YES(O(1), O(n^2)) 203.94/66.73 YES(O(1), O(n^2)) 204.25/66.83 204.25/66.83 204.25/66.83 204.25/66.83 204.25/66.83 204.25/66.83 Runtime Complexity (innermost) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml.xml 204.25/66.83 204.25/66.83 204.25/66.83
204.25/66.83
204.25/66.83
204.25/66.83
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(n^2)).

0 CpxTRS
204.25/66.83 
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳2 CdtProblem
204.25/66.83 
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳4 CdtProblem
204.25/66.83 
↳5 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳6 CdtProblem
204.25/66.83 
↳7 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳8 CdtProblem
204.25/66.83 
↳9 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳10 CdtProblem
204.25/66.83 
↳11 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳12 CdtProblem
204.25/66.83 
↳13 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳14 CdtProblem
204.25/66.83 
↳15 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳16 CdtProblem
204.25/66.83 
↳17 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳18 CdtProblem
204.25/66.83 
↳19 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳20 CdtProblem
204.25/66.83 
↳21 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳22 CdtProblem
204.25/66.83 
↳23 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳24 CdtProblem
204.25/66.83 
↳25 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳26 CdtProblem
204.25/66.83 
↳27 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳28 CdtProblem
204.25/66.83 
↳29 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳30 CdtProblem
204.25/66.83 
↳31 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳32 CdtProblem
204.25/66.83 
↳33 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳34 CdtProblem
204.25/66.83 
↳35 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳36 CdtProblem
204.25/66.83 
↳37 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳38 CdtProblem
204.25/66.83 
↳39 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳40 CdtProblem
204.25/66.83 
↳41 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳42 CdtProblem
204.25/66.83 
↳43 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳44 CdtProblem
204.25/66.83 
↳45 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳46 CdtProblem
204.25/66.83 
↳47 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳48 CdtProblem
204.25/66.83 
↳49 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
204.25/66.83 
↳50 CdtProblem
204.25/66.83 
↳51 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
204.25/66.83 
↳52 CdtProblem
204.25/66.83 
↳53 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳54 CdtProblem
204.25/66.83 
↳55 CdtUnreachableProof (⇔)
204.25/66.83 
↳56 CdtProblem
204.25/66.83 
↳57 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳58 CdtProblem
204.25/66.83 
↳59 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳60 CdtProblem
204.25/66.83 
↳61 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
204.25/66.83 
↳62 CdtProblem
204.25/66.83 
↳63 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))
204.25/66.83 
↳64 CdtProblem
204.25/66.83 
↳65 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
204.25/66.83 
↳66 CdtProblem
204.25/66.83 
↳67 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
204.25/66.83 
↳68 CdtProblem
204.25/66.83 
↳69 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
204.25/66.83 
↳70 CdtProblem
204.25/66.83 
↳71 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
204.25/66.83 
↳72 CdtProblem
204.25/66.83 
↳73 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
204.25/66.83 
↳74 CdtProblem
204.25/66.83 
↳75 SIsEmptyProof (BOTH BOUNDS(ID, ID))
204.25/66.83 
↳76 BOUNDS(O(1), O(1))
204.25/66.83
204.25/66.83 204.25/66.83
204.25/66.83
204.25/66.83

(0) Obligation:

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

active(from(X)) → mark(cons(X, from(s(X)))) 204.25/66.83
active(length(nil)) → mark(0) 204.25/66.83
active(length(cons(X, Y))) → mark(s(length1(Y))) 204.25/66.83
active(length1(X)) → mark(length(X)) 204.25/66.83
active(from(X)) → from(active(X)) 204.25/66.83
active(cons(X1, X2)) → cons(active(X1), X2) 204.25/66.83
active(s(X)) → s(active(X)) 204.25/66.83
from(mark(X)) → mark(from(X)) 204.25/66.83
cons(mark(X1), X2) → mark(cons(X1, X2)) 204.25/66.83
s(mark(X)) → mark(s(X)) 204.25/66.83
proper(from(X)) → from(proper(X)) 204.25/66.83
proper(cons(X1, X2)) → cons(proper(X1), proper(X2)) 204.25/66.83
proper(s(X)) → s(proper(X)) 204.25/66.83
proper(length(X)) → length(proper(X)) 204.25/66.83
proper(nil) → ok(nil) 204.25/66.83
proper(0) → ok(0) 204.25/66.83
proper(length1(X)) → length1(proper(X)) 204.25/66.83
from(ok(X)) → ok(from(X)) 204.25/66.83
cons(ok(X1), ok(X2)) → ok(cons(X1, X2)) 204.25/66.83
s(ok(X)) → ok(s(X)) 204.25/66.83
length(ok(X)) → ok(length(X)) 204.25/66.83
length1(ok(X)) → ok(length1(X)) 204.25/66.83
top(mark(X)) → top(proper(X)) 204.25/66.83
top(ok(X)) → top(active(X))

Rewrite Strategy: INNERMOST
204.25/66.83
204.25/66.83

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

Converted CpxTRS to CDT
204.25/66.83
204.25/66.83

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.83
active(length(nil)) → mark(0) 204.25/66.83
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.83
active(length1(z0)) → mark(length(z0)) 204.25/66.83
active(from(z0)) → from(active(z0)) 204.25/66.83
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.83
active(s(z0)) → s(active(z0)) 204.25/66.83
from(mark(z0)) → mark(from(z0)) 204.25/66.83
from(ok(z0)) → ok(from(z0)) 204.25/66.83
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.83
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.84
s(mark(z0)) → mark(s(z0)) 204.25/66.84
s(ok(z0)) → ok(s(z0)) 204.25/66.84
proper(from(z0)) → from(proper(z0)) 204.25/66.84
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.84
proper(s(z0)) → s(proper(z0)) 204.25/66.84
proper(length(z0)) → length(proper(z0)) 204.25/66.84
proper(nil) → ok(nil) 204.25/66.84
proper(0) → ok(0) 204.25/66.84
proper(length1(z0)) → length1(proper(z0)) 204.25/66.84
length(ok(z0)) → ok(length(z0)) 204.25/66.84
length1(ok(z0)) → ok(length1(z0)) 204.25/66.84
top(mark(z0)) → top(proper(z0)) 204.25/66.84
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(from(z0)) → c(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0)) 204.25/66.84
ACTIVE(length(cons(z0, z1))) → c2(S(length1(z1)), LENGTH1(z1)) 204.25/66.84
ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.84
ACTIVE(from(z0)) → c4(FROM(active(z0)), ACTIVE(z0)) 204.25/66.84
ACTIVE(cons(z0, z1)) → c5(CONS(active(z0), z1), ACTIVE(z0)) 204.25/66.84
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.84
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.84
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.84
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.84
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.84
S(mark(z0)) → c11(S(z0)) 204.25/66.84
S(ok(z0)) → c12(S(z0)) 204.25/66.84
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.84
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.84
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.84
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.84
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.84
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0))
S tuples:

ACTIVE(from(z0)) → c(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0)) 204.25/66.84
ACTIVE(length(cons(z0, z1))) → c2(S(length1(z1)), LENGTH1(z1)) 204.25/66.84
ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.84
ACTIVE(from(z0)) → c4(FROM(active(z0)), ACTIVE(z0)) 204.25/66.84
ACTIVE(cons(z0, z1)) → c5(CONS(active(z0), z1), ACTIVE(z0)) 204.25/66.84
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.84
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.84
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.84
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.84
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.84
S(mark(z0)) → c11(S(z0)) 204.25/66.84
S(ok(z0)) → c12(S(z0)) 204.25/66.84
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.84
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.84
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.84
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.84
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.84
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c19, c20, c21, c22, c23

204.25/66.84
204.25/66.84

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

Removed 2 trailing tuple parts
204.25/66.84
204.25/66.84

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.84
active(length(nil)) → mark(0) 204.25/66.84
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.84
active(length1(z0)) → mark(length(z0)) 204.25/66.84
active(from(z0)) → from(active(z0)) 204.25/66.84
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.84
active(s(z0)) → s(active(z0)) 204.25/66.84
from(mark(z0)) → mark(from(z0)) 204.25/66.84
from(ok(z0)) → ok(from(z0)) 204.25/66.84
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.84
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.84
s(mark(z0)) → mark(s(z0)) 204.25/66.84
s(ok(z0)) → ok(s(z0)) 204.25/66.84
proper(from(z0)) → from(proper(z0)) 204.25/66.84
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.84
proper(s(z0)) → s(proper(z0)) 204.25/66.84
proper(length(z0)) → length(proper(z0)) 204.25/66.84
proper(nil) → ok(nil) 204.25/66.84
proper(0) → ok(0) 204.25/66.84
proper(length1(z0)) → length1(proper(z0)) 204.25/66.84
length(ok(z0)) → ok(length(z0)) 204.25/66.84
length1(ok(z0)) → ok(length1(z0)) 204.25/66.84
top(mark(z0)) → top(proper(z0)) 204.25/66.84
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length(cons(z0, z1))) → c2(S(length1(z1)), LENGTH1(z1)) 204.25/66.84
ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.84
ACTIVE(from(z0)) → c4(FROM(active(z0)), ACTIVE(z0)) 204.25/66.84
ACTIVE(cons(z0, z1)) → c5(CONS(active(z0), z1), ACTIVE(z0)) 204.25/66.84
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.84
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.84
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.84
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.84
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.84
S(mark(z0)) → c11(S(z0)) 204.25/66.84
S(ok(z0)) → c12(S(z0)) 204.25/66.84
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.84
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.84
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.84
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.84
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.84
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.84
ACTIVE(from(z0)) → c(S(z0))
S tuples:

ACTIVE(length(cons(z0, z1))) → c2(S(length1(z1)), LENGTH1(z1)) 204.25/66.84
ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.84
ACTIVE(from(z0)) → c4(FROM(active(z0)), ACTIVE(z0)) 204.25/66.84
ACTIVE(cons(z0, z1)) → c5(CONS(active(z0), z1), ACTIVE(z0)) 204.25/66.84
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.84
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.84
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.84
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.84
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.84
S(mark(z0)) → c11(S(z0)) 204.25/66.84
S(ok(z0)) → c12(S(z0)) 204.25/66.84
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.84
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.84
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.84
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.84
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.84
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.84
ACTIVE(from(z0)) → c(S(z0))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c19, c20, c21, c22, c23, c

204.25/66.84
204.25/66.84

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

Split RHS of tuples not part of any SCC
204.25/66.84
204.25/66.84

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.84
active(length(nil)) → mark(0) 204.25/66.84
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.84
active(length1(z0)) → mark(length(z0)) 204.25/66.84
active(from(z0)) → from(active(z0)) 204.25/66.84
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.84
active(s(z0)) → s(active(z0)) 204.25/66.84
from(mark(z0)) → mark(from(z0)) 204.25/66.84
from(ok(z0)) → ok(from(z0)) 204.25/66.84
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.84
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.84
s(mark(z0)) → mark(s(z0)) 204.25/66.84
s(ok(z0)) → ok(s(z0)) 204.25/66.84
proper(from(z0)) → from(proper(z0)) 204.25/66.84
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.84
proper(s(z0)) → s(proper(z0)) 204.25/66.84
proper(length(z0)) → length(proper(z0)) 204.25/66.84
proper(nil) → ok(nil) 204.25/66.84
proper(0) → ok(0) 204.25/66.84
proper(length1(z0)) → length1(proper(z0)) 204.25/66.84
length(ok(z0)) → ok(length(z0)) 204.25/66.84
length1(ok(z0)) → ok(length1(z0)) 204.25/66.84
top(mark(z0)) → top(proper(z0)) 204.25/66.84
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.84
ACTIVE(from(z0)) → c4(FROM(active(z0)), ACTIVE(z0)) 204.25/66.84
ACTIVE(cons(z0, z1)) → c5(CONS(active(z0), z1), ACTIVE(z0)) 204.25/66.84
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.84
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.84
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.84
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.84
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.84
S(mark(z0)) → c11(S(z0)) 204.25/66.84
S(ok(z0)) → c12(S(z0)) 204.25/66.84
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.84
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.84
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.84
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.84
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.84
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.84
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.84
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.84
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.84
ACTIVE(from(z0)) → c4(FROM(active(z0)), ACTIVE(z0)) 204.25/66.84
ACTIVE(cons(z0, z1)) → c5(CONS(active(z0), z1), ACTIVE(z0)) 204.25/66.84
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.84
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.84
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.84
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.84
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.84
S(mark(z0)) → c11(S(z0)) 204.25/66.84
S(ok(z0)) → c12(S(z0)) 204.25/66.84
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.84
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.84
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.84
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.84
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.84
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.84
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.84
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.84
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c19, c20, c21, c22, c23, c, c1

204.25/66.84
204.25/66.84

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

Use narrowing to replace ACTIVE(from(z0)) → c4(FROM(active(z0)), ACTIVE(z0)) by

ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.84
ACTIVE(from(length(nil))) → c4(FROM(mark(0)), ACTIVE(length(nil))) 204.25/66.84
ACTIVE(from(length(cons(z0, z1)))) → c4(FROM(mark(s(length1(z1)))), ACTIVE(length(cons(z0, z1)))) 204.25/66.84
ACTIVE(from(length1(z0))) → c4(FROM(mark(length(z0))), ACTIVE(length1(z0))) 204.25/66.84
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.84
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.84
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0)))
204.25/66.84
204.25/66.84

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.84
active(length(nil)) → mark(0) 204.25/66.84
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.84
active(length1(z0)) → mark(length(z0)) 204.25/66.84
active(from(z0)) → from(active(z0)) 204.25/66.84
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.84
active(s(z0)) → s(active(z0)) 204.25/66.84
from(mark(z0)) → mark(from(z0)) 204.25/66.84
from(ok(z0)) → ok(from(z0)) 204.25/66.84
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.84
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.84
s(mark(z0)) → mark(s(z0)) 204.25/66.84
s(ok(z0)) → ok(s(z0)) 204.25/66.84
proper(from(z0)) → from(proper(z0)) 204.25/66.84
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.84
proper(s(z0)) → s(proper(z0)) 204.25/66.84
proper(length(z0)) → length(proper(z0)) 204.25/66.84
proper(nil) → ok(nil) 204.25/66.84
proper(0) → ok(0) 204.25/66.84
proper(length1(z0)) → length1(proper(z0)) 204.25/66.84
length(ok(z0)) → ok(length(z0)) 204.25/66.84
length1(ok(z0)) → ok(length1(z0)) 204.25/66.84
top(mark(z0)) → top(proper(z0)) 204.25/66.84
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.84
ACTIVE(cons(z0, z1)) → c5(CONS(active(z0), z1), ACTIVE(z0)) 204.25/66.84
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.84
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.84
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.84
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.84
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.84
S(mark(z0)) → c11(S(z0)) 204.25/66.84
S(ok(z0)) → c12(S(z0)) 204.25/66.84
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.84
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.84
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.84
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.84
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.84
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.84
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.84
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.84
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.84
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.84
ACTIVE(from(length(nil))) → c4(FROM(mark(0)), ACTIVE(length(nil))) 204.25/66.84
ACTIVE(from(length(cons(z0, z1)))) → c4(FROM(mark(s(length1(z1)))), ACTIVE(length(cons(z0, z1)))) 204.25/66.84
ACTIVE(from(length1(z0))) → c4(FROM(mark(length(z0))), ACTIVE(length1(z0))) 204.25/66.84
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.84
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.84
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.84
ACTIVE(cons(z0, z1)) → c5(CONS(active(z0), z1), ACTIVE(z0)) 204.25/66.84
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.84
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.84
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.84
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.84
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.84
S(mark(z0)) → c11(S(z0)) 204.25/66.84
S(ok(z0)) → c12(S(z0)) 204.25/66.84
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.84
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.84
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.84
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.84
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.84
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.84
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.84
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.84
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.84
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.84
ACTIVE(from(length(nil))) → c4(FROM(mark(0)), ACTIVE(length(nil))) 204.25/66.84
ACTIVE(from(length(cons(z0, z1)))) → c4(FROM(mark(s(length1(z1)))), ACTIVE(length(cons(z0, z1)))) 204.25/66.84
ACTIVE(from(length1(z0))) → c4(FROM(mark(length(z0))), ACTIVE(length1(z0))) 204.25/66.84
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.84
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.84
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c19, c20, c21, c22, c23, c, c1, c4

