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:

f(x, empty) → x
f(empty, cons(a, k)) → f(cons(a, k), k)
f(cons(a, k), y) → f(y, k)

Rewrite Strategy: FULL

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(n¹):
The rewrite sequence
f(cons(a, k), cons(a358_0, k359_0)) →⁺ f(k, k359_0)
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [k / cons(a, k), k359_0 / cons(a358_0, k359_0)].
The result substitution is [ ].

(2) BOUNDS(n^1, INF)