The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).

(0) Obligation:

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

p(0) → 0
p(s(x)) → x
minus(x, 0) → x
minus(s(x), s(y)) → minus(x, y)
minus(x, s(y)) → p(minus(x, y))
div(0, s(y)) → 0
div(s(x), s(y)) → s(div(minus(s(x), s(y)), s(y)))
log(s(0), s(s(y))) → 0
log(s(s(x)), s(s(y))) → s(log(div(minus(x, y), s(s(y))), s(s(y))))

Rewrite Strategy: FULL

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(n¹):
The rewrite sequence
minus(s(x), s(y)) →⁺ minus(x, y)
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [x / s(x), y / s(y)].
The result substitution is [ ].

(2) BOUNDS(n^1, INF)