204.25/66.84
204.25/66.84

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

Removed 1 trailing tuple parts
204.25/66.84
204.25/66.84

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.84
active(length(nil)) → mark(0) 204.25/66.84
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.84
active(length1(z0)) → mark(length(z0)) 204.25/66.84
active(from(z0)) → from(active(z0)) 204.25/66.84
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.84
active(s(z0)) → s(active(z0)) 204.25/66.84
from(mark(z0)) → mark(from(z0)) 204.25/66.84
from(ok(z0)) → ok(from(z0)) 204.25/66.84
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.84
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.84
s(mark(z0)) → mark(s(z0)) 204.25/66.84
s(ok(z0)) → ok(s(z0)) 204.25/66.84
proper(from(z0)) → from(proper(z0)) 204.25/66.84
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.84
proper(s(z0)) → s(proper(z0)) 204.25/66.84
proper(length(z0)) → length(proper(z0)) 204.25/66.84
proper(nil) → ok(nil) 204.25/66.84
proper(0) → ok(0) 204.25/66.84
proper(length1(z0)) → length1(proper(z0)) 204.25/66.84
length(ok(z0)) → ok(length(z0)) 204.25/66.84
length1(ok(z0)) → ok(length1(z0)) 204.25/66.84
top(mark(z0)) → top(proper(z0)) 204.25/66.84
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.84
ACTIVE(cons(z0, z1)) → c5(CONS(active(z0), z1), ACTIVE(z0)) 204.25/66.84
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.84
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.84
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.84
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.84
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.84
S(mark(z0)) → c11(S(z0)) 204.25/66.84
S(ok(z0)) → c12(S(z0)) 204.25/66.84
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.84
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.84
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.84
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.86
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.86
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.86
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.86
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.86
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.86
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.86
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(from(length(cons(z0, z1)))) → c4(FROM(mark(s(length1(z1)))), ACTIVE(length(cons(z0, z1)))) 204.25/66.86
ACTIVE(from(length1(z0))) → c4(FROM(mark(length(z0))), ACTIVE(length1(z0))) 204.25/66.86
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.86
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.86
ACTIVE(from(length(nil))) → c4(FROM(mark(0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.86
ACTIVE(cons(z0, z1)) → c5(CONS(active(z0), z1), ACTIVE(z0)) 204.25/66.86
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.86
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.86
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.86
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.86
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.86
S(mark(z0)) → c11(S(z0)) 204.25/66.86
S(ok(z0)) → c12(S(z0)) 204.25/66.86
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.86
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.86
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.86
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.86
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.86
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.86
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.86
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.86
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.86
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.86
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.86
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.86
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(from(length(cons(z0, z1)))) → c4(FROM(mark(s(length1(z1)))), ACTIVE(length(cons(z0, z1)))) 204.25/66.86
ACTIVE(from(length1(z0))) → c4(FROM(mark(length(z0))), ACTIVE(length1(z0))) 204.25/66.86
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.86
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.86
ACTIVE(from(length(nil))) → c4(FROM(mark(0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c19, c20, c21, c22, c23, c, c1, c4, c4

204.25/66.86
204.25/66.86

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

Split RHS of tuples not part of any SCC
204.25/66.86
204.25/66.86

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.86
active(length(nil)) → mark(0) 204.25/66.86
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.86
active(length1(z0)) → mark(length(z0)) 204.25/66.86
active(from(z0)) → from(active(z0)) 204.25/66.86
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.86
active(s(z0)) → s(active(z0)) 204.25/66.86
from(mark(z0)) → mark(from(z0)) 204.25/66.86
from(ok(z0)) → ok(from(z0)) 204.25/66.86
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.86
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.86
s(mark(z0)) → mark(s(z0)) 204.25/66.86
s(ok(z0)) → ok(s(z0)) 204.25/66.86
proper(from(z0)) → from(proper(z0)) 204.25/66.86
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.86
proper(s(z0)) → s(proper(z0)) 204.25/66.86
proper(length(z0)) → length(proper(z0)) 204.25/66.86
proper(nil) → ok(nil) 204.25/66.86
proper(0) → ok(0) 204.25/66.86
proper(length1(z0)) → length1(proper(z0)) 204.25/66.86
length(ok(z0)) → ok(length(z0)) 204.25/66.86
length1(ok(z0)) → ok(length1(z0)) 204.25/66.86
top(mark(z0)) → top(proper(z0)) 204.25/66.86
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.86
ACTIVE(cons(z0, z1)) → c5(CONS(active(z0), z1), ACTIVE(z0)) 204.25/66.86
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.86
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.86
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.86
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.86
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.86
S(mark(z0)) → c11(S(z0)) 204.25/66.86
S(ok(z0)) → c12(S(z0)) 204.25/66.86
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.86
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.86
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.86
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.86
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.86
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.86
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.86
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.86
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.86
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.86
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.86
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.86
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.86
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.86
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.86
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.86
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.86
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.86
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.86
ACTIVE(cons(z0, z1)) → c5(CONS(active(z0), z1), ACTIVE(z0)) 204.25/66.86
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.86
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.86
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.86
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.86
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.86
S(mark(z0)) → c11(S(z0)) 204.25/66.86
S(ok(z0)) → c12(S(z0)) 204.25/66.86
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.86
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.86
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.86
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.86
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.86
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.86
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.86
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.86
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.86
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.86
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.86
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.86
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.86
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.86
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.86
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.86
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.86
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.86
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c19, c20, c21, c22, c23, c, c1, c4, c4, c2

204.25/66.86
204.25/66.86

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

Use narrowing to replace ACTIVE(cons(z0, z1)) → c5(CONS(active(z0), z1), ACTIVE(z0)) by

ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1), ACTIVE(length(nil))) 204.25/66.86
ACTIVE(cons(length(cons(z0, z1)), x1)) → c5(CONS(mark(s(length1(z1))), x1), ACTIVE(length(cons(z0, z1)))) 204.25/66.86
ACTIVE(cons(length1(z0), x1)) → c5(CONS(mark(length(z0)), x1), ACTIVE(length1(z0))) 204.25/66.86
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.86
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
204.25/66.86
204.25/66.86

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.86
active(length(nil)) → mark(0) 204.25/66.86
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.86
active(length1(z0)) → mark(length(z0)) 204.25/66.86
active(from(z0)) → from(active(z0)) 204.25/66.86
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.86
active(s(z0)) → s(active(z0)) 204.25/66.86
from(mark(z0)) → mark(from(z0)) 204.25/66.86
from(ok(z0)) → ok(from(z0)) 204.25/66.86
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.86
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.86
s(mark(z0)) → mark(s(z0)) 204.25/66.86
s(ok(z0)) → ok(s(z0)) 204.25/66.86
proper(from(z0)) → from(proper(z0)) 204.25/66.86
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.86
proper(s(z0)) → s(proper(z0)) 204.25/66.86
proper(length(z0)) → length(proper(z0)) 204.25/66.86
proper(nil) → ok(nil) 204.25/66.86
proper(0) → ok(0) 204.25/66.86
proper(length1(z0)) → length1(proper(z0)) 204.25/66.86
length(ok(z0)) → ok(length(z0)) 204.25/66.86
length1(ok(z0)) → ok(length1(z0)) 204.25/66.86
top(mark(z0)) → top(proper(z0)) 204.25/66.86
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.86
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.86
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.86
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.86
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.86
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.86
S(mark(z0)) → c11(S(z0)) 204.25/66.86
S(ok(z0)) → c12(S(z0)) 204.25/66.86
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.86
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.86
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.86
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.86
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.86
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.86
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.86
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.86
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.86
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.86
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.86
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.86
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.86
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.86
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.86
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.86
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.86
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.86
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.86
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1), ACTIVE(length(nil))) 204.25/66.86
ACTIVE(cons(length(cons(z0, z1)), x1)) → c5(CONS(mark(s(length1(z1))), x1), ACTIVE(length(cons(z0, z1)))) 204.25/66.86
ACTIVE(cons(length1(z0), x1)) → c5(CONS(mark(length(z0)), x1), ACTIVE(length1(z0))) 204.25/66.86
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.86
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.86
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.86
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.86
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.86
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.86
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.86
S(mark(z0)) → c11(S(z0)) 204.25/66.86
S(ok(z0)) → c12(S(z0)) 204.25/66.86
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.86
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.86
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.86
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.86
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.86
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.86
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.86
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.86
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.86
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.86
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.86
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.86
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.86
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.86
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.86
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.86
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.86
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.86
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.86
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1), ACTIVE(length(nil))) 204.25/66.86
ACTIVE(cons(length(cons(z0, z1)), x1)) → c5(CONS(mark(s(length1(z1))), x1), ACTIVE(length(cons(z0, z1)))) 204.25/66.86
ACTIVE(cons(length1(z0), x1)) → c5(CONS(mark(length(z0)), x1), ACTIVE(length1(z0))) 204.25/66.86
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.86
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.86
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c19, c20, c21, c22, c23, c, c1, c4, c4, c2, c5

204.25/66.86
204.25/66.86

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

Removed 1 trailing tuple parts
204.25/66.86
204.25/66.86

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.86
active(length(nil)) → mark(0) 204.25/66.86
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.86
active(length1(z0)) → mark(length(z0)) 204.25/66.86
active(from(z0)) → from(active(z0)) 204.25/66.86
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.86
active(s(z0)) → s(active(z0)) 204.25/66.86
from(mark(z0)) → mark(from(z0)) 204.25/66.86
from(ok(z0)) → ok(from(z0)) 204.25/66.86
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.86
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.86
s(mark(z0)) → mark(s(z0)) 204.25/66.86
s(ok(z0)) → ok(s(z0)) 204.25/66.86
proper(from(z0)) → from(proper(z0)) 204.25/66.86
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.86
proper(s(z0)) → s(proper(z0)) 204.25/66.86
proper(length(z0)) → length(proper(z0)) 204.25/66.86
proper(nil) → ok(nil) 204.25/66.86
proper(0) → ok(0) 204.25/66.86
proper(length1(z0)) → length1(proper(z0)) 204.25/66.86
length(ok(z0)) → ok(length(z0)) 204.25/66.86
length1(ok(z0)) → ok(length1(z0)) 204.25/66.86
top(mark(z0)) → top(proper(z0)) 204.25/66.86
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.86
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.86
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.86
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.86
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.86
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.86
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c5(CONS(mark(s(length1(z1))), x1), ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c5(CONS(mark(length(z0)), x1), ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c5(CONS(mark(s(length1(z1))), x1), ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c5(CONS(mark(length(z0)), x1), ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c19, c20, c21, c22, c23, c, c1, c4, c4, c2, c5, c5

204.25/66.87
204.25/66.87

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

Split RHS of tuples not part of any SCC
204.25/66.87
204.25/66.87

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.87
active(length(nil)) → mark(0) 204.25/66.87
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.87
active(length1(z0)) → mark(length(z0)) 204.25/66.87
active(from(z0)) → from(active(z0)) 204.25/66.87
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.87
active(s(z0)) → s(active(z0)) 204.25/66.87
from(mark(z0)) → mark(from(z0)) 204.25/66.87
from(ok(z0)) → ok(from(z0)) 204.25/66.87
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.87
s(mark(z0)) → mark(s(z0)) 204.25/66.87
s(ok(z0)) → ok(s(z0)) 204.25/66.87
proper(from(z0)) → from(proper(z0)) 204.25/66.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.87
proper(s(z0)) → s(proper(z0)) 204.25/66.87
proper(length(z0)) → length(proper(z0)) 204.25/66.87
proper(nil) → ok(nil) 204.25/66.87
proper(0) → ok(0) 204.25/66.87
proper(length1(z0)) → length1(proper(z0)) 204.25/66.87
length(ok(z0)) → ok(length(z0)) 204.25/66.87
length1(ok(z0)) → ok(length1(z0)) 204.25/66.87
top(mark(z0)) → top(proper(z0)) 204.25/66.87
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c19, c20, c21, c22, c23, c, c1, c4, c4, c2, c5, c5, c17

204.25/66.87
204.25/66.87

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

Use narrowing to replace ACTIVE(s(z0)) → c6(S(active(z0)), ACTIVE(z0)) by

ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0)), ACTIVE(length(nil))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c6(S(mark(s(length1(z1)))), ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c6(S(mark(length(z0))), ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0)))
204.25/66.87
204.25/66.87

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.87
active(length(nil)) → mark(0) 204.25/66.87
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.87
active(length1(z0)) → mark(length(z0)) 204.25/66.87
active(from(z0)) → from(active(z0)) 204.25/66.87
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.87
active(s(z0)) → s(active(z0)) 204.25/66.87
from(mark(z0)) → mark(from(z0)) 204.25/66.87
from(ok(z0)) → ok(from(z0)) 204.25/66.87
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.87
s(mark(z0)) → mark(s(z0)) 204.25/66.87
s(ok(z0)) → ok(s(z0)) 204.25/66.87
proper(from(z0)) → from(proper(z0)) 204.25/66.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.87
proper(s(z0)) → s(proper(z0)) 204.25/66.87
proper(length(z0)) → length(proper(z0)) 204.25/66.87
proper(nil) → ok(nil) 204.25/66.87
proper(0) → ok(0) 204.25/66.87
proper(length1(z0)) → length1(proper(z0)) 204.25/66.87
length(ok(z0)) → ok(length(z0)) 204.25/66.87
length1(ok(z0)) → ok(length1(z0)) 204.25/66.87
top(mark(z0)) → top(proper(z0)) 204.25/66.87
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0)), ACTIVE(length(nil))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c6(S(mark(s(length1(z1)))), ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c6(S(mark(length(z0))), ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0)), ACTIVE(length(nil))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c6(S(mark(s(length1(z1)))), ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c6(S(mark(length(z0))), ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c19, c20, c21, c22, c23, c, c1, c4, c4, c2, c5, c5, c17, c6

204.25/66.87
204.25/66.87

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

Removed 1 trailing tuple parts
204.25/66.87
204.25/66.87

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.87
active(length(nil)) → mark(0) 204.25/66.87
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.87
active(length1(z0)) → mark(length(z0)) 204.25/66.87
active(from(z0)) → from(active(z0)) 204.25/66.87
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.87
active(s(z0)) → s(active(z0)) 204.25/66.87
from(mark(z0)) → mark(from(z0)) 204.25/66.87
from(ok(z0)) → ok(from(z0)) 204.25/66.87
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.87
s(mark(z0)) → mark(s(z0)) 204.25/66.87
s(ok(z0)) → ok(s(z0)) 204.25/66.87
proper(from(z0)) → from(proper(z0)) 204.25/66.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.87
proper(s(z0)) → s(proper(z0)) 204.25/66.87
proper(length(z0)) → length(proper(z0)) 204.25/66.87
proper(nil) → ok(nil) 204.25/66.87
proper(0) → ok(0) 204.25/66.87
proper(length1(z0)) → length1(proper(z0)) 204.25/66.87
length(ok(z0)) → ok(length(z0)) 204.25/66.87
length1(ok(z0)) → ok(length1(z0)) 204.25/66.87
top(mark(z0)) → top(proper(z0)) 204.25/66.87
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c6(S(mark(s(length1(z1)))), ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c6(S(mark(length(z0))), ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c6(S(mark(s(length1(z1)))), ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c6(S(mark(length(z0))), ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c19, c20, c21, c22, c23, c, c1, c4, c4, c2, c5, c5, c17, c6, c6

