADD(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(add(x0, nil)) → c32(ADD(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(add(0, x1)) → c32(ADD(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(add(nil, x1)) → c32(ADD(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(len(s(z0))) → c33(LEN(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(len(cons(z0, z1))) → c33(LEN(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(len(fst(z0, z1))) → c33(LEN(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(len(from(z0))) → c33(LEN(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(len(add(z0, z1))) → c33(LEN(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(len(len(z0))) → c33(LEN(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(len(0)) → c33(LEN(ok(0))) 218.77/71.61
PROPER(len(nil)) → c33(LEN(ok(nil)))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, S, TOP, PROPER

Compound Symbols:

c8, c9, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c34, c36, c, c7, c10, c13, c7, c10, c13, c27, c27, c29, c29, c30, c30, c31, c31, c32, c32, c33, c33, c35

218.77/71.61

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

Removed 2 trailing tuple parts

218.77/71.61

(44) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.77/71.61
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.77/71.61
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.77/71.61
active(add(0, z0)) → mark(z0) 218.77/71.61
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.77/71.61
active(len(nil)) → mark(0) 218.77/71.61
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.77/71.61
active(cons(z0, z1)) → cons(active(z0), z1) 218.77/71.61
active(fst(z0, z1)) → fst(active(z0), z1) 218.77/71.61
active(fst(z0, z1)) → fst(z0, active(z1)) 218.77/71.61
active(from(z0)) → from(active(z0)) 218.77/71.61
active(add(z0, z1)) → add(active(z0), z1) 218.77/71.61
active(add(z0, z1)) → add(z0, active(z1)) 218.77/71.61
active(len(z0)) → len(active(z0)) 218.77/71.61
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.77/71.61
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.77/71.61
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.77/71.61
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.77/71.61
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.77/71.61
from(mark(z0)) → mark(from(z0)) 218.77/71.61
from(ok(z0)) → ok(from(z0)) 218.77/71.61
add(mark(z0), z1) → mark(add(z0, z1)) 218.77/71.61
add(z0, mark(z1)) → mark(add(z0, z1)) 218.77/71.61
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.77/71.61
len(mark(z0)) → mark(len(z0)) 218.77/71.61
len(ok(z0)) → ok(len(z0)) 218.77/71.61
proper(0) → ok(0) 218.77/71.61
proper(s(z0)) → s(proper(z0)) 218.77/71.61
proper(nil) → ok(nil) 218.77/71.61
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.77/71.61
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.77/71.61
proper(from(z0)) → from(proper(z0)) 218.77/71.61
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.77/71.61
proper(len(z0)) → len(proper(z0)) 218.77/71.61
s(ok(z0)) → ok(s(z0)) 218.77/71.61
top(mark(z0)) → top(proper(z0)) 218.77/71.61
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.77/71.61
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.77/71.61
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.77/71.61
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.77/71.61
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.61
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.61
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.61
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.61
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.61
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.61
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.61
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.61
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.61
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.61
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.61
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.61
S(ok(z0)) → c34(S(z0)) 218.77/71.61
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.77/71.61
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.77/71.61
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.77/71.61
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.77/71.61
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.77/71.61
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.77/71.61
ACTIVE(from(z0)) → c(S(z0)) 218.77/71.61
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.77/71.61
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.77/71.61
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.77/71.61
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(s(0)) → c27(S(ok(0))) 218.77/71.61
PROPER(s(nil)) → c27(S(ok(nil))) 218.77/71.61
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(from(0)) → c31(FROM(ok(0))) 218.77/71.61
PROPER(from(nil)) → c31(FROM(ok(nil))) 218.77/71.61
PROPER(add(x0, s(z0))) → c32(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(add(x0, cons(z0, z1))) → c32(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(add(x0, fst(z0, z1))) → c32(ADD(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(add(x0, from(z0))) → c32(ADD(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(add(x0, add(z0, z1))) → c32(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(add(x0, len(z0))) → c32(ADD(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(add(s(z0), x1)) → c32(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(cons(z0, z1), x1)) → c32(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(fst(z0, z1), x1)) → c32(ADD(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(from(z0), x1)) → c32(ADD(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(add(z0, z1), x1)) → c32(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(len(z0), x1)) → c32(ADD(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(x0, 0)) → c32(ADD(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(add(x0, nil)) → c32(ADD(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(add(0, x1)) → c32(ADD(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(add(nil, x1)) → c32(ADD(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(len(s(z0))) → c33(LEN(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(len(cons(z0, z1))) → c33(LEN(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(len(fst(z0, z1))) → c33(LEN(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(len(from(z0))) → c33(LEN(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(len(add(z0, z1))) → c33(LEN(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(len(len(z0))) → c33(LEN(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(len(0)) → c33(LEN(ok(0))) 218.77/71.61
PROPER(len(nil)) → c33(LEN(ok(nil))) 218.77/71.61
TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
TOP(mark(fst(z0, z1))) → c35(TOP(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
TOP(mark(add(z0, z1))) → c35(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
TOP(mark(len(z0))) → c35(TOP(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
TOP(mark(0)) → c35(TOP(ok(0))) 218.77/71.61
TOP(mark(nil)) → c35(TOP(ok(nil)))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.77/71.61
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.77/71.61
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.77/71.61
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.77/71.61
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.61
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.61
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.61
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.61
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.61
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.61
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.61
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.61
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.61
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.61
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.61
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.61
S(ok(z0)) → c34(S(z0)) 218.77/71.61
TOP(ok(z0)) → c36(TOP(active(z0)), ACTIVE(z0)) 218.77/71.61
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.77/71.61
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.77/71.61
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.77/71.61
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.77/71.61
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.77/71.61
ACTIVE(from(z0)) → c(S(z0)) 218.77/71.61
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.77/71.61
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.77/71.61
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.77/71.61
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(s(0)) → c27(S(ok(0))) 218.77/71.61
PROPER(s(nil)) → c27(S(ok(nil))) 218.77/71.61
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(from(0)) → c31(FROM(ok(0))) 218.77/71.61
PROPER(from(nil)) → c31(FROM(ok(nil))) 218.77/71.61
PROPER(add(x0, s(z0))) → c32(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(add(x0, cons(z0, z1))) → c32(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(add(x0, fst(z0, z1))) → c32(ADD(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(add(x0, from(z0))) → c32(ADD(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(add(x0, add(z0, z1))) → c32(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(add(x0, len(z0))) → c32(ADD(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(add(s(z0), x1)) → c32(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(cons(z0, z1), x1)) → c32(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(fst(z0, z1), x1)) → c32(ADD(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(from(z0), x1)) → c32(ADD(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(add(z0, z1), x1)) → c32(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(len(z0), x1)) → c32(ADD(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(x0, 0)) → c32(ADD(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(add(x0, nil)) → c32(ADD(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(add(0, x1)) → c32(ADD(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(add(nil, x1)) → c32(ADD(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(len(s(z0))) → c33(LEN(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(len(cons(z0, z1))) → c33(LEN(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(len(fst(z0, z1))) → c33(LEN(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(len(from(z0))) → c33(LEN(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(len(add(z0, z1))) → c33(LEN(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(len(len(z0))) → c33(LEN(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(len(0)) → c33(LEN(ok(0))) 218.77/71.61
PROPER(len(nil)) → c33(LEN(ok(nil)))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, S, TOP, PROPER

Compound Symbols:

c8, c9, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c34, c36, c, c7, c10, c13, c7, c10, c13, c27, c27, c29, c29, c30, c30, c31, c31, c32, c32, c33, c33, c35, c35

