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:

append(Cons(x, xs), ys) → Cons(x, append(xs, ys))
append(Nil, ys) → ys
goal(x, y) → append(x, y)

Rewrite Strategy: INNERMOST

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(n¹):
The rewrite sequence
append(Cons(x, xs), ys) →⁺ Cons(x, append(xs, ys))
gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
The pumping substitution is [xs / Cons(x, xs)].
The result substitution is [ ].

(2) BOUNDS(n^1, INF)