204.25/66.87
204.25/66.87

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

Split RHS of tuples not part of any SCC
204.25/66.87
204.25/66.87

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.87
active(length(nil)) → mark(0) 204.25/66.87
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.87
active(length1(z0)) → mark(length(z0)) 204.25/66.87
active(from(z0)) → from(active(z0)) 204.25/66.87
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.87
active(s(z0)) → s(active(z0)) 204.25/66.87
from(mark(z0)) → mark(from(z0)) 204.25/66.87
from(ok(z0)) → ok(from(z0)) 204.25/66.87
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.87
s(mark(z0)) → mark(s(z0)) 204.25/66.87
s(ok(z0)) → ok(s(z0)) 204.25/66.87
proper(from(z0)) → from(proper(z0)) 204.25/66.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.87
proper(s(z0)) → s(proper(z0)) 204.25/66.87
proper(length(z0)) → length(proper(z0)) 204.25/66.87
proper(nil) → ok(nil) 204.25/66.87
proper(0) → ok(0) 204.25/66.87
proper(length1(z0)) → length1(proper(z0)) 204.25/66.87
length(ok(z0)) → ok(length(z0)) 204.25/66.87
length1(ok(z0)) → ok(length1(z0)) 204.25/66.87
top(mark(z0)) → top(proper(z0)) 204.25/66.87
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c19, c20, c21, c22, c23, c, c1, c4, c4, c2, c5, c5, c17, c6, c6, c18

204.25/66.87
204.25/66.87

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

Use narrowing to replace PROPER(from(z0)) → c13(FROM(proper(z0)), PROPER(z0)) by

PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.87
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.87
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.87
PROPER(from(nil)) → c13(FROM(ok(nil)), PROPER(nil)) 204.25/66.87
PROPER(from(0)) → c13(FROM(ok(0)), PROPER(0)) 204.25/66.87
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0)))
204.25/66.87
204.25/66.87

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.87
active(length(nil)) → mark(0) 204.25/66.87
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.87
active(length1(z0)) → mark(length(z0)) 204.25/66.87
active(from(z0)) → from(active(z0)) 204.25/66.87
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.87
active(s(z0)) → s(active(z0)) 204.25/66.87
from(mark(z0)) → mark(from(z0)) 204.25/66.87
from(ok(z0)) → ok(from(z0)) 204.25/66.87
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.87
s(mark(z0)) → mark(s(z0)) 204.25/66.87
s(ok(z0)) → ok(s(z0)) 204.25/66.87
proper(from(z0)) → from(proper(z0)) 204.25/66.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.87
proper(s(z0)) → s(proper(z0)) 204.25/66.87
proper(length(z0)) → length(proper(z0)) 204.25/66.87
proper(nil) → ok(nil) 204.25/66.87
proper(0) → ok(0) 204.25/66.87
proper(length1(z0)) → length1(proper(z0)) 204.25/66.87
length(ok(z0)) → ok(length(z0)) 204.25/66.87
length1(ok(z0)) → ok(length1(z0)) 204.25/66.87
top(mark(z0)) → top(proper(z0)) 204.25/66.87
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.87
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.87
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.87
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.87
PROPER(from(nil)) → c13(FROM(ok(nil)), PROPER(nil)) 204.25/66.87
PROPER(from(0)) → c13(FROM(ok(0)), PROPER(0)) 204.25/66.87
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.87
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.87
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.87
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.87
PROPER(from(nil)) → c13(FROM(ok(nil)), PROPER(nil)) 204.25/66.87
PROPER(from(0)) → c13(FROM(ok(0)), PROPER(0)) 204.25/66.87
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c14, c15, c16, c19, c20, c21, c22, c23, c, c1, c4, c4, c2, c5, c5, c17, c6, c6, c18, c13

204.25/66.87
204.25/66.87

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

Removed 2 trailing tuple parts
204.25/66.87
204.25/66.87

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.87
active(length(nil)) → mark(0) 204.25/66.87
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.87
active(length1(z0)) → mark(length(z0)) 204.25/66.87
active(from(z0)) → from(active(z0)) 204.25/66.87
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.87
active(s(z0)) → s(active(z0)) 204.25/66.87
from(mark(z0)) → mark(from(z0)) 204.25/66.87
from(ok(z0)) → ok(from(z0)) 204.25/66.87
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.87
s(mark(z0)) → mark(s(z0)) 204.25/66.87
s(ok(z0)) → ok(s(z0)) 204.25/66.87
proper(from(z0)) → from(proper(z0)) 204.25/66.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.87
proper(s(z0)) → s(proper(z0)) 204.25/66.87
proper(length(z0)) → length(proper(z0)) 204.25/66.87
proper(nil) → ok(nil) 204.25/66.87
proper(0) → ok(0) 204.25/66.87
proper(length1(z0)) → length1(proper(z0)) 204.25/66.87
length(ok(z0)) → ok(length(z0)) 204.25/66.87
length1(ok(z0)) → ok(length1(z0)) 204.25/66.87
top(mark(z0)) → top(proper(z0)) 204.25/66.87
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.87
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.87
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.87
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.87
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.87
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.87
PROPER(from(0)) → c13(FROM(ok(0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.87
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.87
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.87
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.87
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.87
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.87
PROPER(from(0)) → c13(FROM(ok(0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c14, c15, c16, c19, c20, c21, c22, c23, c, c1, c4, c4, c2, c5, c5, c17, c6, c6, c18, c13, c13

204.25/66.87
204.25/66.87

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

Use narrowing to replace PROPER(cons(z0, z1)) → c14(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.87
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.87
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.87
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 204.25/66.87
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 204.25/66.87
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.87
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.87
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 204.25/66.87
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 204.25/66.87
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1))
204.25/66.87
204.25/66.87

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.87
active(length(nil)) → mark(0) 204.25/66.87
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.87
active(length1(z0)) → mark(length(z0)) 204.25/66.87
active(from(z0)) → from(active(z0)) 204.25/66.87
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.87
active(s(z0)) → s(active(z0)) 204.25/66.87
from(mark(z0)) → mark(from(z0)) 204.25/66.87
from(ok(z0)) → ok(from(z0)) 204.25/66.87
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.87
s(mark(z0)) → mark(s(z0)) 204.25/66.87
s(ok(z0)) → ok(s(z0)) 204.25/66.87
proper(from(z0)) → from(proper(z0)) 204.25/66.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.87
proper(s(z0)) → s(proper(z0)) 204.25/66.87
proper(length(z0)) → length(proper(z0)) 204.25/66.87
proper(nil) → ok(nil) 204.25/66.87
proper(0) → ok(0) 204.25/66.87
proper(length1(z0)) → length1(proper(z0)) 204.25/66.87
length(ok(z0)) → ok(length(z0)) 204.25/66.87
length1(ok(z0)) → ok(length1(z0)) 204.25/66.87
top(mark(z0)) → top(proper(z0)) 204.25/66.87
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.87
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.87
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.87
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.87
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.87
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.87
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.87
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.87
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.87
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.87
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 204.25/66.87
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 204.25/66.87
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.87
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.87
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 204.25/66.87
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 204.25/66.87
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.87
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.87
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.87
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.87
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.87
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.87
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.87
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.87
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.87
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.87
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 204.25/66.87
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 204.25/66.87
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.87
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.87
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1)) 204.25/66.87
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 204.25/66.87
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c15, c16, c19, c20, c21, c22, c23, c, c1, c4, c4, c2, c5, c5, c17, c6, c6, c18, c13, c13, c14

204.25/66.87
204.25/66.87

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

Removed 4 trailing tuple parts
204.25/66.87
204.25/66.87

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.87
active(length(nil)) → mark(0) 204.25/66.87
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.87
active(length1(z0)) → mark(length(z0)) 204.25/66.87
active(from(z0)) → from(active(z0)) 204.25/66.87
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.87
active(s(z0)) → s(active(z0)) 204.25/66.87
from(mark(z0)) → mark(from(z0)) 204.25/66.87
from(ok(z0)) → ok(from(z0)) 204.25/66.87
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.87
s(mark(z0)) → mark(s(z0)) 204.25/66.87
s(ok(z0)) → ok(s(z0)) 204.25/66.87
proper(from(z0)) → from(proper(z0)) 204.25/66.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.87
proper(s(z0)) → s(proper(z0)) 204.25/66.87
proper(length(z0)) → length(proper(z0)) 204.25/66.87
proper(nil) → ok(nil) 204.25/66.87
proper(0) → ok(0) 204.25/66.87
proper(length1(z0)) → length1(proper(z0)) 204.25/66.87
length(ok(z0)) → ok(length(z0)) 204.25/66.87
length1(ok(z0)) → ok(length1(z0)) 204.25/66.87
top(mark(z0)) → top(proper(z0)) 204.25/66.87
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.87
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.87
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.87
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.87
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.87
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.87
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.87
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.87
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.87
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.87
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.87
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.87
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.87
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.87
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.87
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.87
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.87
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.87
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.87
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.87
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.87
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.87
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.87
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.87
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.87
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.87
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.87
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.87
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.87
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.87
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c15, c16, c19, c20, c21, c22, c23, c, c1, c4, c4, c2, c5, c5, c17, c6, c6, c18, c13, c13, c14, c14

204.25/66.87
204.25/66.87

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

Use narrowing to replace PROPER(s(z0)) → c15(S(proper(z0)), PROPER(z0)) by

PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.87
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.87
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.87
PROPER(s(nil)) → c15(S(ok(nil)), PROPER(nil)) 204.25/66.87
PROPER(s(0)) → c15(S(ok(0)), PROPER(0)) 204.25/66.87
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0)))
204.25/66.87
204.25/66.87

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.87
active(length(nil)) → mark(0) 204.25/66.87
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.87
active(length1(z0)) → mark(length(z0)) 204.25/66.87
active(from(z0)) → from(active(z0)) 204.25/66.87
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.87
active(s(z0)) → s(active(z0)) 204.25/66.87
from(mark(z0)) → mark(from(z0)) 204.25/66.87
from(ok(z0)) → ok(from(z0)) 204.25/66.87
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.87
s(mark(z0)) → mark(s(z0)) 204.25/66.87
s(ok(z0)) → ok(s(z0)) 204.25/66.87
proper(from(z0)) → from(proper(z0)) 204.25/66.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.87
proper(s(z0)) → s(proper(z0)) 204.25/66.87
proper(length(z0)) → length(proper(z0)) 204.25/66.87
proper(nil) → ok(nil) 204.25/66.87
proper(0) → ok(0) 204.25/66.87
proper(length1(z0)) → length1(proper(z0)) 204.25/66.87
length(ok(z0)) → ok(length(z0)) 204.25/66.87
length1(ok(z0)) → ok(length1(z0)) 204.25/66.87
top(mark(z0)) → top(proper(z0)) 204.25/66.87
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.87
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.87
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.87
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.87
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.87
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.87
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.87
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.87
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.87
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.87
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.87
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.87
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.87
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.87
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.87
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.87
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.87
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.87
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.87
PROPER(s(nil)) → c15(S(ok(nil)), PROPER(nil)) 204.25/66.87
PROPER(s(0)) → c15(S(ok(0)), PROPER(0)) 204.25/66.87
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.87
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.87
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.87
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.87
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.87
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.87
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.87
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.87
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.87
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.87
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.87
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.87
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.87
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.87
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.87
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.87
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.87
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.87
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.87
PROPER(s(nil)) → c15(S(ok(nil)), PROPER(nil)) 204.25/66.87
PROPER(s(0)) → c15(S(ok(0)), PROPER(0)) 204.25/66.87
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c16, c19, c20, c21, c22, c23, c, c1, c4, c4, c2, c5, c5, c17, c6, c6, c18, c13, c13, c14, c14, c15

204.25/66.87
204.25/66.87

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

Removed 2 trailing tuple parts
204.25/66.87
204.25/66.87

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.87
active(length(nil)) → mark(0) 204.25/66.87
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.87
active(length1(z0)) → mark(length(z0)) 204.25/66.87
active(from(z0)) → from(active(z0)) 204.25/66.87
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.87
active(s(z0)) → s(active(z0)) 204.25/66.87
from(mark(z0)) → mark(from(z0)) 204.25/66.87
from(ok(z0)) → ok(from(z0)) 204.25/66.87
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.87
s(mark(z0)) → mark(s(z0)) 204.25/66.87
s(ok(z0)) → ok(s(z0)) 204.25/66.87
proper(from(z0)) → from(proper(z0)) 204.25/66.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.87
proper(s(z0)) → s(proper(z0)) 204.25/66.87
proper(length(z0)) → length(proper(z0)) 204.25/66.87
proper(nil) → ok(nil) 204.25/66.87
proper(0) → ok(0) 204.25/66.87
proper(length1(z0)) → length1(proper(z0)) 204.25/66.87
length(ok(z0)) → ok(length(z0)) 204.25/66.87
length1(ok(z0)) → ok(length1(z0)) 204.25/66.87
top(mark(z0)) → top(proper(z0)) 204.25/66.87
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.87
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.87
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.87
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.87
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.87
S(mark(z0)) → c11(S(z0)) 204.25/66.87
S(ok(z0)) → c12(S(z0)) 204.25/66.87
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.87
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.87
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.87
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.87
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.87
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.87
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.87
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.87
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.87
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.87
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.87
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.87
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.87
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.87
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.87
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.87
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.87
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.87
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.87
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.87
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.87
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.87
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.87
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.87
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.87
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.87
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.87
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.87
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.87
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.88
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.88
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.88
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.88
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.88
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.88
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.88
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.88
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.88
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.88
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.88
PROPER(s(0)) → c15(S(ok(0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.88
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.88
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.88
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.88
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.88
S(mark(z0)) → c11(S(z0)) 204.25/66.88
S(ok(z0)) → c12(S(z0)) 204.25/66.88
PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) 204.25/66.88
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.88
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.88
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.88
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.88
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.88
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.88
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.88
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.88
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.88
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.88
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.88
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.88
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.88
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.88
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.88
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.88
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.88
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.88
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.88
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.88
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.88
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.88
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.88
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.88
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.88
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.88
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.88
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.88
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.88
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.88
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.88
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.88
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.88
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.88
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.88
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.88
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.88
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.88
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.88
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.88
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.88
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.88
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.88
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.88
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.88
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.88
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.88
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.88
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.88
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.88
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.88
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.88
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.88
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.88
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.88
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.88
PROPER(s(0)) → c15(S(ok(0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c16, c19, c20, c21, c22, c23, c, c1, c4, c4, c2, c5, c5, c17, c6, c6, c18, c13, c13, c14, c14, c15, c15

204.25/66.88
204.25/66.88

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

Use narrowing to replace PROPER(length(z0)) → c16(LENGTH(proper(z0)), PROPER(z0)) by

PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.88
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.88
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.88
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.88
PROPER(length(nil)) → c16(LENGTH(ok(nil)), PROPER(nil)) 204.25/66.88
PROPER(length(0)) → c16(LENGTH(ok(0)), PROPER(0)) 204.25/66.88
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0)))
204.25/66.88
204.25/66.88