218.77/71.61

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

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

TOP(ok(fst(0, z0))) → c36(TOP(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
TOP(ok(fst(s(z0), cons(z1, z2)))) → c36(TOP(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
TOP(ok(from(z0))) → c36(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
TOP(ok(add(0, z0))) → c36(TOP(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
TOP(ok(add(s(z0), z1))) → c36(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
TOP(ok(len(nil))) → c36(TOP(mark(0)), ACTIVE(len(nil))) 218.77/71.61
TOP(ok(len(cons(z0, z1)))) → c36(TOP(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
TOP(ok(cons(z0, z1))) → c36(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
TOP(ok(fst(z0, z1))) → c36(TOP(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
TOP(ok(fst(z0, z1))) → c36(TOP(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
TOP(ok(from(z0))) → c36(TOP(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
TOP(ok(add(z0, z1))) → c36(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
TOP(ok(add(z0, z1))) → c36(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
TOP(ok(len(z0))) → c36(TOP(len(active(z0))), ACTIVE(len(z0)))

218.77/71.61

(46) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.77/71.61
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.77/71.61
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.77/71.61
active(add(0, z0)) → mark(z0) 218.77/71.61
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.77/71.61
active(len(nil)) → mark(0) 218.77/71.61
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.77/71.61
active(cons(z0, z1)) → cons(active(z0), z1) 218.77/71.61
active(fst(z0, z1)) → fst(active(z0), z1) 218.77/71.61
active(fst(z0, z1)) → fst(z0, active(z1)) 218.77/71.61
active(from(z0)) → from(active(z0)) 218.77/71.61
active(add(z0, z1)) → add(active(z0), z1) 218.77/71.61
active(add(z0, z1)) → add(z0, active(z1)) 218.77/71.61
active(len(z0)) → len(active(z0)) 218.77/71.61
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.77/71.61
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.77/71.61
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.77/71.61
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.77/71.61
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.77/71.61
from(mark(z0)) → mark(from(z0)) 218.77/71.61
from(ok(z0)) → ok(from(z0)) 218.77/71.61
add(mark(z0), z1) → mark(add(z0, z1)) 218.77/71.61
add(z0, mark(z1)) → mark(add(z0, z1)) 218.77/71.61
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.77/71.61
len(mark(z0)) → mark(len(z0)) 218.77/71.61
len(ok(z0)) → ok(len(z0)) 218.77/71.61
proper(0) → ok(0) 218.77/71.61
proper(s(z0)) → s(proper(z0)) 218.77/71.61
proper(nil) → ok(nil) 218.77/71.61
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.77/71.61
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.77/71.61
proper(from(z0)) → from(proper(z0)) 218.77/71.61
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.77/71.61
proper(len(z0)) → len(proper(z0)) 218.77/71.61
s(ok(z0)) → ok(s(z0)) 218.77/71.61
top(mark(z0)) → top(proper(z0)) 218.77/71.61
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.77/71.61
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.77/71.61
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.77/71.61
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.77/71.61
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.61
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.61
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.61
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.61
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.61
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.61
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.61
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.61
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.61
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.61
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.61
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.61
S(ok(z0)) → c34(S(z0)) 218.77/71.61
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.77/71.61
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.77/71.61
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.77/71.61
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.77/71.61
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.77/71.61
ACTIVE(from(z0)) → c(S(z0)) 218.77/71.61
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.77/71.61
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.77/71.61
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.77/71.61
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(s(0)) → c27(S(ok(0))) 218.77/71.61
PROPER(s(nil)) → c27(S(ok(nil))) 218.77/71.61
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(from(0)) → c31(FROM(ok(0))) 218.77/71.61
PROPER(from(nil)) → c31(FROM(ok(nil))) 218.77/71.61
PROPER(add(x0, s(z0))) → c32(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(add(x0, cons(z0, z1))) → c32(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(add(x0, fst(z0, z1))) → c32(ADD(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(add(x0, from(z0))) → c32(ADD(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(add(x0, add(z0, z1))) → c32(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(add(x0, len(z0))) → c32(ADD(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(add(s(z0), x1)) → c32(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(cons(z0, z1), x1)) → c32(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(fst(z0, z1), x1)) → c32(ADD(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(from(z0), x1)) → c32(ADD(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(add(z0, z1), x1)) → c32(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(len(z0), x1)) → c32(ADD(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(x0, 0)) → c32(ADD(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(add(x0, nil)) → c32(ADD(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(add(0, x1)) → c32(ADD(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(add(nil, x1)) → c32(ADD(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(len(s(z0))) → c33(LEN(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(len(cons(z0, z1))) → c33(LEN(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(len(fst(z0, z1))) → c33(LEN(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(len(from(z0))) → c33(LEN(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(len(add(z0, z1))) → c33(LEN(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(len(len(z0))) → c33(LEN(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(len(0)) → c33(LEN(ok(0))) 218.77/71.61
PROPER(len(nil)) → c33(LEN(ok(nil))) 218.77/71.61
TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
TOP(mark(fst(z0, z1))) → c35(TOP(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
TOP(mark(add(z0, z1))) → c35(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
TOP(mark(len(z0))) → c35(TOP(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
TOP(mark(0)) → c35(TOP(ok(0))) 218.77/71.61
TOP(mark(nil)) → c35(TOP(ok(nil))) 218.77/71.61
TOP(ok(fst(0, z0))) → c36(TOP(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
TOP(ok(fst(s(z0), cons(z1, z2)))) → c36(TOP(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
TOP(ok(from(z0))) → c36(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
TOP(ok(add(0, z0))) → c36(TOP(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
TOP(ok(add(s(z0), z1))) → c36(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
TOP(ok(len(nil))) → c36(TOP(mark(0)), ACTIVE(len(nil))) 218.77/71.61
TOP(ok(len(cons(z0, z1)))) → c36(TOP(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
TOP(ok(cons(z0, z1))) → c36(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
TOP(ok(fst(z0, z1))) → c36(TOP(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
TOP(ok(fst(z0, z1))) → c36(TOP(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
TOP(ok(from(z0))) → c36(TOP(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
TOP(ok(add(z0, z1))) → c36(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
TOP(ok(add(z0, z1))) → c36(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
TOP(ok(len(z0))) → c36(TOP(len(active(z0))), ACTIVE(len(z0)))

S tuples:

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.77/71.61
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.77/71.61
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.77/71.61
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.77/71.61
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.61
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.61
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.61
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.61
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.61
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.61
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.61
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.61
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.61
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.61
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.61
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.61
S(ok(z0)) → c34(S(z0)) 218.77/71.61
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.77/71.61
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.77/71.61
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.77/71.61
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.77/71.61
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.77/71.61
ACTIVE(from(z0)) → c(S(z0)) 218.77/71.61
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.77/71.61
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.77/71.61
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.77/71.61
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(s(0)) → c27(S(ok(0))) 218.77/71.61
PROPER(s(nil)) → c27(S(ok(nil))) 218.77/71.61
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(from(0)) → c31(FROM(ok(0))) 218.77/71.61
PROPER(from(nil)) → c31(FROM(ok(nil))) 218.77/71.61
PROPER(add(x0, s(z0))) → c32(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(add(x0, cons(z0, z1))) → c32(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(add(x0, fst(z0, z1))) → c32(ADD(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(add(x0, from(z0))) → c32(ADD(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(add(x0, add(z0, z1))) → c32(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(add(x0, len(z0))) → c32(ADD(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(add(s(z0), x1)) → c32(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(cons(z0, z1), x1)) → c32(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(fst(z0, z1), x1)) → c32(ADD(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(from(z0), x1)) → c32(ADD(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(add(z0, z1), x1)) → c32(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(len(z0), x1)) → c32(ADD(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(x0, 0)) → c32(ADD(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(add(x0, nil)) → c32(ADD(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(add(0, x1)) → c32(ADD(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(add(nil, x1)) → c32(ADD(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(len(s(z0))) → c33(LEN(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(len(cons(z0, z1))) → c33(LEN(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(len(fst(z0, z1))) → c33(LEN(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(len(from(z0))) → c33(LEN(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(len(add(z0, z1))) → c33(LEN(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(len(len(z0))) → c33(LEN(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(len(0)) → c33(LEN(ok(0))) 218.77/71.61
PROPER(len(nil)) → c33(LEN(ok(nil))) 218.77/71.61
TOP(ok(fst(0, z0))) → c36(TOP(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
TOP(ok(fst(s(z0), cons(z1, z2)))) → c36(TOP(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
TOP(ok(from(z0))) → c36(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
TOP(ok(add(0, z0))) → c36(TOP(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
TOP(ok(add(s(z0), z1))) → c36(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
TOP(ok(len(nil))) → c36(TOP(mark(0)), ACTIVE(len(nil))) 218.77/71.61
TOP(ok(len(cons(z0, z1)))) → c36(TOP(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
TOP(ok(cons(z0, z1))) → c36(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
TOP(ok(fst(z0, z1))) → c36(TOP(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
TOP(ok(fst(z0, z1))) → c36(TOP(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
TOP(ok(from(z0))) → c36(TOP(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
TOP(ok(add(z0, z1))) → c36(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
TOP(ok(add(z0, z1))) → c36(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
TOP(ok(len(z0))) → c36(TOP(len(active(z0))), ACTIVE(len(z0)))

