YES(O(1), O(1)) 0.00/0.54 YES(O(1), O(1)) 0.00/0.55 0.00/0.55 0.00/0.55 0.00/0.55 0.00/0.55 0.00/0.55 Runtime Complexity (innermost) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml.xml 0.00/0.55 0.00/0.55 0.00/0.55
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(0) Obligation:

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

2nd(cons1(X, cons(Y, Z))) → Y 0.00/0.56
2nd(cons(X, X1)) → 2nd(cons1(X, activate(X1))) 0.00/0.56
from(X) → cons(X, n__from(s(X))) 0.00/0.56
from(X) → n__from(X) 0.00/0.56
activate(n__from(X)) → from(X) 0.00/0.56
activate(X) → X

Rewrite Strategy: INNERMOST
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(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)

Converted CpxTRS to CDT
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(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

2nd(cons1(z0, cons(z1, z2))) → z1 0.00/0.56
2nd(cons(z0, z1)) → 2nd(cons1(z0, activate(z1))) 0.00/0.56
from(z0) → cons(z0, n__from(s(z0))) 0.00/0.56
from(z0) → n__from(z0) 0.00/0.56
activate(n__from(z0)) → from(z0) 0.00/0.56
activate(z0) → z0
Tuples:

2ND(cons(z0, z1)) → c1(2ND(cons1(z0, activate(z1))), ACTIVATE(z1)) 0.00/0.56
ACTIVATE(n__from(z0)) → c4(FROM(z0))
S tuples:

2ND(cons(z0, z1)) → c1(2ND(cons1(z0, activate(z1))), ACTIVATE(z1)) 0.00/0.56
ACTIVATE(n__from(z0)) → c4(FROM(z0))
K tuples:none
Defined Rule Symbols:

2nd, from, activate

Defined Pair Symbols:

2ND, ACTIVATE

Compound Symbols:

c1, c4

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

Removed 2 trailing tuple parts
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(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

2nd(cons1(z0, cons(z1, z2))) → z1 0.00/0.56
2nd(cons(z0, z1)) → 2nd(cons1(z0, activate(z1))) 0.00/0.56
from(z0) → cons(z0, n__from(s(z0))) 0.00/0.56
from(z0) → n__from(z0) 0.00/0.56
activate(n__from(z0)) → from(z0) 0.00/0.56
activate(z0) → z0
Tuples:

2ND(cons(z0, z1)) → c1(ACTIVATE(z1)) 0.00/0.56
ACTIVATE(n__from(z0)) → c4
S tuples:

2ND(cons(z0, z1)) → c1(ACTIVATE(z1)) 0.00/0.56
ACTIVATE(n__from(z0)) → c4
K tuples:none
Defined Rule Symbols:

2nd, from, activate

Defined Pair Symbols:

2ND, ACTIVATE

Compound Symbols:

c1, c4

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

Removed 2 trailing nodes:

2ND(cons(z0, z1)) → c1(ACTIVATE(z1)) 0.00/0.56
ACTIVATE(n__from(z0)) → c4
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(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

2nd(cons1(z0, cons(z1, z2))) → z1 0.00/0.56
2nd(cons(z0, z1)) → 2nd(cons1(z0, activate(z1))) 0.00/0.56
from(z0) → cons(z0, n__from(s(z0))) 0.00/0.56
from(z0) → n__from(z0) 0.00/0.56
activate(n__from(z0)) → from(z0) 0.00/0.56
activate(z0) → z0
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:

2nd, from, activate

Defined Pair Symbols:none

Compound Symbols:none

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

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

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0.00/0.58 EOF