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.88
active(length(nil)) → mark(0) 204.25/66.88
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.88
active(length1(z0)) → mark(length(z0)) 204.25/66.88
active(from(z0)) → from(active(z0)) 204.25/66.88
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.88
active(s(z0)) → s(active(z0)) 204.25/66.88
from(mark(z0)) → mark(from(z0)) 204.25/66.88
from(ok(z0)) → ok(from(z0)) 204.25/66.88
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.88
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.88
s(mark(z0)) → mark(s(z0)) 204.25/66.88
s(ok(z0)) → ok(s(z0)) 204.25/66.88
proper(from(z0)) → from(proper(z0)) 204.25/66.88
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.88
proper(s(z0)) → s(proper(z0)) 204.25/66.88
proper(length(z0)) → length(proper(z0)) 204.25/66.88
proper(nil) → ok(nil) 204.25/66.88
proper(0) → ok(0) 204.25/66.88
proper(length1(z0)) → length1(proper(z0)) 204.25/66.88
length(ok(z0)) → ok(length(z0)) 204.25/66.88
length1(ok(z0)) → ok(length1(z0)) 204.25/66.88
top(mark(z0)) → top(proper(z0)) 204.25/66.88
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.88
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.88
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.88
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.88
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.88
S(mark(z0)) → c11(S(z0)) 204.25/66.88
S(ok(z0)) → c12(S(z0)) 204.25/66.88
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.88
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.88
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.88
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.88
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.88
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.88
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.88
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.88
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.88
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.88
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.88
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.88
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.88
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.88
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.88
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.88
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.88
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.88
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.88
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.88
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.88
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.88
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.88
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.88
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.88
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.88
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.88
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.88
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.88
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.88
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.88
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.88
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.88
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.88
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.88
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.88
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.88
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.88
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.88
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.88
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.88
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.88
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.88
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.88
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.88
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.88
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.88
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.88
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.88
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.88
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.88
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.88
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.88
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.88
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.88
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.88
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.88
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.88
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.88
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.88
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.88
PROPER(length(nil)) → c16(LENGTH(ok(nil)), PROPER(nil)) 204.25/66.88
PROPER(length(0)) → c16(LENGTH(ok(0)), PROPER(0)) 204.25/66.88
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.88
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.88
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.88
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.88
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.88
S(mark(z0)) → c11(S(z0)) 204.25/66.88
S(ok(z0)) → c12(S(z0)) 204.25/66.88
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.88
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.88
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.88
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.88
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.88
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.88
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.88
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.88
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.88
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.88
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.88
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.88
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.88
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.88
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.88
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.88
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.88
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.88
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.88
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.88
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.88
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.88
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.88
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.88
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.88
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.88
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.88
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.88
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.88
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.88
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.88
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.88
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.88
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.88
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.89
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.89
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.89
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.89
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.89
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.89
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.89
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.89
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.89
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.89
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.89
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length(nil)) → c16(LENGTH(ok(nil)), PROPER(nil)) 204.25/66.89
PROPER(length(0)) → c16(LENGTH(ok(0)), PROPER(0)) 204.25/66.89
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c19, c20, c21, c22, c23, c, c1, c4, c4, c2, c5, c5, c17, c6, c6, c18, c13, c13, c14, c14, c15, c15, c16

204.25/66.89
204.25/66.89

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

Removed 2 trailing tuple parts
204.25/66.89
204.25/66.89

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.89
active(length(nil)) → mark(0) 204.25/66.89
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.89
active(length1(z0)) → mark(length(z0)) 204.25/66.89
active(from(z0)) → from(active(z0)) 204.25/66.89
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.89
active(s(z0)) → s(active(z0)) 204.25/66.89
from(mark(z0)) → mark(from(z0)) 204.25/66.89
from(ok(z0)) → ok(from(z0)) 204.25/66.89
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.89
s(mark(z0)) → mark(s(z0)) 204.25/66.89
s(ok(z0)) → ok(s(z0)) 204.25/66.89
proper(from(z0)) → from(proper(z0)) 204.25/66.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.89
proper(s(z0)) → s(proper(z0)) 204.25/66.89
proper(length(z0)) → length(proper(z0)) 204.25/66.89
proper(nil) → ok(nil) 204.25/66.89
proper(0) → ok(0) 204.25/66.89
proper(length1(z0)) → length1(proper(z0)) 204.25/66.89
length(ok(z0)) → ok(length(z0)) 204.25/66.89
length1(ok(z0)) → ok(length1(z0)) 204.25/66.89
top(mark(z0)) → top(proper(z0)) 204.25/66.89
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.89
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.89
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.89
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.89
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.89
S(mark(z0)) → c11(S(z0)) 204.25/66.89
S(ok(z0)) → c12(S(z0)) 204.25/66.89
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.89
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.89
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.89
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.89
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.89
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.89
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.89
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.89
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.89
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.89
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.89
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.89
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.89
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.89
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.89
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.89
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.89
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.89
PROPER(length(0)) → c16(LENGTH(ok(0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.89
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.89
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.89
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.89
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.89
S(mark(z0)) → c11(S(z0)) 204.25/66.89
S(ok(z0)) → c12(S(z0)) 204.25/66.89
PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) 204.25/66.89
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.89
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.89
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.89
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.89
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.89
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.89
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.89
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.89
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.89
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.89
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.89
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.89
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.89
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.89
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.89
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.89
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.89
PROPER(length(0)) → c16(LENGTH(ok(0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, PROPER, LENGTH, LENGTH1, TOP

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c19, c20, c21, c22, c23, c, c1, c4, c4, c2, c5, c5, c17, c6, c6, c18, c13, c13, c14, c14, c15, c15, c16, c16

204.25/66.89
204.25/66.89

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

Use narrowing to replace PROPER(length1(z0)) → c19(LENGTH1(proper(z0)), PROPER(z0)) by

PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length1(nil)) → c19(LENGTH1(ok(nil)), PROPER(nil)) 204.25/66.89
PROPER(length1(0)) → c19(LENGTH1(ok(0)), PROPER(0)) 204.25/66.89
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0)))
204.25/66.89
204.25/66.89

(42) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.89
active(length(nil)) → mark(0) 204.25/66.89
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.89
active(length1(z0)) → mark(length(z0)) 204.25/66.89
active(from(z0)) → from(active(z0)) 204.25/66.89
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.89
active(s(z0)) → s(active(z0)) 204.25/66.89
from(mark(z0)) → mark(from(z0)) 204.25/66.89
from(ok(z0)) → ok(from(z0)) 204.25/66.89
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.89
s(mark(z0)) → mark(s(z0)) 204.25/66.89
s(ok(z0)) → ok(s(z0)) 204.25/66.89
proper(from(z0)) → from(proper(z0)) 204.25/66.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.89
proper(s(z0)) → s(proper(z0)) 204.25/66.89
proper(length(z0)) → length(proper(z0)) 204.25/66.89
proper(nil) → ok(nil) 204.25/66.89
proper(0) → ok(0) 204.25/66.89
proper(length1(z0)) → length1(proper(z0)) 204.25/66.89
length(ok(z0)) → ok(length(z0)) 204.25/66.89
length1(ok(z0)) → ok(length1(z0)) 204.25/66.89
top(mark(z0)) → top(proper(z0)) 204.25/66.89
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.89
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.89
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.89
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.89
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.89
S(mark(z0)) → c11(S(z0)) 204.25/66.89
S(ok(z0)) → c12(S(z0)) 204.25/66.89
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.89
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.89
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.89
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.89
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.89
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.89
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.89
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.89
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.89
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.89
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.89
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.89
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.89
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.89
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.89
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.89
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.89
PROPER(length(0)) → c16(LENGTH(ok(0))) 204.25/66.89
PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length1(nil)) → c19(LENGTH1(ok(nil)), PROPER(nil)) 204.25/66.89
PROPER(length1(0)) → c19(LENGTH1(ok(0)), PROPER(0)) 204.25/66.89
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.89
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.89
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.89
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.89
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.89
S(mark(z0)) → c11(S(z0)) 204.25/66.89
S(ok(z0)) → c12(S(z0)) 204.25/66.89
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.89
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.89
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.89
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.89
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.89
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.89
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.89
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.89
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.89
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.89
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.89
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.89
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.89
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.89
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.89
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.89
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.89
PROPER(length(0)) → c16(LENGTH(ok(0))) 204.25/66.89
PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length1(nil)) → c19(LENGTH1(ok(nil)), PROPER(nil)) 204.25/66.89
PROPER(length1(0)) → c19(LENGTH1(ok(0)), PROPER(0)) 204.25/66.89
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, LENGTH, LENGTH1, TOP, PROPER

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c20, c21, c22, c23, c, c1, c4, c4, c2, c5, c5, c17, c6, c6, c18, c13, c13, c14, c14, c15, c15, c16, c16, c19

204.25/66.89
204.25/66.89

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

Removed 2 trailing tuple parts
204.25/66.89
204.25/66.89

(44) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.89
active(length(nil)) → mark(0) 204.25/66.89
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.89
active(length1(z0)) → mark(length(z0)) 204.25/66.89
active(from(z0)) → from(active(z0)) 204.25/66.89
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.89
active(s(z0)) → s(active(z0)) 204.25/66.89
from(mark(z0)) → mark(from(z0)) 204.25/66.89
from(ok(z0)) → ok(from(z0)) 204.25/66.89
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.89
s(mark(z0)) → mark(s(z0)) 204.25/66.89
s(ok(z0)) → ok(s(z0)) 204.25/66.89
proper(from(z0)) → from(proper(z0)) 204.25/66.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.89
proper(s(z0)) → s(proper(z0)) 204.25/66.89
proper(length(z0)) → length(proper(z0)) 204.25/66.89
proper(nil) → ok(nil) 204.25/66.89
proper(0) → ok(0) 204.25/66.89
proper(length1(z0)) → length1(proper(z0)) 204.25/66.89
length(ok(z0)) → ok(length(z0)) 204.25/66.89
length1(ok(z0)) → ok(length1(z0)) 204.25/66.89
top(mark(z0)) → top(proper(z0)) 204.25/66.89
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.89
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.89
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.89
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.89
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.89
S(mark(z0)) → c11(S(z0)) 204.25/66.89
S(ok(z0)) → c12(S(z0)) 204.25/66.89
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.89
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.89
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.89
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.89
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.89
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.89
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.89
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.89
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.89
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.89
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.89
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.89
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.89
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.89
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.89
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.89
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.89
PROPER(length(0)) → c16(LENGTH(ok(0))) 204.25/66.89
PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length1(nil)) → c19(LENGTH1(ok(nil))) 204.25/66.89
PROPER(length1(0)) → c19(LENGTH1(ok(0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.89
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.89
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.89
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.89
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.89
S(mark(z0)) → c11(S(z0)) 204.25/66.89
S(ok(z0)) → c12(S(z0)) 204.25/66.89
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.89
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.89
TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) 204.25/66.89
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.89
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.89
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.89
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.89
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.89
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.89
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.89
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.89
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.89
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.89
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.89
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.89
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.89
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.89
PROPER(length(0)) → c16(LENGTH(ok(0))) 204.25/66.89
PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length1(nil)) → c19(LENGTH1(ok(nil))) 204.25/66.89
PROPER(length1(0)) → c19(LENGTH1(ok(0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, LENGTH, LENGTH1, TOP, PROPER

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c20, c21, c22, c23, c, c1, c4, c4, c2, c5, c5, c17, c6, c6, c18, c13, c13, c14, c14, c15, c15, c16, c16, c19, c19

204.25/66.89
204.25/66.89

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

Use narrowing to replace TOP(mark(z0)) → c22(TOP(proper(z0)), PROPER(z0)) by

TOP(mark(from(z0))) → c22(TOP(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
TOP(mark(cons(z0, z1))) → c22(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
TOP(mark(s(z0))) → c22(TOP(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
TOP(mark(length(z0))) → c22(TOP(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
TOP(mark(nil)) → c22(TOP(ok(nil)), PROPER(nil)) 204.25/66.89
TOP(mark(0)) → c22(TOP(ok(0)), PROPER(0)) 204.25/66.89
TOP(mark(length1(z0))) → c22(TOP(length1(proper(z0))), PROPER(length1(z0)))
204.25/66.89
204.25/66.89

(46) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.89
active(length(nil)) → mark(0) 204.25/66.89
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.89
active(length1(z0)) → mark(length(z0)) 204.25/66.89
active(from(z0)) → from(active(z0)) 204.25/66.89
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.89
active(s(z0)) → s(active(z0)) 204.25/66.89
from(mark(z0)) → mark(from(z0)) 204.25/66.89
from(ok(z0)) → ok(from(z0)) 204.25/66.89
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.89
s(mark(z0)) → mark(s(z0)) 204.25/66.89
s(ok(z0)) → ok(s(z0)) 204.25/66.89
proper(from(z0)) → from(proper(z0)) 204.25/66.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.89
proper(s(z0)) → s(proper(z0)) 204.25/66.89
proper(length(z0)) → length(proper(z0)) 204.25/66.89
proper(nil) → ok(nil) 204.25/66.89
proper(0) → ok(0) 204.25/66.89
proper(length1(z0)) → length1(proper(z0)) 204.25/66.89
length(ok(z0)) → ok(length(z0)) 204.25/66.89
length1(ok(z0)) → ok(length1(z0)) 204.25/66.89
top(mark(z0)) → top(proper(z0)) 204.25/66.89
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.89
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.89
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.89
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.89
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.89
S(mark(z0)) → c11(S(z0)) 204.25/66.89
S(ok(z0)) → c12(S(z0)) 204.25/66.89
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.89
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.89
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.89
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.89
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.89
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.89
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.89
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.89
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.89
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.89
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.89
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.89
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.89
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.89
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.89
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.89
PROPER(length(0)) → c16(LENGTH(ok(0))) 204.25/66.89
PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length1(nil)) → c19(LENGTH1(ok(nil))) 204.25/66.89
PROPER(length1(0)) → c19(LENGTH1(ok(0))) 204.25/66.89
TOP(mark(from(z0))) → c22(TOP(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
TOP(mark(cons(z0, z1))) → c22(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
TOP(mark(s(z0))) → c22(TOP(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
TOP(mark(length(z0))) → c22(TOP(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
TOP(mark(nil)) → c22(TOP(ok(nil)), PROPER(nil)) 204.25/66.89
TOP(mark(0)) → c22(TOP(ok(0)), PROPER(0)) 204.25/66.89
TOP(mark(length1(z0))) → c22(TOP(length1(proper(z0))), PROPER(length1(z0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.89
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.89
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.89
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.89
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.89
S(mark(z0)) → c11(S(z0)) 204.25/66.89
S(ok(z0)) → c12(S(z0)) 204.25/66.89
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.89
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.89
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.89
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.89
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.89
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.89
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.89
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.89
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.89
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.89
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.89
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.89
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.89
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.89
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.89
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.89
PROPER(length(0)) → c16(LENGTH(ok(0))) 204.25/66.89
PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length1(nil)) → c19(LENGTH1(ok(nil))) 204.25/66.89
PROPER(length1(0)) → c19(LENGTH1(ok(0))) 204.25/66.89
TOP(mark(from(z0))) → c22(TOP(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
TOP(mark(cons(z0, z1))) → c22(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
TOP(mark(s(z0))) → c22(TOP(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
TOP(mark(length(z0))) → c22(TOP(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
TOP(mark(nil)) → c22(TOP(ok(nil)), PROPER(nil)) 204.25/66.89
TOP(mark(0)) → c22(TOP(ok(0)), PROPER(0)) 204.25/66.89
TOP(mark(length1(z0))) → c22(TOP(length1(proper(z0))), PROPER(length1(z0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, LENGTH, LENGTH1, TOP, PROPER

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c20, c21, c23, c, c1, c4, c4, c2, c5, c5, c17, c6, c6, c18, c13, c13, c14, c14, c15, c15, c16, c16, c19, c19, c22