K tuples:

TOP(mark(z0)) → c35(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

ACTIVE, CONS, FST, FROM, ADD, LEN, S, PROPER, TOP

Compound Symbols:

c8, c9, c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c34, c, c7, c10, c13, c7, c10, c13, c27, c27, c29, c29, c30, c30, c31, c31, c32, c32, c33, c33, c35, c35, c36

218.77/71.61

(47) CdtUnreachableProof (EQUIVALENT transformation)

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

ACTIVE(fst(z0, z1)) → c8(FST(active(z0), z1), ACTIVE(z0)) 218.77/71.61
ACTIVE(fst(z0, z1)) → c9(FST(z0, active(z1)), ACTIVE(z1)) 218.77/71.61
ACTIVE(add(z0, z1)) → c11(ADD(active(z0), z1), ACTIVE(z0)) 218.77/71.61
ACTIVE(add(z0, z1)) → c12(ADD(z0, active(z1)), ACTIVE(z1)) 218.77/71.61
ACTIVE(fst(s(z0), cons(z1, z2))) → c(CONS(z1, fst(z0, z2))) 218.77/71.61
ACTIVE(fst(s(z0), cons(z1, z2))) → c(FST(z0, z2)) 218.77/71.61
ACTIVE(add(s(z0), z1)) → c(S(add(z0, z1))) 218.77/71.61
ACTIVE(add(s(z0), z1)) → c(ADD(z0, z1)) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c(S(len(z1))) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c(LEN(z1)) 218.77/71.61
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0)))) 218.77/71.61
ACTIVE(from(z0)) → c(S(z0)) 218.77/71.61
ACTIVE(cons(fst(0, z0), x1)) → c7(CONS(mark(nil), x1), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(cons(fst(s(z0), cons(z1, z2)), x1)) → c7(CONS(mark(cons(z1, fst(z0, z2))), x1), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(cons(from(z0), x1)) → c7(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(cons(add(0, z0), x1)) → c7(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(cons(add(s(z0), z1), x1)) → c7(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(cons(len(cons(z0, z1)), x1)) → c7(CONS(mark(s(len(z1))), x1), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(cons(cons(z0, z1), x1)) → c7(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(active(z0), z1), x1), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(cons(fst(z0, z1), x1)) → c7(CONS(fst(z0, active(z1)), x1), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(cons(from(z0), x1)) → c7(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(cons(add(z0, z1), x1)) → c7(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(cons(len(z0), x1)) → c7(CONS(len(active(z0)), x1), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(from(fst(0, z0))) → c10(FROM(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(from(fst(s(z0), cons(z1, z2)))) → c10(FROM(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(from(add(0, z0))) → c10(FROM(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(from(add(s(z0), z1))) → c10(FROM(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(from(len(cons(z0, z1)))) → c10(FROM(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(from(fst(z0, z1))) → c10(FROM(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(from(add(z0, z1))) → c10(FROM(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(from(add(z0, z1))) → c10(FROM(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(from(len(z0))) → c10(FROM(len(active(z0))), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(len(fst(0, z0))) → c13(LEN(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
ACTIVE(len(fst(s(z0), cons(z1, z2)))) → c13(LEN(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
ACTIVE(len(from(z0))) → c13(LEN(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(len(add(0, z0))) → c13(LEN(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
ACTIVE(len(add(s(z0), z1))) → c13(LEN(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
ACTIVE(len(len(cons(z0, z1)))) → c13(LEN(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
ACTIVE(len(cons(z0, z1))) → c13(LEN(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(len(fst(z0, z1))) → c13(LEN(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
ACTIVE(len(from(z0))) → c13(LEN(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
ACTIVE(len(add(z0, z1))) → c13(LEN(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(len(add(z0, z1))) → c13(LEN(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
ACTIVE(len(len(z0))) → c13(LEN(len(active(z0))), ACTIVE(len(z0))) 218.77/71.61
ACTIVE(cons(len(nil), x1)) → c7(CONS(mark(0), x1)) 218.77/71.61
ACTIVE(from(len(nil))) → c10(FROM(mark(0))) 218.77/71.61
ACTIVE(len(len(nil))) → c13(LEN(mark(0))) 218.77/71.61
PROPER(s(s(z0))) → c27(S(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(s(cons(z0, z1))) → c27(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(s(fst(z0, z1))) → c27(S(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(s(from(z0))) → c27(S(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(s(add(z0, z1))) → c27(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(s(len(z0))) → c27(S(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(s(0)) → c27(S(ok(0))) 218.77/71.61
PROPER(s(nil)) → c27(S(ok(nil))) 218.77/71.61
PROPER(cons(x0, s(z0))) → c29(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(cons(x0, cons(z0, z1))) → c29(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(cons(x0, fst(z0, z1))) → c29(CONS(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(cons(x0, from(z0))) → c29(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(cons(x0, add(z0, z1))) → c29(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(cons(x0, len(z0))) → c29(CONS(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(cons(s(z0), x1)) → c29(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(cons(z0, z1), x1)) → c29(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(fst(z0, z1), x1)) → c29(CONS(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(from(z0), x1)) → c29(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(add(z0, z1), x1)) → c29(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(cons(len(z0), x1)) → c29(CONS(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(cons(x0, 0)) → c29(CONS(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(cons(x0, nil)) → c29(CONS(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(cons(0, x1)) → c29(CONS(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(cons(nil, x1)) → c29(CONS(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(fst(x0, s(z0))) → c30(FST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(fst(x0, cons(z0, z1))) → c30(FST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(fst(x0, fst(z0, z1))) → c30(FST(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(fst(x0, from(z0))) → c30(FST(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(fst(x0, add(z0, z1))) → c30(FST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(fst(x0, len(z0))) → c30(FST(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(fst(s(z0), x1)) → c30(FST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(cons(z0, z1), x1)) → c30(FST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(fst(z0, z1), x1)) → c30(FST(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(from(z0), x1)) → c30(FST(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(add(z0, z1), x1)) → c30(FST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(fst(len(z0), x1)) → c30(FST(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(fst(x0, 0)) → c30(FST(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(fst(x0, nil)) → c30(FST(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(fst(0, x1)) → c30(FST(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(fst(nil, x1)) → c30(FST(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(from(s(z0))) → c31(FROM(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(from(cons(z0, z1))) → c31(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(from(fst(z0, z1))) → c31(FROM(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(from(from(z0))) → c31(FROM(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(from(add(z0, z1))) → c31(FROM(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(from(len(z0))) → c31(FROM(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(from(0)) → c31(FROM(ok(0))) 218.77/71.61
PROPER(from(nil)) → c31(FROM(ok(nil))) 218.77/71.61
PROPER(add(x0, s(z0))) → c32(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 218.77/71.61
PROPER(add(x0, cons(z0, z1))) → c32(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(add(x0, fst(z0, z1))) → c32(ADD(proper(x0), fst(proper(z0), proper(z1))), PROPER(x0), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(add(x0, from(z0))) → c32(ADD(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 218.77/71.61
PROPER(add(x0, add(z0, z1))) → c32(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 218.77/71.61
PROPER(add(x0, len(z0))) → c32(ADD(proper(x0), len(proper(z0))), PROPER(x0), PROPER(len(z0))) 218.77/71.61
PROPER(add(s(z0), x1)) → c32(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(cons(z0, z1), x1)) → c32(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(fst(z0, z1), x1)) → c32(ADD(fst(proper(z0), proper(z1)), proper(x1)), PROPER(fst(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(from(z0), x1)) → c32(ADD(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(add(z0, z1), x1)) → c32(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 218.77/71.61
PROPER(add(len(z0), x1)) → c32(ADD(len(proper(z0)), proper(x1)), PROPER(len(z0)), PROPER(x1)) 218.77/71.61
PROPER(add(x0, 0)) → c32(ADD(proper(x0), ok(0)), PROPER(x0)) 218.77/71.61
PROPER(add(x0, nil)) → c32(ADD(proper(x0), ok(nil)), PROPER(x0)) 218.77/71.61
PROPER(add(0, x1)) → c32(ADD(ok(0), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(add(nil, x1)) → c32(ADD(ok(nil), proper(x1)), PROPER(x1)) 218.77/71.61
PROPER(len(s(z0))) → c33(LEN(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
PROPER(len(cons(z0, z1))) → c33(LEN(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
PROPER(len(fst(z0, z1))) → c33(LEN(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
PROPER(len(from(z0))) → c33(LEN(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
PROPER(len(add(z0, z1))) → c33(LEN(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
PROPER(len(len(z0))) → c33(LEN(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
PROPER(len(0)) → c33(LEN(ok(0))) 218.77/71.61
PROPER(len(nil)) → c33(LEN(ok(nil))) 218.77/71.61
TOP(mark(s(z0))) → c35(TOP(s(proper(z0))), PROPER(s(z0))) 218.77/71.61
TOP(mark(cons(z0, z1))) → c35(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 218.77/71.61
TOP(mark(fst(z0, z1))) → c35(TOP(fst(proper(z0), proper(z1))), PROPER(fst(z0, z1))) 218.77/71.61
TOP(mark(from(z0))) → c35(TOP(from(proper(z0))), PROPER(from(z0))) 218.77/71.61
TOP(mark(add(z0, z1))) → c35(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 218.77/71.61
TOP(mark(len(z0))) → c35(TOP(len(proper(z0))), PROPER(len(z0))) 218.77/71.61
TOP(ok(fst(0, z0))) → c36(TOP(mark(nil)), ACTIVE(fst(0, z0))) 218.77/71.61
TOP(ok(fst(s(z0), cons(z1, z2)))) → c36(TOP(mark(cons(z1, fst(z0, z2)))), ACTIVE(fst(s(z0), cons(z1, z2)))) 218.77/71.61
TOP(ok(from(z0))) → c36(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 218.77/71.61
TOP(ok(add(0, z0))) → c36(TOP(mark(z0)), ACTIVE(add(0, z0))) 218.77/71.61
TOP(ok(add(s(z0), z1))) → c36(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 218.77/71.61
TOP(ok(len(nil))) → c36(TOP(mark(0)), ACTIVE(len(nil))) 218.77/71.61
TOP(ok(len(cons(z0, z1)))) → c36(TOP(mark(s(len(z1)))), ACTIVE(len(cons(z0, z1)))) 218.77/71.61
TOP(ok(cons(z0, z1))) → c36(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 218.77/71.61
TOP(ok(fst(z0, z1))) → c36(TOP(fst(active(z0), z1)), ACTIVE(fst(z0, z1))) 218.77/71.61
TOP(ok(fst(z0, z1))) → c36(TOP(fst(z0, active(z1))), ACTIVE(fst(z0, z1))) 218.77/71.61
TOP(ok(from(z0))) → c36(TOP(from(active(z0))), ACTIVE(from(z0))) 218.77/71.61
TOP(ok(add(z0, z1))) → c36(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 218.77/71.61
TOP(ok(add(z0, z1))) → c36(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 218.77/71.61
TOP(ok(len(z0))) → c36(TOP(len(active(z0))), ACTIVE(len(z0)))

