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:

r(xs, ys, zs, nil) → xs
r(xs, nil, zs, cons(w, ws)) → r(xs, xs, cons(succ(zero), zs), ws)
r(xs, cons(y, ys), nil, cons(w, ws)) → r(xs, xs, cons(succ(zero), nil), ws)
r(xs, cons(y, ys), cons(z, zs), cons(w, ws)) → r(ys, cons(y, ys), zs, cons(succ(zero), cons(w, ws)))

Rewrite Strategy: INNERMOST

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(n¹):
The rewrite sequence
r(nil, nil, zs, cons(w, cons(w63_0, ws64_0))) →⁺ r(nil, nil, cons(succ(zero), cons(succ(zero), zs)), ws64_0)
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [ws64_0 / cons(w, cons(w63_0, ws64_0))].
The result substitution is [zs / cons(succ(zero), cons(succ(zero), zs))].

(2) BOUNDS(n^1, INF)