204.25/66.89
204.25/66.89

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

Removed 2 trailing tuple parts
204.25/66.89
204.25/66.89

(48) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.89
active(length(nil)) → mark(0) 204.25/66.89
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.89
active(length1(z0)) → mark(length(z0)) 204.25/66.89
active(from(z0)) → from(active(z0)) 204.25/66.89
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.89
active(s(z0)) → s(active(z0)) 204.25/66.89
from(mark(z0)) → mark(from(z0)) 204.25/66.89
from(ok(z0)) → ok(from(z0)) 204.25/66.89
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.89
s(mark(z0)) → mark(s(z0)) 204.25/66.89
s(ok(z0)) → ok(s(z0)) 204.25/66.89
proper(from(z0)) → from(proper(z0)) 204.25/66.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.89
proper(s(z0)) → s(proper(z0)) 204.25/66.89
proper(length(z0)) → length(proper(z0)) 204.25/66.89
proper(nil) → ok(nil) 204.25/66.89
proper(0) → ok(0) 204.25/66.89
proper(length1(z0)) → length1(proper(z0)) 204.25/66.89
length(ok(z0)) → ok(length(z0)) 204.25/66.89
length1(ok(z0)) → ok(length1(z0)) 204.25/66.89
top(mark(z0)) → top(proper(z0)) 204.25/66.89
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.89
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.89
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.89
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.89
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.89
S(mark(z0)) → c11(S(z0)) 204.25/66.89
S(ok(z0)) → c12(S(z0)) 204.25/66.89
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.89
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.89
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.89
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.89
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.89
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.89
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.89
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.89
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.89
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.89
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.89
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.89
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.89
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.89
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.89
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.89
PROPER(length(0)) → c16(LENGTH(ok(0))) 204.25/66.89
PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length1(nil)) → c19(LENGTH1(ok(nil))) 204.25/66.89
PROPER(length1(0)) → c19(LENGTH1(ok(0))) 204.25/66.89
TOP(mark(from(z0))) → c22(TOP(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
TOP(mark(cons(z0, z1))) → c22(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
TOP(mark(s(z0))) → c22(TOP(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
TOP(mark(length(z0))) → c22(TOP(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
TOP(mark(length1(z0))) → c22(TOP(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
TOP(mark(nil)) → c22(TOP(ok(nil))) 204.25/66.89
TOP(mark(0)) → c22(TOP(ok(0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.89
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.89
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.89
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.89
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.89
S(mark(z0)) → c11(S(z0)) 204.25/66.89
S(ok(z0)) → c12(S(z0)) 204.25/66.89
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.89
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.89
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.89
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.89
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.89
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.89
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.89
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.89
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.89
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.89
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.89
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.89
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.89
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.89
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.89
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.89
PROPER(length(0)) → c16(LENGTH(ok(0))) 204.25/66.89
PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length1(nil)) → c19(LENGTH1(ok(nil))) 204.25/66.89
PROPER(length1(0)) → c19(LENGTH1(ok(0))) 204.25/66.89
TOP(mark(from(z0))) → c22(TOP(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
TOP(mark(cons(z0, z1))) → c22(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
TOP(mark(s(z0))) → c22(TOP(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
TOP(mark(length(z0))) → c22(TOP(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
TOP(mark(length1(z0))) → c22(TOP(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
TOP(mark(nil)) → c22(TOP(ok(nil))) 204.25/66.89
TOP(mark(0)) → c22(TOP(ok(0)))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, LENGTH, LENGTH1, TOP, PROPER

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c20, c21, c23, c, c1, c4, c4, c2, c5, c5, c17, c6, c6, c18, c13, c13, c14, c14, c15, c15, c16, c16, c19, c19, c22, c22

204.25/66.89
204.25/66.89

(49) 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(nil)) → c22(TOP(ok(nil)))
We considered the (Usable) Rules:

proper(from(z0)) → from(proper(z0)) 204.25/66.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.89
proper(s(z0)) → s(proper(z0)) 204.25/66.89
proper(length(z0)) → length(proper(z0)) 204.25/66.89
proper(nil) → ok(nil) 204.25/66.89
proper(0) → ok(0) 204.25/66.89
proper(length1(z0)) → length1(proper(z0)) 204.25/66.89
length1(ok(z0)) → ok(length1(z0)) 204.25/66.89
length(ok(z0)) → ok(length(z0)) 204.25/66.89
s(mark(z0)) → mark(s(z0)) 204.25/66.89
s(ok(z0)) → ok(s(z0)) 204.25/66.89
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.89
from(mark(z0)) → mark(from(z0)) 204.25/66.89
from(ok(z0)) → ok(from(z0)) 204.25/66.89
active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.89
active(length(nil)) → mark(0) 204.25/66.89
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.89
active(length1(z0)) → mark(length(z0)) 204.25/66.89
active(from(z0)) → from(active(z0)) 204.25/66.89
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.89
active(s(z0)) → s(active(z0))
And the Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.89
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.89
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.89
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.89
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.89
S(mark(z0)) → c11(S(z0)) 204.25/66.89
S(ok(z0)) → c12(S(z0)) 204.25/66.89
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.89
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.89
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.89
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.89
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.89
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.89
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.89
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.89
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.89
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.89
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.89
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.89
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.89
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.89
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.89
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.89
PROPER(length(0)) → c16(LENGTH(ok(0))) 204.25/66.89
PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length1(nil)) → c19(LENGTH1(ok(nil))) 204.25/66.89
PROPER(length1(0)) → c19(LENGTH1(ok(0))) 204.25/66.89
TOP(mark(from(z0))) → c22(TOP(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
TOP(mark(cons(z0, z1))) → c22(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
TOP(mark(s(z0))) → c22(TOP(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
TOP(mark(length(z0))) → c22(TOP(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
TOP(mark(length1(z0))) → c22(TOP(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
TOP(mark(nil)) → c22(TOP(ok(nil))) 204.25/66.89
TOP(mark(0)) → c22(TOP(ok(0)))
The order we found is given by the following interpretation:
Polynomial interpretation : 204.25/66.89

POL(0) = 0    204.25/66.89
POL(ACTIVE(x1)) = 0    204.25/66.89
POL(CONS(x1, x2)) = 0    204.25/66.89
POL(FROM(x1)) = 0    204.25/66.89
POL(LENGTH(x1)) = 0    204.25/66.89
POL(LENGTH1(x1)) = 0    204.25/66.89
POL(PROPER(x1)) = 0    204.25/66.89
POL(S(x1)) = 0    204.25/66.89
POL(TOP(x1)) = x1    204.25/66.89
POL(active(x1)) = 0    204.25/66.89
POL(c(x1)) = x1    204.25/66.89
POL(c1(x1)) = x1    204.25/66.89
POL(c10(x1)) = x1    204.25/66.89
POL(c11(x1)) = x1    204.25/66.89
POL(c12(x1)) = x1    204.25/66.89
POL(c13(x1)) = x1    204.25/66.89
POL(c13(x1, x2)) = x1 + x2    204.25/66.89
POL(c14(x1, x2)) = x1 + x2    204.25/66.89
POL(c14(x1, x2, x3)) = x1 + x2 + x3    204.25/66.89
POL(c15(x1)) = x1    204.25/66.89
POL(c15(x1, x2)) = x1 + x2    204.25/66.89
POL(c16(x1)) = x1    204.25/66.89
POL(c16(x1, x2)) = x1 + x2    204.25/66.89
POL(c17(x1)) = x1    204.25/66.89
POL(c18(x1)) = x1    204.25/66.89
POL(c19(x1)) = x1    204.25/66.89
POL(c19(x1, x2)) = x1 + x2    204.25/66.89
POL(c2(x1)) = x1    204.25/66.89
POL(c20(x1)) = x1    204.25/66.89
POL(c21(x1)) = x1    204.25/66.89
POL(c22(x1)) = x1    204.25/66.89
POL(c22(x1, x2)) = x1 + x2    204.25/66.89
POL(c23(x1, x2)) = x1 + x2    204.25/66.89
POL(c3(x1)) = x1    204.25/66.89
POL(c4(x1)) = x1    204.25/66.89
POL(c4(x1, x2)) = x1 + x2    204.25/66.89
POL(c5(x1)) = x1    204.25/66.89
POL(c5(x1, x2)) = x1 + x2    204.25/66.89
POL(c6(x1)) = x1    204.25/66.89
POL(c6(x1, x2)) = x1 + x2    204.25/66.89
POL(c7(x1)) = x1    204.25/66.89
POL(c8(x1)) = x1    204.25/66.89
POL(c9(x1)) = x1    204.25/66.89
POL(cons(x1, x2)) = 0    204.25/66.89
POL(from(x1)) = 0    204.25/66.89
POL(length(x1)) = 0    204.25/66.89
POL(length1(x1)) = 0    204.25/66.89
POL(mark(x1)) = x1    204.25/66.89
POL(nil) = [1]    204.25/66.89
POL(ok(x1)) = 0    204.25/66.89
POL(proper(x1)) = 0    204.25/66.89
POL(s(x1)) = 0   
204.25/66.89
204.25/66.89

(50) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.89
active(length(nil)) → mark(0) 204.25/66.89
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.89
active(length1(z0)) → mark(length(z0)) 204.25/66.89
active(from(z0)) → from(active(z0)) 204.25/66.89
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.89
active(s(z0)) → s(active(z0)) 204.25/66.89
from(mark(z0)) → mark(from(z0)) 204.25/66.89
from(ok(z0)) → ok(from(z0)) 204.25/66.89
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.89
s(mark(z0)) → mark(s(z0)) 204.25/66.89
s(ok(z0)) → ok(s(z0)) 204.25/66.89
proper(from(z0)) → from(proper(z0)) 204.25/66.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.89
proper(s(z0)) → s(proper(z0)) 204.25/66.89
proper(length(z0)) → length(proper(z0)) 204.25/66.89
proper(nil) → ok(nil) 204.25/66.89
proper(0) → ok(0) 204.25/66.89
proper(length1(z0)) → length1(proper(z0)) 204.25/66.89
length(ok(z0)) → ok(length(z0)) 204.25/66.89
length1(ok(z0)) → ok(length1(z0)) 204.25/66.89
top(mark(z0)) → top(proper(z0)) 204.25/66.89
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.89
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.89
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.89
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.89
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.89
S(mark(z0)) → c11(S(z0)) 204.25/66.89
S(ok(z0)) → c12(S(z0)) 204.25/66.89
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.89
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.89
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.89
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.89
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.89
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.89
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.89
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.89
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.89
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.89
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.89
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.89
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.89
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.89
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.89
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.89
PROPER(length(0)) → c16(LENGTH(ok(0))) 204.25/66.89
PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length1(nil)) → c19(LENGTH1(ok(nil))) 204.25/66.89
PROPER(length1(0)) → c19(LENGTH1(ok(0))) 204.25/66.89
TOP(mark(from(z0))) → c22(TOP(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
TOP(mark(cons(z0, z1))) → c22(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
TOP(mark(s(z0))) → c22(TOP(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
TOP(mark(length(z0))) → c22(TOP(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
TOP(mark(length1(z0))) → c22(TOP(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
TOP(mark(nil)) → c22(TOP(ok(nil))) 204.25/66.89
TOP(mark(0)) → c22(TOP(ok(0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.89
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.89
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.89
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.89
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.89
S(mark(z0)) → c11(S(z0)) 204.25/66.89
S(ok(z0)) → c12(S(z0)) 204.25/66.89
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.89
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.89
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.89
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.89
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.89
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.89
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.89
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.89
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.89
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.89
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.89
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.89
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.89
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.89
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.89
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.89
PROPER(length(0)) → c16(LENGTH(ok(0))) 204.25/66.89
PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length1(nil)) → c19(LENGTH1(ok(nil))) 204.25/66.89
PROPER(length1(0)) → c19(LENGTH1(ok(0))) 204.25/66.89
TOP(mark(from(z0))) → c22(TOP(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
TOP(mark(cons(z0, z1))) → c22(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
TOP(mark(s(z0))) → c22(TOP(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
TOP(mark(length(z0))) → c22(TOP(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
TOP(mark(length1(z0))) → c22(TOP(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
TOP(mark(0)) → c22(TOP(ok(0)))
K tuples:

TOP(mark(nil)) → c22(TOP(ok(nil)))
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, LENGTH, LENGTH1, TOP, PROPER

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c20, c21, c23, c, c1, c4, c4, c2, c5, c5, c17, c6, c6, c18, c13, c13, c14, c14, c15, c15, c16, c16, c19, c19, c22, c22

204.25/66.89
204.25/66.89

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

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

TOP(mark(0)) → c22(TOP(ok(0)))
We considered the (Usable) Rules:

proper(from(z0)) → from(proper(z0)) 204.25/66.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.89
proper(s(z0)) → s(proper(z0)) 204.25/66.89
proper(length(z0)) → length(proper(z0)) 204.25/66.89
proper(nil) → ok(nil) 204.25/66.89
proper(0) → ok(0) 204.25/66.89
proper(length1(z0)) → length1(proper(z0)) 204.25/66.89
length1(ok(z0)) → ok(length1(z0)) 204.25/66.89
length(ok(z0)) → ok(length(z0)) 204.25/66.89
s(mark(z0)) → mark(s(z0)) 204.25/66.89
s(ok(z0)) → ok(s(z0)) 204.25/66.89
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.89
from(mark(z0)) → mark(from(z0)) 204.25/66.89
from(ok(z0)) → ok(from(z0)) 204.25/66.89
active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.89
active(length(nil)) → mark(0) 204.25/66.89
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.89
active(length1(z0)) → mark(length(z0)) 204.25/66.89
active(from(z0)) → from(active(z0)) 204.25/66.89
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.89
active(s(z0)) → s(active(z0))
And the Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.89
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.89
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.89
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.89
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.89
S(mark(z0)) → c11(S(z0)) 204.25/66.89
S(ok(z0)) → c12(S(z0)) 204.25/66.89
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.89
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.89
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.89
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.89
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.89
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.89
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.89
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.89
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.89
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.89
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.89
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.89
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.89
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.89
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.89
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.89
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.89
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.89
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.89
PROPER(length(0)) → c16(LENGTH(ok(0))) 204.25/66.89
PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
PROPER(length1(nil)) → c19(LENGTH1(ok(nil))) 204.25/66.89
PROPER(length1(0)) → c19(LENGTH1(ok(0))) 204.25/66.89
TOP(mark(from(z0))) → c22(TOP(from(proper(z0))), PROPER(from(z0))) 204.25/66.89
TOP(mark(cons(z0, z1))) → c22(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.89
TOP(mark(s(z0))) → c22(TOP(s(proper(z0))), PROPER(s(z0))) 204.25/66.89
TOP(mark(length(z0))) → c22(TOP(length(proper(z0))), PROPER(length(z0))) 204.25/66.89
TOP(mark(length1(z0))) → c22(TOP(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.89
TOP(mark(nil)) → c22(TOP(ok(nil))) 204.25/66.89
TOP(mark(0)) → c22(TOP(ok(0)))
The order we found is given by the following interpretation:
Polynomial interpretation : 204.25/66.89

POL(0) = [1]    204.25/66.89
POL(ACTIVE(x1)) = 0    204.25/66.89
POL(CONS(x1, x2)) = 0    204.25/66.89
POL(FROM(x1)) = 0    204.25/66.89
POL(LENGTH(x1)) = 0    204.25/66.89
POL(LENGTH1(x1)) = 0    204.25/66.89
POL(PROPER(x1)) = 0    204.25/66.89
POL(S(x1)) = 0    204.25/66.89
POL(TOP(x1)) = x1    204.25/66.89
POL(active(x1)) = x1    204.25/66.89
POL(c(x1)) = x1    204.25/66.89
POL(c1(x1)) = x1    204.25/66.89
POL(c10(x1)) = x1    204.25/66.89
POL(c11(x1)) = x1    204.25/66.89
POL(c12(x1)) = x1    204.25/66.89
POL(c13(x1)) = x1    204.25/66.89
POL(c13(x1, x2)) = x1 + x2    204.25/66.89
POL(c14(x1, x2)) = x1 + x2    204.25/66.89
POL(c14(x1, x2, x3)) = x1 + x2 + x3    204.25/66.89
POL(c15(x1)) = x1    204.25/66.89
POL(c15(x1, x2)) = x1 + x2    204.25/66.89
POL(c16(x1)) = x1    204.25/66.89
POL(c16(x1, x2)) = x1 + x2    204.25/66.89
POL(c17(x1)) = x1    204.25/66.89
POL(c18(x1)) = x1    204.25/66.89
POL(c19(x1)) = x1    204.25/66.89
POL(c19(x1, x2)) = x1 + x2    204.25/66.89
POL(c2(x1)) = x1    204.25/66.89
POL(c20(x1)) = x1    204.25/66.89
POL(c21(x1)) = x1    204.25/66.89
POL(c22(x1)) = x1    204.25/66.89
POL(c22(x1, x2)) = x1 + x2    204.25/66.89
POL(c23(x1, x2)) = x1 + x2    204.25/66.89
POL(c3(x1)) = x1    204.25/66.89
POL(c4(x1)) = x1    204.25/66.89
POL(c4(x1, x2)) = x1 + x2    204.25/66.89
POL(c5(x1)) = x1    204.25/66.89
POL(c5(x1, x2)) = x1 + x2    204.25/66.89
POL(c6(x1)) = x1    204.25/66.89
POL(c6(x1, x2)) = x1 + x2    204.25/66.89
POL(c7(x1)) = x1    204.25/66.89
POL(c8(x1)) = x1    204.25/66.89
POL(c9(x1)) = x1    204.25/66.89
POL(cons(x1, x2)) = [2]    204.25/66.89
POL(from(x1)) = [2]    204.25/66.89
POL(length(x1)) = [2]    204.25/66.89
POL(length1(x1)) = [2]    204.25/66.89
POL(mark(x1)) = [2]    204.25/66.89
POL(nil) = 0    204.25/66.89
POL(ok(x1)) = x1    204.25/66.89
POL(proper(x1)) = 0    204.25/66.89
POL(s(x1)) = [2]   
204.25/66.89
204.25/66.89