218.77/71.61

(48) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.77/71.61
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.77/71.61
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.77/71.61
active(add(0, z0)) → mark(z0) 218.77/71.61
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.77/71.61
active(len(nil)) → mark(0) 218.77/71.61
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.77/71.61
active(cons(z0, z1)) → cons(active(z0), z1) 218.77/71.61
active(fst(z0, z1)) → fst(active(z0), z1) 218.77/71.61
active(fst(z0, z1)) → fst(z0, active(z1)) 218.77/71.61
active(from(z0)) → from(active(z0)) 218.77/71.61
active(add(z0, z1)) → add(active(z0), z1) 218.77/71.61
active(add(z0, z1)) → add(z0, active(z1)) 218.77/71.61
active(len(z0)) → len(active(z0)) 218.77/71.61
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.77/71.61
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.77/71.61
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.77/71.61
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.77/71.61
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.77/71.61
from(mark(z0)) → mark(from(z0)) 218.77/71.61
from(ok(z0)) → ok(from(z0)) 218.77/71.61
add(mark(z0), z1) → mark(add(z0, z1)) 218.77/71.61
add(z0, mark(z1)) → mark(add(z0, z1)) 218.77/71.61
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.77/71.61
len(mark(z0)) → mark(len(z0)) 218.77/71.61
len(ok(z0)) → ok(len(z0)) 218.77/71.61
proper(0) → ok(0) 218.77/71.61
proper(s(z0)) → s(proper(z0)) 218.77/71.61
proper(nil) → ok(nil) 218.77/71.61
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.77/71.61
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.77/71.61
proper(from(z0)) → from(proper(z0)) 218.77/71.61
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.77/71.61
proper(len(z0)) → len(proper(z0)) 218.77/71.61
s(ok(z0)) → ok(s(z0)) 218.77/71.61
top(mark(z0)) → top(proper(z0)) 218.77/71.61
top(ok(z0)) → top(active(z0))

Tuples:

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.61
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.61
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.61
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.61
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.61
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.61
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.61
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.61
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.61
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.61
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.61
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.61
S(ok(z0)) → c34(S(z0)) 218.77/71.61
TOP(mark(0)) → c35(TOP(ok(0))) 218.77/71.61
TOP(mark(nil)) → c35(TOP(ok(nil)))

S tuples:

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.61
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.61
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.61
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.61
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.61
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.61
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.61
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.61
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.61
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.61
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.61
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.61
S(ok(z0)) → c34(S(z0))

