The Runtime Complexity (innermost) 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:

f(empty, l) → l
f(cons(x, k), l) → g(k, l, cons(x, k))
g(a, b, c) → f(a, cons(b, c))

Rewrite Strategy: INNERMOST

(1) DecreasingLoopProof (EQUIVALENT transformation)

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

(2) BOUNDS(n^1, INF)