(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(0, 1, x) → f(s(x), x, x)
f(x, y, s(z)) → s(f(0, 1, z))
Rewrite Strategy: INNERMOST
(1) CpxTrsToCpxRelTrsProof (BOTH BOUNDS(ID, ID) transformation)
Transformed TRS to relative TRS where S is empty.
(2) Obligation:
Runtime Complexity Relative TRS:
The TRS R consists of the following rules:
f(0, 1, x) → f(s(x), x, x)
f(x, y, s(z)) → s(f(0, 1, z))
S is empty.
Rewrite Strategy: INNERMOST
(3) DecreasingLoopProof (EQUIVALENT transformation)
The following loop(s) give(s) rise to the lower bound Ω(n1):
The rewrite sequence
f(0, 1, s(z8_2)) →+ s(f(0, 1, z8_2))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
The pumping substitution is [z8_2 / s(z8_2)].
The result substitution is [ ].
(4) BOUNDS(n^1, INF)