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(x, h(y)) → h(f(f(h(a), y), x))

Rewrite Strategy: FULL

(1) InfiniteLowerBoundProof (EQUIVALENT transformation)

The loop following loop proves infinite runtime complexity:
The rewrite sequence
f(h(h(y344_0)), h(h(y6_0))) →⁺ h(h(f(h(h(f(f(h(a), a), f(h(a), y344_0)))), h(h(f(f(h(a), a), f(h(a), y6_0)))))))
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 [y344_0 / f(f(h(a), a), f(h(a), y344_0)), y6_0 / f(f(h(a), a), f(h(a), y6_0))].

(2) BOUNDS(INF, INF)