(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(x) → s(x)
f(s(s(x))) → s(f(f(x)))
Rewrite Strategy: FULL
(1) DecreasingLoopProof (EQUIVALENT transformation)
The following loop(s) give(s) rise to the lower bound Ω(n1):
The rewrite sequence
f(s(s(x))) →+ s(f(f(x)))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0].
The pumping substitution is [x / s(s(x))].
The result substitution is [ ].
(2) BOUNDS(n^1, INF)