### (0) Obligation:

Runtime Complexity TRS:

The TRS R consists of the following rules:

f(g(a)) → a

f(f(x)) → b

g(x) → f(g(x))

Rewrite Strategy: FULL

### (1) InfiniteLowerBoundProof (EQUIVALENT transformation)

The loop following loop proves infinite runtime complexity:

The rewrite sequence

g(x) →^{+} f(g(x))

gives rise to a decreasing loop by considering the right hand sides subterm at position [0].

The pumping substitution is [ ].

The result substitution is [ ].

### (2) BOUNDS(INF, INF)