YES(O(1), O(1)) 0.00/0.52 YES(O(1), O(1)) 0.00/0.53 0.00/0.53 0.00/0.53 0.00/0.53 0.00/0.53 0.00/0.53 Runtime Complexity (innermost) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml.xml 0.00/0.53 0.00/0.53 0.00/0.53
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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))
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↳2 CdtProblem
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↳3 SIsEmptyProof (BOTH BOUNDS(ID, ID))
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↳4 BOUNDS(O(1), O(1))
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(0) Obligation:

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

not(x) → xor(x, true) 0.00/0.53
implies(x, y) → xor(and(x, y), xor(x, true)) 0.00/0.53
or(x, y) → xor(and(x, y), xor(x, y)) 0.00/0.53
=(x, y) → xor(x, xor(y, true))

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:

not(z0) → xor(z0, true) 0.00/0.53
implies(z0, z1) → xor(and(z0, z1), xor(z0, true)) 0.00/0.53
or(z0, z1) → xor(and(z0, z1), xor(z0, z1)) 0.00/0.53
=(z0, z1) → xor(z0, xor(z1, true))
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:

not, implies, or, =

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

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0.00/0.58 EOF