YES(O(1), O(1)) 0.00/0.53 YES(O(1), O(1)) 0.00/0.54 0.00/0.54 0.00/0.54 0.00/0.54 0.00/0.54 0.00/0.54 Runtime Complexity (innermost) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml.xml 0.00/0.54 0.00/0.54 0.00/0.54
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0.00/0.54
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The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(1)).

0 CpxTRS
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↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))
0.00/0.54 
↳2 CdtProblem
0.00/0.54 
↳3 SIsEmptyProof (BOTH BOUNDS(ID, ID))
0.00/0.54 
↳4 BOUNDS(O(1), O(1))
0.00/0.54
0.00/0.54 0.00/0.54
0.00/0.54
0.00/0.54

(0) Obligation:

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

fst(0, Z) → nil 0.00/0.54
fst(s, cons(Y)) → cons(Y) 0.00/0.54
from(X) → cons(X) 0.00/0.54
add(0, X) → X 0.00/0.54
add(s, Y) → s 0.00/0.54
len(nil) → 0 0.00/0.54
len(cons(X)) → s

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

Converted CpxTRS to CDT
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0.00/0.54

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

fst(0, z0) → nil 0.00/0.54
fst(s, cons(z0)) → cons(z0) 0.00/0.54
from(z0) → cons(z0) 0.00/0.54
add(0, z0) → z0 0.00/0.54
add(s, z0) → s 0.00/0.54
len(nil) → 0 0.00/0.54
len(cons(z0)) → s
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:

fst, from, add, len

Defined Pair Symbols:none

Compound Symbols:none

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

The set S is empty
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0.00/0.54

(4) BOUNDS(O(1), O(1))

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0.00/0.54
0.00/0.58 EOF