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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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