K tuples:none
Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

CONS, FST, FROM, ADD, LEN, S, TOP

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c34, c35

218.77/71.61

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

Removed 2 trailing tuple parts

218.77/71.61

(50) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.77/71.61
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.77/71.61
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.77/71.61
active(add(0, z0)) → mark(z0) 218.77/71.61
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.77/71.61
active(len(nil)) → mark(0) 218.77/71.61
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.77/71.61
active(cons(z0, z1)) → cons(active(z0), z1) 218.77/71.61
active(fst(z0, z1)) → fst(active(z0), z1) 218.77/71.61
active(fst(z0, z1)) → fst(z0, active(z1)) 218.77/71.61
active(from(z0)) → from(active(z0)) 218.77/71.61
active(add(z0, z1)) → add(active(z0), z1) 218.77/71.61
active(add(z0, z1)) → add(z0, active(z1)) 218.77/71.61
active(len(z0)) → len(active(z0)) 218.77/71.61
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.77/71.61
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.77/71.62
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.77/71.62
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.77/71.62
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.77/71.62
from(mark(z0)) → mark(from(z0)) 218.77/71.62
from(ok(z0)) → ok(from(z0)) 218.77/71.62
add(mark(z0), z1) → mark(add(z0, z1)) 218.77/71.62
add(z0, mark(z1)) → mark(add(z0, z1)) 218.77/71.62
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.77/71.62
len(mark(z0)) → mark(len(z0)) 218.77/71.62
len(ok(z0)) → ok(len(z0)) 218.77/71.62
proper(0) → ok(0) 218.77/71.62
proper(s(z0)) → s(proper(z0)) 218.77/71.62
proper(nil) → ok(nil) 218.77/71.62
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.77/71.62
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.77/71.62
proper(from(z0)) → from(proper(z0)) 218.77/71.62
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.77/71.62
proper(len(z0)) → len(proper(z0)) 218.77/71.62
s(ok(z0)) → ok(s(z0)) 218.77/71.62
top(mark(z0)) → top(proper(z0)) 218.77/71.62
top(ok(z0)) → top(active(z0))

Tuples:

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0)) 218.77/71.62
TOP(mark(0)) → c35 218.77/71.62
TOP(mark(nil)) → c35

S tuples:

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

K tuples:none
Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

CONS, FST, FROM, ADD, LEN, S, TOP

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c34, c35

218.77/71.62

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

Removed 2 trailing nodes:

TOP(mark(0)) → c35 218.77/71.62
TOP(mark(nil)) → c35

218.77/71.62

(52) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.77/71.62
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.77/71.62
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.77/71.62
active(add(0, z0)) → mark(z0) 218.77/71.62
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.77/71.62
active(len(nil)) → mark(0) 218.77/71.62
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.77/71.62
active(cons(z0, z1)) → cons(active(z0), z1) 218.77/71.62
active(fst(z0, z1)) → fst(active(z0), z1) 218.77/71.62
active(fst(z0, z1)) → fst(z0, active(z1)) 218.77/71.62
active(from(z0)) → from(active(z0)) 218.77/71.62
active(add(z0, z1)) → add(active(z0), z1) 218.77/71.62
active(add(z0, z1)) → add(z0, active(z1)) 218.77/71.62
active(len(z0)) → len(active(z0)) 218.77/71.62
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.77/71.62
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.77/71.62
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.77/71.62
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.77/71.62
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.77/71.62
from(mark(z0)) → mark(from(z0)) 218.77/71.62
from(ok(z0)) → ok(from(z0)) 218.77/71.62
add(mark(z0), z1) → mark(add(z0, z1)) 218.77/71.62
add(z0, mark(z1)) → mark(add(z0, z1)) 218.77/71.62
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.77/71.62
len(mark(z0)) → mark(len(z0)) 218.77/71.62
len(ok(z0)) → ok(len(z0)) 218.77/71.62
proper(0) → ok(0) 218.77/71.62
proper(s(z0)) → s(proper(z0)) 218.77/71.62
proper(nil) → ok(nil) 218.77/71.62
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.77/71.62
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.77/71.62
proper(from(z0)) → from(proper(z0)) 218.77/71.62
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.77/71.62
proper(len(z0)) → len(proper(z0)) 218.77/71.62
s(ok(z0)) → ok(s(z0)) 218.77/71.62
top(mark(z0)) → top(proper(z0)) 218.77/71.62
top(ok(z0)) → top(active(z0))

Tuples:

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

S tuples:

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

K tuples:none
Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

CONS, FST, FROM, ADD, LEN, S

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c34

218.77/71.62

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

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

FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1))

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

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 218.77/71.62

POL(ADD(x₁, x₂)) = 0 218.77/71.62
POL(CONS(x₁, x₂)) = 0 218.77/71.62
POL(FROM(x₁)) = 0 218.77/71.62
POL(FST(x₁, x₂)) = [4]x₁ + [4]x₂ 218.77/71.62
POL(LEN(x₁)) = 0 218.77/71.62
POL(S(x₁)) = 0 218.77/71.62
POL(c14(x₁)) = x₁ 218.77/71.62
POL(c15(x₁)) = x₁ 218.77/71.62
POL(c16(x₁)) = x₁ 218.77/71.62
POL(c17(x₁)) = x₁ 218.77/71.62
POL(c18(x₁)) = x₁ 218.77/71.62
POL(c19(x₁)) = x₁ 218.77/71.62
POL(c20(x₁)) = x₁ 218.77/71.62
POL(c21(x₁)) = x₁ 218.77/71.62
POL(c22(x₁)) = x₁ 218.77/71.62
POL(c23(x₁)) = x₁ 218.77/71.62
POL(c24(x₁)) = x₁ 218.77/71.62
POL(c25(x₁)) = x₁ 218.77/71.62
POL(c34(x₁)) = x₁ 218.77/71.62
POL(mark(x₁)) = [4] + x₁ 218.77/71.62
POL(ok(x₁)) = x₁

218.77/71.62

(54) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.77/71.62
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.77/71.62
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.77/71.62
active(add(0, z0)) → mark(z0) 218.77/71.62
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.77/71.62
active(len(nil)) → mark(0) 218.77/71.62
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.77/71.62
active(cons(z0, z1)) → cons(active(z0), z1) 218.77/71.62
active(fst(z0, z1)) → fst(active(z0), z1) 218.77/71.62
active(fst(z0, z1)) → fst(z0, active(z1)) 218.77/71.62
active(from(z0)) → from(active(z0)) 218.77/71.62
active(add(z0, z1)) → add(active(z0), z1) 218.77/71.62
active(add(z0, z1)) → add(z0, active(z1)) 218.77/71.62
active(len(z0)) → len(active(z0)) 218.77/71.62
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.77/71.62
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.77/71.62
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.77/71.62
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.77/71.62
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.77/71.62
from(mark(z0)) → mark(from(z0)) 218.77/71.62
from(ok(z0)) → ok(from(z0)) 218.77/71.62
add(mark(z0), z1) → mark(add(z0, z1)) 218.77/71.62
add(z0, mark(z1)) → mark(add(z0, z1)) 218.77/71.62
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.77/71.62
len(mark(z0)) → mark(len(z0)) 218.77/71.62
len(ok(z0)) → ok(len(z0)) 218.77/71.62
proper(0) → ok(0) 218.77/71.62
proper(s(z0)) → s(proper(z0)) 218.77/71.62
proper(nil) → ok(nil) 218.77/71.62
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.77/71.62
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.77/71.62
proper(from(z0)) → from(proper(z0)) 218.77/71.62
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.77/71.62
proper(len(z0)) → len(proper(z0)) 218.77/71.62
s(ok(z0)) → ok(s(z0)) 218.77/71.62
top(mark(z0)) → top(proper(z0)) 218.77/71.62
top(ok(z0)) → top(active(z0))

Tuples:

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

S tuples:

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

K tuples:

FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

CONS, FST, FROM, ADD, LEN, S

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c34

218.77/71.62

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

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

FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

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

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 218.77/71.62

POL(ADD(x₁, x₂)) = 0 218.77/71.62
POL(CONS(x₁, x₂)) = 0 218.77/71.62
POL(FROM(x₁)) = x₁ + x₁² + x₁³ 218.77/71.62
POL(FST(x₁, x₂)) = x₂ + x₂² + x₂³ 218.77/71.62
POL(LEN(x₁)) = x₁ + x₁² + x₁³ 218.77/71.62
POL(S(x₁)) = x₁ + x₁² + x₁³ 218.77/71.62
POL(c14(x₁)) = x₁ 218.77/71.62
POL(c15(x₁)) = x₁ 218.77/71.62
POL(c16(x₁)) = x₁ 218.77/71.62
POL(c17(x₁)) = x₁ 218.77/71.62
POL(c18(x₁)) = x₁ 218.77/71.62
POL(c19(x₁)) = x₁ 218.77/71.62
POL(c20(x₁)) = x₁ 218.77/71.62
POL(c21(x₁)) = x₁ 218.77/71.62
POL(c22(x₁)) = x₁ 218.77/71.62
POL(c23(x₁)) = x₁ 218.77/71.62
POL(c24(x₁)) = x₁ 218.77/71.62
POL(c25(x₁)) = x₁ 218.77/71.62
POL(c34(x₁)) = x₁ 218.77/71.62
POL(mark(x₁)) = [1] + x₁ 218.77/71.62
POL(ok(x₁)) = [1] + x₁

218.77/71.62

(56) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.77/71.62
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.77/71.62
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.77/71.62
active(add(0, z0)) → mark(z0) 218.77/71.62
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.77/71.62
active(len(nil)) → mark(0) 218.77/71.62
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.77/71.62
active(cons(z0, z1)) → cons(active(z0), z1) 218.77/71.62
active(fst(z0, z1)) → fst(active(z0), z1) 218.77/71.62
active(fst(z0, z1)) → fst(z0, active(z1)) 218.77/71.62
active(from(z0)) → from(active(z0)) 218.77/71.62
active(add(z0, z1)) → add(active(z0), z1) 218.77/71.62
active(add(z0, z1)) → add(z0, active(z1)) 218.77/71.62
active(len(z0)) → len(active(z0)) 218.77/71.62
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.77/71.62
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.77/71.62
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.77/71.62
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.77/71.62
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.77/71.62
from(mark(z0)) → mark(from(z0)) 218.77/71.62
from(ok(z0)) → ok(from(z0)) 218.77/71.62
add(mark(z0), z1) → mark(add(z0, z1)) 218.77/71.62
add(z0, mark(z1)) → mark(add(z0, z1)) 218.77/71.62
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.77/71.62
len(mark(z0)) → mark(len(z0)) 218.77/71.62
len(ok(z0)) → ok(len(z0)) 218.77/71.62
proper(0) → ok(0) 218.77/71.62
proper(s(z0)) → s(proper(z0)) 218.77/71.62
proper(nil) → ok(nil) 218.77/71.62
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.77/71.62
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.77/71.62
proper(from(z0)) → from(proper(z0)) 218.77/71.62
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.77/71.62
proper(len(z0)) → len(proper(z0)) 218.77/71.62
s(ok(z0)) → ok(s(z0)) 218.77/71.62
top(mark(z0)) → top(proper(z0)) 218.77/71.62
top(ok(z0)) → top(active(z0))

Tuples:

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

S tuples:

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1))

K tuples:

FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

CONS, FST, FROM, ADD, LEN, S

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c34

218.77/71.62

(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.

ADD(z0, mark(z1)) → c22(ADD(z0, z1))

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

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 218.77/71.62

POL(ADD(x₁, x₂)) = x₂ 218.77/71.62
POL(CONS(x₁, x₂)) = 0 218.77/71.62
POL(FROM(x₁)) = [3]x₁ 218.77/71.62
POL(FST(x₁, x₂)) = [3]x₁ + [5]x₂ 218.77/71.62
POL(LEN(x₁)) = [3]x₁ 218.77/71.62
POL(S(x₁)) = [3]x₁ 218.77/71.62
POL(c14(x₁)) = x₁ 218.77/71.62
POL(c15(x₁)) = x₁ 218.77/71.62
POL(c16(x₁)) = x₁ 218.77/71.62
POL(c17(x₁)) = x₁ 218.77/71.62
POL(c18(x₁)) = x₁ 218.77/71.62
POL(c19(x₁)) = x₁ 218.77/71.62
POL(c20(x₁)) = x₁ 218.77/71.62
POL(c21(x₁)) = x₁ 218.77/71.62
POL(c22(x₁)) = x₁ 218.77/71.62
POL(c23(x₁)) = x₁ 218.77/71.62
POL(c24(x₁)) = x₁ 218.77/71.62
POL(c25(x₁)) = x₁ 218.77/71.62
POL(c34(x₁)) = x₁ 218.77/71.62
POL(mark(x₁)) = [1] + x₁ 218.77/71.62
POL(ok(x₁)) = x₁

218.77/71.62

(58) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.77/71.62
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.77/71.62
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.77/71.62
active(add(0, z0)) → mark(z0) 218.77/71.62
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.77/71.62
active(len(nil)) → mark(0) 218.77/71.62
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.77/71.62
active(cons(z0, z1)) → cons(active(z0), z1) 218.77/71.62
active(fst(z0, z1)) → fst(active(z0), z1) 218.77/71.62
active(fst(z0, z1)) → fst(z0, active(z1)) 218.77/71.62
active(from(z0)) → from(active(z0)) 218.77/71.62
active(add(z0, z1)) → add(active(z0), z1) 218.77/71.62
active(add(z0, z1)) → add(z0, active(z1)) 218.77/71.62
active(len(z0)) → len(active(z0)) 218.77/71.62
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.77/71.62
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.77/71.62
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.77/71.62
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.77/71.62
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.77/71.62
from(mark(z0)) → mark(from(z0)) 218.77/71.62
from(ok(z0)) → ok(from(z0)) 218.77/71.62
add(mark(z0), z1) → mark(add(z0, z1)) 218.77/71.62
add(z0, mark(z1)) → mark(add(z0, z1)) 218.77/71.62
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.77/71.62
len(mark(z0)) → mark(len(z0)) 218.77/71.62
len(ok(z0)) → ok(len(z0)) 218.77/71.62
proper(0) → ok(0) 218.77/71.62
proper(s(z0)) → s(proper(z0)) 218.77/71.62
proper(nil) → ok(nil) 218.77/71.62
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.77/71.62
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.77/71.62
proper(from(z0)) → from(proper(z0)) 218.77/71.62
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.77/71.62
proper(len(z0)) → len(proper(z0)) 218.77/71.62
s(ok(z0)) → ok(s(z0)) 218.77/71.62
top(mark(z0)) → top(proper(z0)) 218.77/71.62
top(ok(z0)) → top(active(z0))

Tuples:

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

S tuples:

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1))

K tuples:

FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

CONS, FST, FROM, ADD, LEN, S

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c34

218.77/71.62

(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.

