The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).

(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

from(X) → cons(X, from(s(X)))
first(0, Z) → nil
first(s(X), cons(Y, Z)) → cons(Y, first(X, Z))
sel(0, cons(X, Z)) → 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
from(X) →⁺ cons(X, from(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)