(52) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.89
active(length(nil)) → mark(0) 204.25/66.89
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.89
active(length1(z0)) → mark(length(z0)) 204.25/66.89
active(from(z0)) → from(active(z0)) 204.25/66.89
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.89
active(s(z0)) → s(active(z0)) 204.25/66.89
from(mark(z0)) → mark(from(z0)) 204.25/66.89
from(ok(z0)) → ok(from(z0)) 204.25/66.89
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.89
s(mark(z0)) → mark(s(z0)) 204.25/66.89
s(ok(z0)) → ok(s(z0)) 204.25/66.89
proper(from(z0)) → from(proper(z0)) 204.25/66.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.89
proper(s(z0)) → s(proper(z0)) 204.25/66.89
proper(length(z0)) → length(proper(z0)) 204.25/66.89
proper(nil) → ok(nil) 204.25/66.89
proper(0) → ok(0) 204.25/66.89
proper(length1(z0)) → length1(proper(z0)) 204.25/66.89
length(ok(z0)) → ok(length(z0)) 204.25/66.89
length1(ok(z0)) → ok(length1(z0)) 204.25/66.89
top(mark(z0)) → top(proper(z0)) 204.25/66.89
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.89
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.89
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.89
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.89
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.89
S(mark(z0)) → c11(S(z0)) 204.25/66.89
S(ok(z0)) → c12(S(z0)) 204.25/66.89
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.89
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.89
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.89
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.89
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.89
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.89
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.89
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.89
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.89
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.89
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.89
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.90
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.90
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.90
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.90
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.90
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.90
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.90
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.90
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.90
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.90
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.90
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.90
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.90
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.90
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.90
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.90
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.90
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.90
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.90
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.90
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.90
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.90
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.90
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.90
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.90
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.90
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.90
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.90
PROPER(length(0)) → c16(LENGTH(ok(0))) 204.25/66.90
PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.90
PROPER(length1(nil)) → c19(LENGTH1(ok(nil))) 204.25/66.90
PROPER(length1(0)) → c19(LENGTH1(ok(0))) 204.25/66.90
TOP(mark(from(z0))) → c22(TOP(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
TOP(mark(cons(z0, z1))) → c22(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
TOP(mark(s(z0))) → c22(TOP(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
TOP(mark(length(z0))) → c22(TOP(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
TOP(mark(length1(z0))) → c22(TOP(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.90
TOP(mark(nil)) → c22(TOP(ok(nil))) 204.25/66.90
TOP(mark(0)) → c22(TOP(ok(0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.90
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.90
S(mark(z0)) → c11(S(z0)) 204.25/66.90
S(ok(z0)) → c12(S(z0)) 204.25/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.90
TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) 204.25/66.90
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.90
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.90
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.90
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.90
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.90
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.90
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.90
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.90
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.90
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.90
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.90
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.90
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.90
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.90
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.90
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.90
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.90
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.90
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.90
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.90
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.90
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.90
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.90
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.90
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.90
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.90
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.90
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.90
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.90
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.90
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.90
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.90
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.90
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.90
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.90
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.90
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.90
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.90
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.90
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.90
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.90
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.90
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.90
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.90
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.90
PROPER(length(0)) → c16(LENGTH(ok(0))) 204.25/66.90
PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.90
PROPER(length1(nil)) → c19(LENGTH1(ok(nil))) 204.25/66.90
PROPER(length1(0)) → c19(LENGTH1(ok(0))) 204.25/66.90
TOP(mark(from(z0))) → c22(TOP(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
TOP(mark(cons(z0, z1))) → c22(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
TOP(mark(s(z0))) → c22(TOP(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
TOP(mark(length(z0))) → c22(TOP(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
TOP(mark(length1(z0))) → c22(TOP(length1(proper(z0))), PROPER(length1(z0)))
K tuples:

TOP(mark(nil)) → c22(TOP(ok(nil))) 204.25/66.90
TOP(mark(0)) → c22(TOP(ok(0)))
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, LENGTH, LENGTH1, TOP, PROPER

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c20, c21, c23, c, c1, c4, c4, c2, c5, c5, c17, c6, c6, c18, c13, c13, c14, c14, c15, c15, c16, c16, c19, c19, c22, c22

204.25/66.90
204.25/66.90

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

Use narrowing to replace TOP(ok(z0)) → c23(TOP(active(z0)), ACTIVE(z0)) by

TOP(ok(from(z0))) → c23(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.90
TOP(ok(length(nil))) → c23(TOP(mark(0)), ACTIVE(length(nil))) 204.25/66.90
TOP(ok(length(cons(z0, z1)))) → c23(TOP(mark(s(length1(z1)))), ACTIVE(length(cons(z0, z1)))) 204.25/66.90
TOP(ok(length1(z0))) → c23(TOP(mark(length(z0))), ACTIVE(length1(z0))) 204.25/66.90
TOP(ok(from(z0))) → c23(TOP(from(active(z0))), ACTIVE(from(z0))) 204.25/66.90
TOP(ok(cons(z0, z1))) → c23(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.90
TOP(ok(s(z0))) → c23(TOP(s(active(z0))), ACTIVE(s(z0)))
204.25/66.90
204.25/66.90

(54) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.25/66.90
active(length(nil)) → mark(0) 204.25/66.90
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.25/66.90
active(length1(z0)) → mark(length(z0)) 204.25/66.90
active(from(z0)) → from(active(z0)) 204.25/66.90
active(cons(z0, z1)) → cons(active(z0), z1) 204.25/66.90
active(s(z0)) → s(active(z0)) 204.25/66.90
from(mark(z0)) → mark(from(z0)) 204.25/66.90
from(ok(z0)) → ok(from(z0)) 204.25/66.90
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.25/66.90
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.25/66.90
s(mark(z0)) → mark(s(z0)) 204.25/66.90
s(ok(z0)) → ok(s(z0)) 204.25/66.90
proper(from(z0)) → from(proper(z0)) 204.25/66.90
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.25/66.90
proper(s(z0)) → s(proper(z0)) 204.25/66.90
proper(length(z0)) → length(proper(z0)) 204.25/66.90
proper(nil) → ok(nil) 204.25/66.90
proper(0) → ok(0) 204.25/66.90
proper(length1(z0)) → length1(proper(z0)) 204.25/66.90
length(ok(z0)) → ok(length(z0)) 204.25/66.90
length1(ok(z0)) → ok(length1(z0)) 204.25/66.90
top(mark(z0)) → top(proper(z0)) 204.25/66.90
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.90
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.90
S(mark(z0)) → c11(S(z0)) 204.25/66.90
S(ok(z0)) → c12(S(z0)) 204.25/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.90
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.90
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.90
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.90
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.90
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.90
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.90
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.90
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.90
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.90
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.90
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.90
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.90
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.90
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.90
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.90
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.90
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.90
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.90
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.90
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.90
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.90
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.90
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.90
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.90
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.90
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.90
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.90
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.90
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.90
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.90
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.90
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.90
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.90
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.90
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.90
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.90
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.90
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.90
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.90
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.90
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.90
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.90
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.90
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.90
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.90
PROPER(length(0)) → c16(LENGTH(ok(0))) 204.25/66.90
PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.90
PROPER(length1(nil)) → c19(LENGTH1(ok(nil))) 204.25/66.90
PROPER(length1(0)) → c19(LENGTH1(ok(0))) 204.25/66.90
TOP(mark(from(z0))) → c22(TOP(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
TOP(mark(cons(z0, z1))) → c22(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
TOP(mark(s(z0))) → c22(TOP(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
TOP(mark(length(z0))) → c22(TOP(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
TOP(mark(length1(z0))) → c22(TOP(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.90
TOP(mark(nil)) → c22(TOP(ok(nil))) 204.25/66.90
TOP(mark(0)) → c22(TOP(ok(0))) 204.25/66.90
TOP(ok(from(z0))) → c23(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.90
TOP(ok(length(nil))) → c23(TOP(mark(0)), ACTIVE(length(nil))) 204.25/66.90
TOP(ok(length(cons(z0, z1)))) → c23(TOP(mark(s(length1(z1)))), ACTIVE(length(cons(z0, z1)))) 204.25/66.90
TOP(ok(length1(z0))) → c23(TOP(mark(length(z0))), ACTIVE(length1(z0))) 204.25/66.90
TOP(ok(from(z0))) → c23(TOP(from(active(z0))), ACTIVE(from(z0))) 204.25/66.90
TOP(ok(cons(z0, z1))) → c23(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.90
TOP(ok(s(z0))) → c23(TOP(s(active(z0))), ACTIVE(s(z0)))
S tuples:

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.25/66.90
FROM(mark(z0)) → c7(FROM(z0)) 204.25/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.25/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.25/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.25/66.90
S(mark(z0)) → c11(S(z0)) 204.25/66.90
S(ok(z0)) → c12(S(z0)) 204.25/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.25/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.25/66.90
ACTIVE(from(z0)) → c(S(z0)) 204.25/66.90
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.25/66.90
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.25/66.90
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.90
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.25/66.90
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.25/66.90
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.25/66.90
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.25/66.90
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.25/66.90
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.25/66.90
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.25/66.90
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.25/66.90
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.25/66.90
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.25/66.90
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.25/66.90
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.25/66.90
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.25/66.90
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.25/66.90
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.25/66.90
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.25/66.90
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.25/66.90
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.25/66.90
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.25/66.90
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.25/66.90
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.25/66.90
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.90
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.25/66.90
PROPER(from(0)) → c13(FROM(ok(0))) 204.25/66.90
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.25/66.90
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.25/66.90
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.25/66.90
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.25/66.90
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.25/66.90
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.25/66.90
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.25/66.90
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.25/66.90
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.25/66.90
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.25/66.90
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.25/66.90
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.25/66.90
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.25/66.90
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.90
PROPER(s(nil)) → c15(S(ok(nil))) 204.25/66.90
PROPER(s(0)) → c15(S(ok(0))) 204.25/66.90
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.25/66.90
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.25/66.90
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.25/66.90
PROPER(length(0)) → c16(LENGTH(ok(0))) 204.25/66.90
PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.25/66.90
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.25/66.90
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.25/66.90
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.60/66.90
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0))) 204.60/66.90
PROPER(length1(nil)) → c19(LENGTH1(ok(nil))) 204.60/66.90
PROPER(length1(0)) → c19(LENGTH1(ok(0))) 204.60/66.90
TOP(mark(from(z0))) → c22(TOP(from(proper(z0))), PROPER(from(z0))) 204.60/66.90
TOP(mark(cons(z0, z1))) → c22(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.60/66.90
TOP(mark(s(z0))) → c22(TOP(s(proper(z0))), PROPER(s(z0))) 204.60/66.90
TOP(mark(length(z0))) → c22(TOP(length(proper(z0))), PROPER(length(z0))) 204.60/66.90
TOP(mark(length1(z0))) → c22(TOP(length1(proper(z0))), PROPER(length1(z0))) 204.60/66.90
TOP(ok(from(z0))) → c23(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.60/66.90
TOP(ok(length(nil))) → c23(TOP(mark(0)), ACTIVE(length(nil))) 204.60/66.90
TOP(ok(length(cons(z0, z1)))) → c23(TOP(mark(s(length1(z1)))), ACTIVE(length(cons(z0, z1)))) 204.60/66.90
TOP(ok(length1(z0))) → c23(TOP(mark(length(z0))), ACTIVE(length1(z0))) 204.60/66.90
TOP(ok(from(z0))) → c23(TOP(from(active(z0))), ACTIVE(from(z0))) 204.60/66.90
TOP(ok(cons(z0, z1))) → c23(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.60/66.90
TOP(ok(s(z0))) → c23(TOP(s(active(z0))), ACTIVE(s(z0)))
K tuples:

TOP(mark(nil)) → c22(TOP(ok(nil))) 204.60/66.90
TOP(mark(0)) → c22(TOP(ok(0)))
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

ACTIVE, FROM, CONS, S, LENGTH, LENGTH1, PROPER, TOP

Compound Symbols:

c3, c7, c8, c9, c10, c11, c12, c20, c21, c, c1, c4, c4, c2, c5, c5, c17, c6, c6, c18, c13, c13, c14, c14, c15, c15, c16, c16, c19, c19, c22, c22, c23

204.60/66.90
204.60/66.90

(55) CdtUnreachableProof (EQUIVALENT transformation)

