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:

is_empty(nil) → true
is_empty(cons(x, l)) → false
hd(cons(x, l)) → x
tl(cons(x, l)) → l
append(l1, l2) → ifappend(l1, l2, is_empty(l1))
ifappend(l1, l2, true) → l2
ifappend(l1, l2, false) → cons(hd(l1), append(tl(l1), l2))

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(x25_0, l26_0), l2) →⁺ cons(hd(cons(x25_0, l26_0)), append(l26_0, l2))
gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
The pumping substitution is [l26_0 / cons(x25_0, l26_0)].
The result substitution is [ ].

(2) BOUNDS(n^1, INF)