### (0) Obligation:

Runtime Complexity TRS:

The TRS R consists of the following rules:

f(X) → cons(X, f(g(X)))

g(0) → s(0)

g(s(X)) → s(s(g(X)))

sel(0, cons(X, Y)) → X

sel(s(X), cons(Y, Z)) → sel(X, Z)

Rewrite Strategy: FULL

### (1) InfiniteLowerBoundProof (EQUIVALENT transformation)

The loop following loop proves infinite runtime complexity:

The rewrite sequence

f(X) →^{+} cons(X, f(g(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 / g(X)].

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