MAYBE 45.55/39.69 MAYBE 45.55/39.69 45.55/39.69 45.55/39.69 45.55/39.69 45.55/39.69 45.55/39.69 Runtime Complexity (innermost) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml.xml 45.55/39.69 45.55/39.69 45.55/39.69
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The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), INFINITE).

0 CpxTRS
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↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))
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↳2 CdtProblem
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↳3 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳4 CdtProblem
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(0) Obligation:

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

h(f(x, y)) → f(y, f(h(h(x)), a))

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:

h(f(z0, z1)) → f(z1, f(h(h(z0)), a))
Tuples:

H(f(z0, z1)) → c(H(h(z0)), H(z0))
S tuples:

H(f(z0, z1)) → c(H(h(z0)), H(z0))
K tuples:none
Defined Rule Symbols:

h

Defined Pair Symbols:

H

Compound Symbols:

c

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

Use narrowing to replace H(f(z0, z1)) → c(H(h(z0)), H(z0)) by

H(f(f(z0, z1), x1)) → c(H(f(z1, f(h(h(z0)), a))), H(f(z0, z1)))
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(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

h(f(z0, z1)) → f(z1, f(h(h(z0)), a))
Tuples:

H(f(f(z0, z1), x1)) → c(H(f(z1, f(h(h(z0)), a))), H(f(z0, z1)))
S tuples:

H(f(f(z0, z1), x1)) → c(H(f(z1, f(h(h(z0)), a))), H(f(z0, z1)))
K tuples:none
Defined Rule Symbols:

h

Defined Pair Symbols:

H

Compound Symbols:

c

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45.65/39.74 EOF