The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).

(0) Obligation:

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

from(X) → cons(X, n__from(s(X)))
after(0, XS) → XS
after(s(N), cons(X, XS)) → after(N, activate(XS))
from(X) → n__from(X)
activate(n__from(X)) → from(X)
activate(X) → X

Rewrite Strategy: FULL

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(n¹):
The rewrite sequence
after(s(N), cons(X, XS)) →⁺ after(N, XS)
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [N / s(N), XS / cons(X, XS)].
The result substitution is [ ].

(2) BOUNDS(n^1, INF)