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, l1)
ifappend(l1, l2, nil) → l2
ifappend(l1, l2, cons(x, l)) → cons(x, append(l, 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(x41_0, l42_0), l2) →⁺ cons(x41_0, append(l42_0, l2))
gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
The pumping substitution is [l42_0 / cons(x41_0, l42_0)].
The result substitution is [ ].

(2) BOUNDS(n^1, INF)