(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)) → cons(x, 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: FULL

(1) InfiniteLowerBoundProof (EQUIVALENT transformation)

The loop following loop proves infinite runtime complexity:
The rewrite sequence
append(cons(x37_0, l38_0), l2) →+ cons(hd(cons(x37_0, l38_0)), append(cons(x37_0, l38_0), l2))
gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
The pumping substitution is [ ].
The result substitution is [ ].