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

(0) Obligation:

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

f(h(x), y) → h(f(y, f(x, h(a))))

Rewrite Strategy: FULL

(1) InfiniteLowerBoundProof (EQUIVALENT transformation)

The loop following loop proves infinite runtime complexity:
The rewrite sequence
f(h(h(x5_0)), h(h(x363_0))) →⁺ h(h(f(h(h(f(f(x5_0, h(a)), f(a, h(a))))), h(h(f(f(x363_0, h(a)), f(a, h(a))))))))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0].
The pumping substitution is [ ].
The result substitution is [x5_0 / f(f(x5_0, h(a)), f(a, h(a))), x363_0 / f(f(x363_0, h(a)), f(a, h(a)))].

(2) BOUNDS(INF, INF)