The Runtime Complexity (innermost) 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(m, n, s(r)) → p(m, r, n)
p(m, s(n), 0) → p(0, n, m)
p(m, 0, 0) → m

Rewrite Strategy: INNERMOST

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(n¹):
The rewrite sequence
p(m, s(r3_1), s(r)) →⁺ p(m, r3_1, r)
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [r3_1 / s(r3_1), r / s(r)].
The result substitution is [ ].

(2) BOUNDS(n^1, INF)