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:

h(x, c(y, z)) → h(c(s(y), x), z)
h(c(s(x), c(s(0), y)), z) → h(y, c(s(0), c(x, z)))

Rewrite Strategy: INNERMOST

(1) DecreasingLoopProof (EQUIVALENT transformation)

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

(2) BOUNDS(n^1, INF)