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

ACTIVE(length1(z0)) → c3(LENGTH(z0)) 204.60/66.90
ACTIVE(from(z0)) → c(S(z0)) 204.60/66.90
ACTIVE(length(cons(z0, z1))) → c1(S(length1(z1))) 204.60/66.90
ACTIVE(length(cons(z0, z1))) → c1(LENGTH1(z1)) 204.60/66.90
ACTIVE(from(from(z0))) → c4(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.60/66.90
ACTIVE(from(from(z0))) → c4(FROM(from(active(z0))), ACTIVE(from(z0))) 204.60/66.90
ACTIVE(from(cons(z0, z1))) → c4(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.60/66.90
ACTIVE(from(s(z0))) → c4(FROM(s(active(z0))), ACTIVE(s(z0))) 204.60/66.90
ACTIVE(from(length(nil))) → c4(FROM(mark(0))) 204.60/66.90
ACTIVE(from(length(cons(z0, z1)))) → c2(FROM(mark(s(length1(z1))))) 204.60/66.90
ACTIVE(from(length(cons(z0, z1)))) → c2(ACTIVE(length(cons(z0, z1)))) 204.60/66.90
ACTIVE(from(length1(z0))) → c2(FROM(mark(length(z0)))) 204.60/66.90
ACTIVE(from(length1(z0))) → c2(ACTIVE(length1(z0))) 204.60/66.90
ACTIVE(cons(from(z0), x1)) → c5(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0))) 204.60/66.90
ACTIVE(cons(from(z0), x1)) → c5(CONS(from(active(z0)), x1), ACTIVE(from(z0))) 204.60/66.90
ACTIVE(cons(cons(z0, z1), x1)) → c5(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 204.60/66.90
ACTIVE(cons(s(z0), x1)) → c5(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 204.60/66.90
ACTIVE(cons(length(nil), x1)) → c5(CONS(mark(0), x1)) 204.60/66.90
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(CONS(mark(s(length1(z1))), x1)) 204.60/66.90
ACTIVE(cons(length(cons(z0, z1)), x1)) → c17(ACTIVE(length(cons(z0, z1)))) 204.60/66.90
ACTIVE(cons(length1(z0), x1)) → c17(CONS(mark(length(z0)), x1)) 204.60/66.90
ACTIVE(cons(length1(z0), x1)) → c17(ACTIVE(length1(z0))) 204.60/66.90
ACTIVE(s(from(z0))) → c6(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.60/66.90
ACTIVE(s(from(z0))) → c6(S(from(active(z0))), ACTIVE(from(z0))) 204.60/66.90
ACTIVE(s(cons(z0, z1))) → c6(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.60/66.90
ACTIVE(s(s(z0))) → c6(S(s(active(z0))), ACTIVE(s(z0))) 204.60/66.90
ACTIVE(s(length(nil))) → c6(S(mark(0))) 204.60/66.90
ACTIVE(s(length(cons(z0, z1)))) → c18(S(mark(s(length1(z1))))) 204.60/66.90
ACTIVE(s(length(cons(z0, z1)))) → c18(ACTIVE(length(cons(z0, z1)))) 204.60/66.90
ACTIVE(s(length1(z0))) → c18(S(mark(length(z0)))) 204.60/66.90
ACTIVE(s(length1(z0))) → c18(ACTIVE(length1(z0))) 204.60/66.90
PROPER(from(from(z0))) → c13(FROM(from(proper(z0))), PROPER(from(z0))) 204.60/66.90
PROPER(from(cons(z0, z1))) → c13(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.60/66.90
PROPER(from(s(z0))) → c13(FROM(s(proper(z0))), PROPER(s(z0))) 204.60/66.90
PROPER(from(length(z0))) → c13(FROM(length(proper(z0))), PROPER(length(z0))) 204.60/66.90
PROPER(from(length1(z0))) → c13(FROM(length1(proper(z0))), PROPER(length1(z0))) 204.60/66.90
PROPER(from(nil)) → c13(FROM(ok(nil))) 204.60/66.90
PROPER(from(0)) → c13(FROM(ok(0))) 204.60/66.90
PROPER(cons(x0, from(z0))) → c14(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0))) 204.60/66.90
PROPER(cons(x0, cons(z0, z1))) → c14(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 204.60/66.90
PROPER(cons(x0, s(z0))) → c14(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 204.60/66.90
PROPER(cons(x0, length(z0))) → c14(CONS(proper(x0), length(proper(z0))), PROPER(x0), PROPER(length(z0))) 204.60/66.90
PROPER(cons(x0, length1(z0))) → c14(CONS(proper(x0), length1(proper(z0))), PROPER(x0), PROPER(length1(z0))) 204.60/66.90
PROPER(cons(from(z0), x1)) → c14(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1)) 204.60/66.90
PROPER(cons(cons(z0, z1), x1)) → c14(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 204.60/66.90
PROPER(cons(s(z0), x1)) → c14(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 204.60/66.90
PROPER(cons(length(z0), x1)) → c14(CONS(length(proper(z0)), proper(x1)), PROPER(length(z0)), PROPER(x1)) 204.60/66.90
PROPER(cons(length1(z0), x1)) → c14(CONS(length1(proper(z0)), proper(x1)), PROPER(length1(z0)), PROPER(x1)) 204.60/66.90
PROPER(cons(x0, nil)) → c14(CONS(proper(x0), ok(nil)), PROPER(x0)) 204.60/66.90
PROPER(cons(x0, 0)) → c14(CONS(proper(x0), ok(0)), PROPER(x0)) 204.60/66.90
PROPER(cons(nil, x1)) → c14(CONS(ok(nil), proper(x1)), PROPER(x1)) 204.60/66.90
PROPER(cons(0, x1)) → c14(CONS(ok(0), proper(x1)), PROPER(x1)) 204.60/66.90
PROPER(s(from(z0))) → c15(S(from(proper(z0))), PROPER(from(z0))) 204.60/66.90
PROPER(s(cons(z0, z1))) → c15(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.60/66.90
PROPER(s(s(z0))) → c15(S(s(proper(z0))), PROPER(s(z0))) 204.60/66.90
PROPER(s(length(z0))) → c15(S(length(proper(z0))), PROPER(length(z0))) 204.60/66.90
PROPER(s(length1(z0))) → c15(S(length1(proper(z0))), PROPER(length1(z0))) 204.60/66.90
PROPER(s(nil)) → c15(S(ok(nil))) 204.60/66.90
PROPER(s(0)) → c15(S(ok(0))) 204.60/66.90
PROPER(length(from(z0))) → c16(LENGTH(from(proper(z0))), PROPER(from(z0))) 204.60/66.90
PROPER(length(cons(z0, z1))) → c16(LENGTH(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.60/66.90
PROPER(length(s(z0))) → c16(LENGTH(s(proper(z0))), PROPER(s(z0))) 204.60/66.90
PROPER(length(length(z0))) → c16(LENGTH(length(proper(z0))), PROPER(length(z0))) 204.60/66.90
PROPER(length(length1(z0))) → c16(LENGTH(length1(proper(z0))), PROPER(length1(z0))) 204.60/66.90
PROPER(length(nil)) → c16(LENGTH(ok(nil))) 204.60/66.90
PROPER(length(0)) → c16(LENGTH(ok(0))) 204.60/66.90
PROPER(length1(from(z0))) → c19(LENGTH1(from(proper(z0))), PROPER(from(z0))) 204.60/66.90
PROPER(length1(cons(z0, z1))) → c19(LENGTH1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.60/66.90
PROPER(length1(s(z0))) → c19(LENGTH1(s(proper(z0))), PROPER(s(z0))) 204.60/66.90
PROPER(length1(length(z0))) → c19(LENGTH1(length(proper(z0))), PROPER(length(z0))) 204.60/66.90
PROPER(length1(length1(z0))) → c19(LENGTH1(length1(proper(z0))), PROPER(length1(z0))) 204.60/66.90
PROPER(length1(nil)) → c19(LENGTH1(ok(nil))) 204.60/66.90
PROPER(length1(0)) → c19(LENGTH1(ok(0))) 204.60/66.90
TOP(mark(from(z0))) → c22(TOP(from(proper(z0))), PROPER(from(z0))) 204.60/66.90
TOP(mark(cons(z0, z1))) → c22(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 204.60/66.90
TOP(mark(s(z0))) → c22(TOP(s(proper(z0))), PROPER(s(z0))) 204.60/66.90
TOP(mark(length(z0))) → c22(TOP(length(proper(z0))), PROPER(length(z0))) 204.60/66.90
TOP(mark(length1(z0))) → c22(TOP(length1(proper(z0))), PROPER(length1(z0))) 204.60/66.90
TOP(ok(from(z0))) → c23(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0))) 204.60/66.90
TOP(ok(length(nil))) → c23(TOP(mark(0)), ACTIVE(length(nil))) 204.60/66.90
TOP(ok(length(cons(z0, z1)))) → c23(TOP(mark(s(length1(z1)))), ACTIVE(length(cons(z0, z1)))) 204.60/66.90
TOP(ok(length1(z0))) → c23(TOP(mark(length(z0))), ACTIVE(length1(z0))) 204.60/66.90
TOP(ok(from(z0))) → c23(TOP(from(active(z0))), ACTIVE(from(z0))) 204.60/66.90
TOP(ok(cons(z0, z1))) → c23(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 204.60/66.90
TOP(ok(s(z0))) → c23(TOP(s(active(z0))), ACTIVE(s(z0)))
204.60/66.90
204.60/66.90

(56) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.60/66.90
active(length(nil)) → mark(0) 204.60/66.90
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.60/66.90
active(length1(z0)) → mark(length(z0)) 204.60/66.90
active(from(z0)) → from(active(z0)) 204.60/66.90
active(cons(z0, z1)) → cons(active(z0), z1) 204.60/66.90
active(s(z0)) → s(active(z0)) 204.60/66.90
from(mark(z0)) → mark(from(z0)) 204.60/66.90
from(ok(z0)) → ok(from(z0)) 204.60/66.90
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.60/66.90
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.60/66.90
s(mark(z0)) → mark(s(z0)) 204.60/66.90
s(ok(z0)) → ok(s(z0)) 204.60/66.90
proper(from(z0)) → from(proper(z0)) 204.60/66.90
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.60/66.90
proper(s(z0)) → s(proper(z0)) 204.60/66.90
proper(length(z0)) → length(proper(z0)) 204.60/66.90
proper(nil) → ok(nil) 204.60/66.90
proper(0) → ok(0) 204.60/66.90
proper(length1(z0)) → length1(proper(z0)) 204.60/66.90
length(ok(z0)) → ok(length(z0)) 204.60/66.90
length1(ok(z0)) → ok(length1(z0)) 204.60/66.90
top(mark(z0)) → top(proper(z0)) 204.60/66.90
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.60/66.90
TOP(mark(nil)) → c22(TOP(ok(nil))) 204.60/66.90
TOP(mark(0)) → c22(TOP(ok(0)))
S tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
K tuples:

TOP(mark(nil)) → c22(TOP(ok(nil))) 204.60/66.90
TOP(mark(0)) → c22(TOP(ok(0)))
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

FROM, CONS, S, LENGTH, LENGTH1, TOP

Compound Symbols:

c7, c8, c9, c10, c11, c12, c20, c21, c22

204.60/66.90
204.60/66.90

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

Removed 2 trailing tuple parts
204.60/66.90
204.60/66.90

(58) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.60/66.90
active(length(nil)) → mark(0) 204.60/66.90
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.60/66.90
active(length1(z0)) → mark(length(z0)) 204.60/66.90
active(from(z0)) → from(active(z0)) 204.60/66.90
active(cons(z0, z1)) → cons(active(z0), z1) 204.60/66.90
active(s(z0)) → s(active(z0)) 204.60/66.90
from(mark(z0)) → mark(from(z0)) 204.60/66.90
from(ok(z0)) → ok(from(z0)) 204.60/66.90
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.60/66.90
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.60/66.90
s(mark(z0)) → mark(s(z0)) 204.60/66.90
s(ok(z0)) → ok(s(z0)) 204.60/66.90
proper(from(z0)) → from(proper(z0)) 204.60/66.90
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.60/66.90
proper(s(z0)) → s(proper(z0)) 204.60/66.90
proper(length(z0)) → length(proper(z0)) 204.60/66.90
proper(nil) → ok(nil) 204.60/66.90
proper(0) → ok(0) 204.60/66.90
proper(length1(z0)) → length1(proper(z0)) 204.60/66.90
length(ok(z0)) → ok(length(z0)) 204.60/66.90
length1(ok(z0)) → ok(length1(z0)) 204.60/66.90
top(mark(z0)) → top(proper(z0)) 204.60/66.90
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.60/66.90
TOP(mark(nil)) → c22 204.60/66.90
TOP(mark(0)) → c22
S tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
K tuples:

TOP(mark(nil)) → c22 204.60/66.90
TOP(mark(0)) → c22
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

FROM, CONS, S, LENGTH, LENGTH1, TOP

Compound Symbols:

c7, c8, c9, c10, c11, c12, c20, c21, c22

204.60/66.90
204.60/66.90

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

Removed 2 trailing nodes:

TOP(mark(nil)) → c22 204.60/66.90
TOP(mark(0)) → c22
204.60/66.90
204.60/66.90

(60) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.60/66.90
active(length(nil)) → mark(0) 204.60/66.90
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.60/66.90
active(length1(z0)) → mark(length(z0)) 204.60/66.90
active(from(z0)) → from(active(z0)) 204.60/66.90
active(cons(z0, z1)) → cons(active(z0), z1) 204.60/66.90
active(s(z0)) → s(active(z0)) 204.60/66.90
from(mark(z0)) → mark(from(z0)) 204.60/66.90
from(ok(z0)) → ok(from(z0)) 204.60/66.90
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.60/66.90
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.60/66.90
s(mark(z0)) → mark(s(z0)) 204.60/66.90
s(ok(z0)) → ok(s(z0)) 204.60/66.90
proper(from(z0)) → from(proper(z0)) 204.60/66.90
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.60/66.90
proper(s(z0)) → s(proper(z0)) 204.60/66.90
proper(length(z0)) → length(proper(z0)) 204.60/66.90
proper(nil) → ok(nil) 204.60/66.90
proper(0) → ok(0) 204.60/66.90
proper(length1(z0)) → length1(proper(z0)) 204.60/66.90
length(ok(z0)) → ok(length(z0)) 204.60/66.90
length1(ok(z0)) → ok(length1(z0)) 204.60/66.90
top(mark(z0)) → top(proper(z0)) 204.60/66.90
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
S tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
K tuples:none
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

FROM, CONS, S, LENGTH, LENGTH1

Compound Symbols:

c7, c8, c9, c10, c11, c12, c20, c21

204.60/66.90
204.60/66.90

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

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

FROM(mark(z0)) → c7(FROM(z0))
We considered the (Usable) Rules:none
And the Tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 204.60/66.90

POL(CONS(x1, x2)) = 0    204.60/66.90
POL(FROM(x1)) = [2]x1    204.60/66.90
POL(LENGTH(x1)) = [5]x1    204.60/66.90
POL(LENGTH1(x1)) = 0    204.60/66.90
POL(S(x1)) = 0    204.60/66.90
POL(c10(x1)) = x1    204.60/66.90
POL(c11(x1)) = x1    204.60/66.90
POL(c12(x1)) = x1    204.60/66.90
POL(c20(x1)) = x1    204.60/66.90
POL(c21(x1)) = x1    204.60/66.90
POL(c7(x1)) = x1    204.60/66.90
POL(c8(x1)) = x1    204.60/66.90
POL(c9(x1)) = x1    204.60/66.90
POL(mark(x1)) = [1] + x1    204.60/66.90
POL(ok(x1)) = x1   
204.60/66.90
204.60/66.90

(62) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.60/66.90
active(length(nil)) → mark(0) 204.60/66.90
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.60/66.90
active(length1(z0)) → mark(length(z0)) 204.60/66.90
active(from(z0)) → from(active(z0)) 204.60/66.90
active(cons(z0, z1)) → cons(active(z0), z1) 204.60/66.90
active(s(z0)) → s(active(z0)) 204.60/66.90
from(mark(z0)) → mark(from(z0)) 204.60/66.90
from(ok(z0)) → ok(from(z0)) 204.60/66.90
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.60/66.90
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.60/66.90
s(mark(z0)) → mark(s(z0)) 204.60/66.90
s(ok(z0)) → ok(s(z0)) 204.60/66.90
proper(from(z0)) → from(proper(z0)) 204.60/66.90
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.60/66.90
proper(s(z0)) → s(proper(z0)) 204.60/66.90
proper(length(z0)) → length(proper(z0)) 204.60/66.90
proper(nil) → ok(nil) 204.60/66.90
proper(0) → ok(0) 204.60/66.90
proper(length1(z0)) → length1(proper(z0)) 204.60/66.90
length(ok(z0)) → ok(length(z0)) 204.60/66.90
length1(ok(z0)) → ok(length1(z0)) 204.60/66.90
top(mark(z0)) → top(proper(z0)) 204.60/66.90
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
S tuples:

FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
K tuples:

FROM(mark(z0)) → c7(FROM(z0))
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

FROM, CONS, S, LENGTH, LENGTH1

Compound Symbols:

c7, c8, c9, c10, c11, c12, c20, c21

204.60/66.90
204.60/66.90

(63) 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.

