### (0) Obligation:

Runtime Complexity TRS:

The TRS R consists of the following rules:

f(0) → cons(0, f(s(0)))

f(s(0)) → f(p(s(0)))

p(s(0)) → 0

Rewrite Strategy: FULL

### (1) InfiniteLowerBoundProof (EQUIVALENT transformation)

The loop following loop proves infinite runtime complexity:

The rewrite sequence

f(0) →^{+} cons(0, f(0))

gives rise to a decreasing loop by considering the right hand sides subterm at position [1].

The pumping substitution is [ ].

The result substitution is [ ].

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