### (0) Obligation:

Runtime Complexity TRS:

The TRS R consists of the following rules:

cons(x, cons(y, z)) → big

inf(x) → cons(x, inf(s(x)))

Rewrite Strategy: FULL

### (1) InfiniteLowerBoundProof (EQUIVALENT transformation)

The loop following loop proves infinite runtime complexity:

The rewrite sequence

inf(x) →^{+} cons(x, inf(s(x)))

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

The pumping substitution is [ ].

The result substitution is [x / s(x)].

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