CONS(mark(z0), z1) → c14(CONS(z0, z1))

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

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 218.77/71.62

POL(ADD(x₁, x₂)) = 0 218.77/71.62
POL(CONS(x₁, x₂)) = [2]x₁ + x₂ 218.77/71.62
POL(FROM(x₁)) = [5]x₁ 218.77/71.62
POL(FST(x₁, x₂)) = [3]x₁ + [5]x₂ 218.77/71.62
POL(LEN(x₁)) = [3]x₁ 218.77/71.62
POL(S(x₁)) = [5]x₁ 218.77/71.62
POL(c14(x₁)) = x₁ 218.77/71.62
POL(c15(x₁)) = x₁ 218.77/71.62
POL(c16(x₁)) = x₁ 218.77/71.62
POL(c17(x₁)) = x₁ 218.77/71.62
POL(c18(x₁)) = x₁ 218.77/71.62
POL(c19(x₁)) = x₁ 218.77/71.62
POL(c20(x₁)) = x₁ 218.77/71.62
POL(c21(x₁)) = x₁ 218.77/71.62
POL(c22(x₁)) = x₁ 218.77/71.62
POL(c23(x₁)) = x₁ 218.77/71.62
POL(c24(x₁)) = x₁ 218.77/71.62
POL(c25(x₁)) = x₁ 218.77/71.62
POL(c34(x₁)) = x₁ 218.77/71.62
POL(mark(x₁)) = [1] + x₁ 218.77/71.62
POL(ok(x₁)) = x₁

218.77/71.62

(60) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.77/71.62
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.77/71.62
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.77/71.62
active(add(0, z0)) → mark(z0) 218.77/71.62
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.77/71.62
active(len(nil)) → mark(0) 218.77/71.62
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.77/71.62
active(cons(z0, z1)) → cons(active(z0), z1) 218.77/71.62
active(fst(z0, z1)) → fst(active(z0), z1) 218.77/71.62
active(fst(z0, z1)) → fst(z0, active(z1)) 218.77/71.62
active(from(z0)) → from(active(z0)) 218.77/71.62
active(add(z0, z1)) → add(active(z0), z1) 218.77/71.62
active(add(z0, z1)) → add(z0, active(z1)) 218.77/71.62
active(len(z0)) → len(active(z0)) 218.77/71.62
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.77/71.62
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.77/71.62
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.77/71.62
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.77/71.62
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.77/71.62
from(mark(z0)) → mark(from(z0)) 218.77/71.62
from(ok(z0)) → ok(from(z0)) 218.77/71.62
add(mark(z0), z1) → mark(add(z0, z1)) 218.77/71.62
add(z0, mark(z1)) → mark(add(z0, z1)) 218.77/71.62
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.77/71.62
len(mark(z0)) → mark(len(z0)) 218.77/71.62
len(ok(z0)) → ok(len(z0)) 218.77/71.62
proper(0) → ok(0) 218.77/71.62
proper(s(z0)) → s(proper(z0)) 218.77/71.62
proper(nil) → ok(nil) 218.77/71.62
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.77/71.62
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.77/71.62
proper(from(z0)) → from(proper(z0)) 218.77/71.62
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.77/71.62
proper(len(z0)) → len(proper(z0)) 218.77/71.62
s(ok(z0)) → ok(s(z0)) 218.77/71.62
top(mark(z0)) → top(proper(z0)) 218.77/71.62
top(ok(z0)) → top(active(z0))

Tuples:

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

S tuples:

CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1))

K tuples:

FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
CONS(mark(z0), z1) → c14(CONS(z0, z1))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

CONS, FST, FROM, ADD, LEN, S

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c34

218.77/71.62

(61) 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.

CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1))

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

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 218.77/71.62

POL(ADD(x₁, x₂)) = 0 218.77/71.62
POL(CONS(x₁, x₂)) = x₂² 218.77/71.62
POL(FROM(x₁)) = 0 218.77/71.62
POL(FST(x₁, x₂)) = 0 218.77/71.62
POL(LEN(x₁)) = 0 218.77/71.62
POL(S(x₁)) = [3]x₁ + [3]x₁² 218.77/71.62
POL(c14(x₁)) = x₁ 218.77/71.62
POL(c15(x₁)) = x₁ 218.77/71.62
POL(c16(x₁)) = x₁ 218.77/71.62
POL(c17(x₁)) = x₁ 218.77/71.62
POL(c18(x₁)) = x₁ 218.77/71.62
POL(c19(x₁)) = x₁ 218.77/71.62
POL(c20(x₁)) = x₁ 218.77/71.62
POL(c21(x₁)) = x₁ 218.77/71.62
POL(c22(x₁)) = x₁ 218.77/71.62
POL(c23(x₁)) = x₁ 218.77/71.62
POL(c24(x₁)) = x₁ 218.77/71.62
POL(c25(x₁)) = x₁ 218.77/71.62
POL(c34(x₁)) = x₁ 218.77/71.62
POL(mark(x₁)) = 0 218.77/71.62
POL(ok(x₁)) = [1] + x₁

218.77/71.62

(62) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.77/71.62
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.77/71.62
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.77/71.62
active(add(0, z0)) → mark(z0) 218.77/71.62
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.77/71.62
active(len(nil)) → mark(0) 218.77/71.62
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.77/71.62
active(cons(z0, z1)) → cons(active(z0), z1) 218.77/71.62
active(fst(z0, z1)) → fst(active(z0), z1) 218.77/71.62
active(fst(z0, z1)) → fst(z0, active(z1)) 218.77/71.62
active(from(z0)) → from(active(z0)) 218.77/71.62
active(add(z0, z1)) → add(active(z0), z1) 218.77/71.62
active(add(z0, z1)) → add(z0, active(z1)) 218.77/71.62
active(len(z0)) → len(active(z0)) 218.77/71.62
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.77/71.62
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.77/71.62
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.77/71.62
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.77/71.62
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.77/71.62
from(mark(z0)) → mark(from(z0)) 218.77/71.62
from(ok(z0)) → ok(from(z0)) 218.77/71.62
add(mark(z0), z1) → mark(add(z0, z1)) 218.77/71.62
add(z0, mark(z1)) → mark(add(z0, z1)) 218.77/71.62
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.77/71.62
len(mark(z0)) → mark(len(z0)) 218.77/71.62
len(ok(z0)) → ok(len(z0)) 218.77/71.62
proper(0) → ok(0) 218.77/71.62
proper(s(z0)) → s(proper(z0)) 218.77/71.62
proper(nil) → ok(nil) 218.77/71.62
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.77/71.62
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.77/71.62
proper(from(z0)) → from(proper(z0)) 218.77/71.62
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.77/71.62
proper(len(z0)) → len(proper(z0)) 218.77/71.62
s(ok(z0)) → ok(s(z0)) 218.77/71.62
top(mark(z0)) → top(proper(z0)) 218.77/71.62
top(ok(z0)) → top(active(z0))

Tuples:

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

S tuples:

ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1))

K tuples:

FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

CONS, FST, FROM, ADD, LEN, S

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c34

218.77/71.62

(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.

ADD(mark(z0), z1) → c21(ADD(z0, z1))

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

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 218.77/71.62

POL(ADD(x₁, x₂)) = [2]x₁ 218.77/71.62
POL(CONS(x₁, x₂)) = [3]x₁ + [3]x₂ 218.77/71.62
POL(FROM(x₁)) = [3]x₁ 218.77/71.62
POL(FST(x₁, x₂)) = [3]x₁ + [3]x₂ 218.77/71.62
POL(LEN(x₁)) = [3]x₁ 218.77/71.62
POL(S(x₁)) = [5]x₁ 218.77/71.62
POL(c14(x₁)) = x₁ 218.77/71.62
POL(c15(x₁)) = x₁ 218.77/71.62
POL(c16(x₁)) = x₁ 218.77/71.62
POL(c17(x₁)) = x₁ 218.77/71.62
POL(c18(x₁)) = x₁ 218.77/71.62
POL(c19(x₁)) = x₁ 218.77/71.62
POL(c20(x₁)) = x₁ 218.77/71.62
POL(c21(x₁)) = x₁ 218.77/71.62
POL(c22(x₁)) = x₁ 218.77/71.62
POL(c23(x₁)) = x₁ 218.77/71.62
POL(c24(x₁)) = x₁ 218.77/71.62
POL(c25(x₁)) = x₁ 218.77/71.62
POL(c34(x₁)) = x₁ 218.77/71.62
POL(mark(x₁)) = [1] + x₁ 218.77/71.62
POL(ok(x₁)) = x₁