LENGTH1(ok(z0)) → c21(LENGTH1(z0))
We considered the (Usable) Rules:none
And the Tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 204.60/66.90

POL(CONS(x1, x2)) = 0    204.60/66.90
POL(FROM(x1)) = 0    204.60/66.90
POL(LENGTH(x1)) = 0    204.60/66.90
POL(LENGTH1(x1)) = x12    204.60/66.90
POL(S(x1)) = 0    204.60/66.90
POL(c10(x1)) = x1    204.60/66.90
POL(c11(x1)) = x1    204.60/66.90
POL(c12(x1)) = x1    204.60/66.90
POL(c20(x1)) = x1    204.60/66.90
POL(c21(x1)) = x1    204.60/66.90
POL(c7(x1)) = x1    204.60/66.90
POL(c8(x1)) = x1    204.60/66.90
POL(c9(x1)) = x1    204.60/66.90
POL(mark(x1)) = 0    204.60/66.90
POL(ok(x1)) = [1] + x1   
204.60/66.90
204.60/66.90

(64) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.60/66.90
active(length(nil)) → mark(0) 204.60/66.90
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.60/66.90
active(length1(z0)) → mark(length(z0)) 204.60/66.90
active(from(z0)) → from(active(z0)) 204.60/66.90
active(cons(z0, z1)) → cons(active(z0), z1) 204.60/66.90
active(s(z0)) → s(active(z0)) 204.60/66.90
from(mark(z0)) → mark(from(z0)) 204.60/66.90
from(ok(z0)) → ok(from(z0)) 204.60/66.90
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.60/66.90
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.60/66.90
s(mark(z0)) → mark(s(z0)) 204.60/66.90
s(ok(z0)) → ok(s(z0)) 204.60/66.90
proper(from(z0)) → from(proper(z0)) 204.60/66.90
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.60/66.90
proper(s(z0)) → s(proper(z0)) 204.60/66.90
proper(length(z0)) → length(proper(z0)) 204.60/66.90
proper(nil) → ok(nil) 204.60/66.90
proper(0) → ok(0) 204.60/66.90
proper(length1(z0)) → length1(proper(z0)) 204.60/66.90
length(ok(z0)) → ok(length(z0)) 204.60/66.90
length1(ok(z0)) → ok(length1(z0)) 204.60/66.90
top(mark(z0)) → top(proper(z0)) 204.60/66.90
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
S tuples:

FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0))
K tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

FROM, CONS, S, LENGTH, LENGTH1

Compound Symbols:

c7, c8, c9, c10, c11, c12, c20, c21

204.60/66.90
204.60/66.90

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

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

CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0))
We considered the (Usable) Rules:none
And the Tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 204.60/66.90

POL(CONS(x1, x2)) = [2]x1    204.60/66.90
POL(FROM(x1)) = 0    204.60/66.90
POL(LENGTH(x1)) = x1    204.60/66.90
POL(LENGTH1(x1)) = [5]x1    204.60/66.90
POL(S(x1)) = 0    204.60/66.90
POL(c10(x1)) = x1    204.60/66.90
POL(c11(x1)) = x1    204.60/66.90
POL(c12(x1)) = x1    204.60/66.90
POL(c20(x1)) = x1    204.60/66.90
POL(c21(x1)) = x1    204.60/66.90
POL(c7(x1)) = x1    204.60/66.90
POL(c8(x1)) = x1    204.60/66.90
POL(c9(x1)) = x1    204.60/66.90
POL(mark(x1)) = x1    204.60/66.90
POL(ok(x1)) = [1] + x1   
204.60/66.90
204.60/66.90

(66) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.60/66.90
active(length(nil)) → mark(0) 204.60/66.90
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.60/66.90
active(length1(z0)) → mark(length(z0)) 204.60/66.90
active(from(z0)) → from(active(z0)) 204.60/66.90
active(cons(z0, z1)) → cons(active(z0), z1) 204.60/66.90
active(s(z0)) → s(active(z0)) 204.60/66.90
from(mark(z0)) → mark(from(z0)) 204.60/66.90
from(ok(z0)) → ok(from(z0)) 204.60/66.90
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.60/66.90
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.60/66.90
s(mark(z0)) → mark(s(z0)) 204.60/66.90
s(ok(z0)) → ok(s(z0)) 204.60/66.90
proper(from(z0)) → from(proper(z0)) 204.60/66.90
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.60/66.90
proper(s(z0)) → s(proper(z0)) 204.60/66.90
proper(length(z0)) → length(proper(z0)) 204.60/66.90
proper(nil) → ok(nil) 204.60/66.90
proper(0) → ok(0) 204.60/66.90
proper(length1(z0)) → length1(proper(z0)) 204.60/66.90
length(ok(z0)) → ok(length(z0)) 204.60/66.90
length1(ok(z0)) → ok(length1(z0)) 204.60/66.90
top(mark(z0)) → top(proper(z0)) 204.60/66.90
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
S tuples:

FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0))
K tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0))
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

FROM, CONS, S, LENGTH, LENGTH1

Compound Symbols:

c7, c8, c9, c10, c11, c12, c20, c21

204.60/66.90
204.60/66.90

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

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

FROM(ok(z0)) → c8(FROM(z0))
We considered the (Usable) Rules:none
And the Tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 204.60/66.90

POL(CONS(x1, x2)) = x1 + [3]x2    204.60/66.90
POL(FROM(x1)) = [3]x1    204.60/66.90
POL(LENGTH(x1)) = [5]x1    204.60/66.90
POL(LENGTH1(x1)) = [5]x1    204.60/66.90
POL(S(x1)) = 0    204.60/66.90
POL(c10(x1)) = x1    204.60/66.90
POL(c11(x1)) = x1    204.60/66.90
POL(c12(x1)) = x1    204.60/66.90
POL(c20(x1)) = x1    204.60/66.90
POL(c21(x1)) = x1    204.60/66.90
POL(c7(x1)) = x1    204.60/66.90
POL(c8(x1)) = x1    204.60/66.90
POL(c9(x1)) = x1    204.60/66.90
POL(mark(x1)) = x1    204.60/66.90
POL(ok(x1)) = [2] + x1   
204.60/66.90
204.60/66.90

(68) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.60/66.90
active(length(nil)) → mark(0) 204.60/66.90
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.60/66.90
active(length1(z0)) → mark(length(z0)) 204.60/66.90
active(from(z0)) → from(active(z0)) 204.60/66.90
active(cons(z0, z1)) → cons(active(z0), z1) 204.60/66.90
active(s(z0)) → s(active(z0)) 204.60/66.90
from(mark(z0)) → mark(from(z0)) 204.60/66.90
from(ok(z0)) → ok(from(z0)) 204.60/66.90
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.60/66.90
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.60/66.90
s(mark(z0)) → mark(s(z0)) 204.60/66.90
s(ok(z0)) → ok(s(z0)) 204.60/66.90
proper(from(z0)) → from(proper(z0)) 204.60/66.90
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.60/66.90
proper(s(z0)) → s(proper(z0)) 204.60/66.90
proper(length(z0)) → length(proper(z0)) 204.60/66.90
proper(nil) → ok(nil) 204.60/66.90
proper(0) → ok(0) 204.60/66.90
proper(length1(z0)) → length1(proper(z0)) 204.60/66.90
length(ok(z0)) → ok(length(z0)) 204.60/66.90
length1(ok(z0)) → ok(length1(z0)) 204.60/66.90
top(mark(z0)) → top(proper(z0)) 204.60/66.90
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
S tuples:

CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0))
K tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0))
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

FROM, CONS, S, LENGTH, LENGTH1

Compound Symbols:

c7, c8, c9, c10, c11, c12, c20, c21

204.60/66.90
204.60/66.90

(69) 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) → c9(CONS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 204.60/66.90

POL(CONS(x1, x2)) = x1 + [5]x2    204.60/66.90
POL(FROM(x1)) = [3]x1    204.60/66.90
POL(LENGTH(x1)) = [3]x1    204.60/66.90
POL(LENGTH1(x1)) = [5]x1    204.60/66.90
POL(S(x1)) = 0    204.60/66.90
POL(c10(x1)) = x1    204.60/66.90
POL(c11(x1)) = x1    204.60/66.90
POL(c12(x1)) = x1    204.60/66.90
POL(c20(x1)) = x1    204.60/66.90
POL(c21(x1)) = x1    204.60/66.90
POL(c7(x1)) = x1    204.60/66.90
POL(c8(x1)) = x1    204.60/66.90
POL(c9(x1)) = x1    204.60/66.90
POL(mark(x1)) = [1] + x1    204.60/66.90
POL(ok(x1)) = [1] + x1   
204.60/66.90
204.60/66.90

(70) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.60/66.90
active(length(nil)) → mark(0) 204.60/66.90
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.60/66.90
active(length1(z0)) → mark(length(z0)) 204.60/66.90
active(from(z0)) → from(active(z0)) 204.60/66.90
active(cons(z0, z1)) → cons(active(z0), z1) 204.60/66.90
active(s(z0)) → s(active(z0)) 204.60/66.90
from(mark(z0)) → mark(from(z0)) 204.60/66.90
from(ok(z0)) → ok(from(z0)) 204.60/66.90
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.60/66.90
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.60/66.90
s(mark(z0)) → mark(s(z0)) 204.60/66.90
s(ok(z0)) → ok(s(z0)) 204.60/66.90
proper(from(z0)) → from(proper(z0)) 204.60/66.90
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.60/66.90
proper(s(z0)) → s(proper(z0)) 204.60/66.90
proper(length(z0)) → length(proper(z0)) 204.60/66.90
proper(nil) → ok(nil) 204.60/66.90
proper(0) → ok(0) 204.60/66.90
proper(length1(z0)) → length1(proper(z0)) 204.60/66.90
length(ok(z0)) → ok(length(z0)) 204.60/66.90
length1(ok(z0)) → ok(length1(z0)) 204.60/66.90
top(mark(z0)) → top(proper(z0)) 204.60/66.90
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
S tuples:

S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0))
K tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1))
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

FROM, CONS, S, LENGTH, LENGTH1

Compound Symbols:

c7, c8, c9, c10, c11, c12, c20, c21

204.60/66.90
204.60/66.90

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

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

S(mark(z0)) → c11(S(z0))
We considered the (Usable) Rules:none
And the Tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 204.60/66.90

POL(CONS(x1, x2)) = [5]x1 + [3]x2    204.60/66.90
POL(FROM(x1)) = [3]x1    204.60/66.90
POL(LENGTH(x1)) = [5]x1    204.60/66.90
POL(LENGTH1(x1)) = [5]x1    204.60/66.90
POL(S(x1)) = [2]x1    204.60/66.90
POL(c10(x1)) = x1    204.60/66.90
POL(c11(x1)) = x1    204.60/66.90
POL(c12(x1)) = x1    204.60/66.90
POL(c20(x1)) = x1    204.60/66.90
POL(c21(x1)) = x1    204.60/66.90
POL(c7(x1)) = x1    204.60/66.90
POL(c8(x1)) = x1    204.60/66.90
POL(c9(x1)) = x1    204.60/66.90
POL(mark(x1)) = [1] + x1    204.60/66.90
POL(ok(x1)) = x1   
204.60/66.90
204.60/66.90

(72) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.60/66.90
active(length(nil)) → mark(0) 204.60/66.90
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.60/66.90
active(length1(z0)) → mark(length(z0)) 204.60/66.90
active(from(z0)) → from(active(z0)) 204.60/66.90
active(cons(z0, z1)) → cons(active(z0), z1) 204.60/66.90
active(s(z0)) → s(active(z0)) 204.60/66.90
from(mark(z0)) → mark(from(z0)) 204.60/66.90
from(ok(z0)) → ok(from(z0)) 204.60/66.90
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.60/66.90
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.60/66.90
s(mark(z0)) → mark(s(z0)) 204.60/66.90
s(ok(z0)) → ok(s(z0)) 204.60/66.90
proper(from(z0)) → from(proper(z0)) 204.60/66.90
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.60/66.90
proper(s(z0)) → s(proper(z0)) 204.60/66.90
proper(length(z0)) → length(proper(z0)) 204.60/66.90
proper(nil) → ok(nil) 204.60/66.90
proper(0) → ok(0) 204.60/66.90
proper(length1(z0)) → length1(proper(z0)) 204.60/66.90
length(ok(z0)) → ok(length(z0)) 204.60/66.90
length1(ok(z0)) → ok(length1(z0)) 204.60/66.90
top(mark(z0)) → top(proper(z0)) 204.60/66.90
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
S tuples:

S(ok(z0)) → c12(S(z0))
K tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0))
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

FROM, CONS, S, LENGTH, LENGTH1

Compound Symbols:

c7, c8, c9, c10, c11, c12, c20, c21

204.60/66.90
204.60/66.90

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

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

S(ok(z0)) → c12(S(z0))
We considered the (Usable) Rules:none
And the Tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 204.60/66.90

POL(CONS(x1, x2)) = [5]x1 + [3]x2    204.60/66.90
POL(FROM(x1)) = [3]x1    204.60/66.90
POL(LENGTH(x1)) = [5]x1    204.60/66.90
POL(LENGTH1(x1)) = [5]x1    204.60/66.90
POL(S(x1)) = [5]x1    204.60/66.90
POL(c10(x1)) = x1    204.60/66.90
POL(c11(x1)) = x1    204.60/66.90
POL(c12(x1)) = x1    204.60/66.90
POL(c20(x1)) = x1    204.60/66.90
POL(c21(x1)) = x1    204.60/66.90
POL(c7(x1)) = x1    204.60/66.90
POL(c8(x1)) = x1    204.60/66.90
POL(c9(x1)) = x1    204.60/66.90
POL(mark(x1)) = x1    204.60/66.90
POL(ok(x1)) = [1] + x1   
204.60/66.90
204.60/66.90

(74) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(from(z0)) → mark(cons(z0, from(s(z0)))) 204.60/66.90
active(length(nil)) → mark(0) 204.60/66.90
active(length(cons(z0, z1))) → mark(s(length1(z1))) 204.60/66.90
active(length1(z0)) → mark(length(z0)) 204.60/66.90
active(from(z0)) → from(active(z0)) 204.60/66.90
active(cons(z0, z1)) → cons(active(z0), z1) 204.60/66.90
active(s(z0)) → s(active(z0)) 204.60/66.90
from(mark(z0)) → mark(from(z0)) 204.60/66.90
from(ok(z0)) → ok(from(z0)) 204.60/66.90
cons(mark(z0), z1) → mark(cons(z0, z1)) 204.60/66.90
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 204.60/66.90
s(mark(z0)) → mark(s(z0)) 204.60/66.90
s(ok(z0)) → ok(s(z0)) 204.60/66.90
proper(from(z0)) → from(proper(z0)) 204.60/66.90
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 204.60/66.90
proper(s(z0)) → s(proper(z0)) 204.60/66.90
proper(length(z0)) → length(proper(z0)) 204.60/66.90
proper(nil) → ok(nil) 204.60/66.90
proper(0) → ok(0) 204.60/66.90
proper(length1(z0)) → length1(proper(z0)) 204.60/66.90
length(ok(z0)) → ok(length(z0)) 204.60/66.90
length1(ok(z0)) → ok(length1(z0)) 204.60/66.90
top(mark(z0)) → top(proper(z0)) 204.60/66.90
top(ok(z0)) → top(active(z0))
Tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0))
S tuples:none
K tuples:

FROM(mark(z0)) → c7(FROM(z0)) 204.60/66.90
LENGTH1(ok(z0)) → c21(LENGTH1(z0)) 204.60/66.90
CONS(ok(z0), ok(z1)) → c10(CONS(z0, z1)) 204.60/66.90
LENGTH(ok(z0)) → c20(LENGTH(z0)) 204.60/66.90
FROM(ok(z0)) → c8(FROM(z0)) 204.60/66.90
CONS(mark(z0), z1) → c9(CONS(z0, z1)) 204.60/66.90
S(mark(z0)) → c11(S(z0)) 204.60/66.90
S(ok(z0)) → c12(S(z0))
Defined Rule Symbols:

active, from, cons, s, proper, length, length1, top

Defined Pair Symbols:

FROM, CONS, S, LENGTH, LENGTH1

Compound Symbols:

c7, c8, c9, c10, c11, c12, c20, c21

204.60/66.90
204.60/66.90

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

The set S is empty
204.60/66.90
204.60/66.90

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

204.60/66.90
204.60/66.90
204.60/66.97 EOF