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:

cond(true, x, y) → cond(gr(x, y), p(x), y)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
p(0) → 0
p(s(x)) → x

Rewrite Strategy: INNERMOST

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(n¹):
The rewrite sequence
cond(true, s(x4_1), 0) →⁺ cond(true, x4_1, 0)
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [x4_1 / s(x4_1)].
The result substitution is [ ].

(2) BOUNDS(n^1, INF)