218.77/71.62

(64) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.77/71.62
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.77/71.62
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.77/71.62
active(add(0, z0)) → mark(z0) 218.77/71.62
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.77/71.62
active(len(nil)) → mark(0) 218.77/71.62
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.77/71.62
active(cons(z0, z1)) → cons(active(z0), z1) 218.77/71.62
active(fst(z0, z1)) → fst(active(z0), z1) 218.77/71.62
active(fst(z0, z1)) → fst(z0, active(z1)) 218.77/71.62
active(from(z0)) → from(active(z0)) 218.77/71.62
active(add(z0, z1)) → add(active(z0), z1) 218.77/71.62
active(add(z0, z1)) → add(z0, active(z1)) 218.77/71.62
active(len(z0)) → len(active(z0)) 218.77/71.62
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.77/71.62
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.77/71.62
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.77/71.62
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.77/71.62
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.77/71.62
from(mark(z0)) → mark(from(z0)) 218.77/71.62
from(ok(z0)) → ok(from(z0)) 218.77/71.62
add(mark(z0), z1) → mark(add(z0, z1)) 218.77/71.62
add(z0, mark(z1)) → mark(add(z0, z1)) 218.77/71.62
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.77/71.62
len(mark(z0)) → mark(len(z0)) 218.77/71.62
len(ok(z0)) → ok(len(z0)) 218.77/71.62
proper(0) → ok(0) 218.77/71.62
proper(s(z0)) → s(proper(z0)) 218.77/71.62
proper(nil) → ok(nil) 218.77/71.62
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.77/71.62
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.77/71.62
proper(from(z0)) → from(proper(z0)) 218.77/71.62
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.77/71.62
proper(len(z0)) → len(proper(z0)) 218.77/71.62
s(ok(z0)) → ok(s(z0)) 218.77/71.62
top(mark(z0)) → top(proper(z0)) 218.77/71.62
top(ok(z0)) → top(active(z0))

Tuples:

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

S tuples:

ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1))

K tuples:

FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

CONS, FST, FROM, ADD, LEN, S

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c34

218.77/71.62

(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.

ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1))

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

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 218.77/71.62

POL(ADD(x₁, x₂)) = x₁ 218.77/71.62
POL(CONS(x₁, x₂)) = [5]x₁ + [5]x₂ 218.77/71.62
POL(FROM(x₁)) = [3]x₁ 218.77/71.62
POL(FST(x₁, x₂)) = [3]x₁ + [3]x₂ 218.77/71.62
POL(LEN(x₁)) = [3]x₁ 218.77/71.62
POL(S(x₁)) = [3]x₁ 218.77/71.62
POL(c14(x₁)) = x₁ 218.77/71.62
POL(c15(x₁)) = x₁ 218.77/71.62
POL(c16(x₁)) = x₁ 218.77/71.62
POL(c17(x₁)) = x₁ 218.77/71.62
POL(c18(x₁)) = x₁ 218.77/71.62
POL(c19(x₁)) = x₁ 218.77/71.62
POL(c20(x₁)) = x₁ 218.77/71.62
POL(c21(x₁)) = x₁ 218.77/71.62
POL(c22(x₁)) = x₁ 218.77/71.62
POL(c23(x₁)) = x₁ 218.77/71.62
POL(c24(x₁)) = x₁ 218.77/71.62
POL(c25(x₁)) = x₁ 218.77/71.62
POL(c34(x₁)) = x₁ 218.77/71.62
POL(mark(x₁)) = x₁ 218.77/71.62
POL(ok(x₁)) = [1] + x₁

218.77/71.62

(66) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fst(0, z0)) → mark(nil) 218.77/71.62
active(fst(s(z0), cons(z1, z2))) → mark(cons(z1, fst(z0, z2))) 218.77/71.62
active(from(z0)) → mark(cons(z0, from(s(z0)))) 218.77/71.62
active(add(0, z0)) → mark(z0) 218.77/71.62
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 218.77/71.62
active(len(nil)) → mark(0) 218.77/71.62
active(len(cons(z0, z1))) → mark(s(len(z1))) 218.77/71.62
active(cons(z0, z1)) → cons(active(z0), z1) 218.77/71.62
active(fst(z0, z1)) → fst(active(z0), z1) 218.77/71.62
active(fst(z0, z1)) → fst(z0, active(z1)) 218.77/71.62
active(from(z0)) → from(active(z0)) 218.77/71.62
active(add(z0, z1)) → add(active(z0), z1) 218.77/71.62
active(add(z0, z1)) → add(z0, active(z1)) 218.77/71.62
active(len(z0)) → len(active(z0)) 218.77/71.62
cons(mark(z0), z1) → mark(cons(z0, z1)) 218.77/71.62
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 218.77/71.62
fst(mark(z0), z1) → mark(fst(z0, z1)) 218.77/71.62
fst(z0, mark(z1)) → mark(fst(z0, z1)) 218.77/71.62
fst(ok(z0), ok(z1)) → ok(fst(z0, z1)) 218.77/71.62
from(mark(z0)) → mark(from(z0)) 218.77/71.62
from(ok(z0)) → ok(from(z0)) 218.77/71.62
add(mark(z0), z1) → mark(add(z0, z1)) 218.77/71.62
add(z0, mark(z1)) → mark(add(z0, z1)) 218.77/71.62
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 218.77/71.62
len(mark(z0)) → mark(len(z0)) 218.77/71.62
len(ok(z0)) → ok(len(z0)) 218.77/71.62
proper(0) → ok(0) 218.77/71.62
proper(s(z0)) → s(proper(z0)) 218.77/71.62
proper(nil) → ok(nil) 218.77/71.62
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 218.77/71.62
proper(fst(z0, z1)) → fst(proper(z0), proper(z1)) 218.77/71.62
proper(from(z0)) → from(proper(z0)) 218.77/71.62
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 218.77/71.62
proper(len(z0)) → len(proper(z0)) 218.77/71.62
s(ok(z0)) → ok(s(z0)) 218.77/71.62
top(mark(z0)) → top(proper(z0)) 218.77/71.62
top(ok(z0)) → top(active(z0))

Tuples:

CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0))

S tuples:none
K tuples:

FST(mark(z0), z1) → c16(FST(z0, z1)) 218.77/71.62
FST(z0, mark(z1)) → c17(FST(z0, z1)) 218.77/71.62
FST(ok(z0), ok(z1)) → c18(FST(z0, z1)) 218.77/71.62
FROM(mark(z0)) → c19(FROM(z0)) 218.77/71.62
FROM(ok(z0)) → c20(FROM(z0)) 218.77/71.62
LEN(mark(z0)) → c24(LEN(z0)) 218.77/71.62
LEN(ok(z0)) → c25(LEN(z0)) 218.77/71.62
S(ok(z0)) → c34(S(z0)) 218.77/71.62
ADD(z0, mark(z1)) → c22(ADD(z0, z1)) 218.77/71.62
CONS(mark(z0), z1) → c14(CONS(z0, z1)) 218.77/71.62
CONS(ok(z0), ok(z1)) → c15(CONS(z0, z1)) 218.77/71.62
ADD(mark(z0), z1) → c21(ADD(z0, z1)) 218.77/71.62
ADD(ok(z0), ok(z1)) → c23(ADD(z0, z1))

Defined Rule Symbols:

active, cons, fst, from, add, len, proper, s, top

Defined Pair Symbols:

CONS, FST, FROM, ADD, LEN, S

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c34

218.77/71.62

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

The set S is empty

218.77/71.62

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

218.77/71.62