### (0) Obligation:

Runtime Complexity TRS:

The TRS R consists of the following rules:

f(s(x), x) → f(s(x), round(x))

round(0) → 0

round(0) → s(0)

round(s(0)) → s(0)

round(s(s(x))) → s(s(round(x)))

Rewrite Strategy: FULL

### (1) InfiniteLowerBoundProof (EQUIVALENT transformation)

The loop following loop proves infinite runtime complexity:

The rewrite sequence

f(s(0), 0) →^{+} f(s(0), 0)

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

The pumping substitution is [ ].

The result substitution is [ ].

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