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:

ge(x, 0) → true
ge(0, s(y)) → false
ge(s(x), s(y)) → ge(x, y)
rev(x) → if(x, eq(0, length(x)), nil, 0, length(x))
if(x, true, z, c, l) → z
if(x, false, z, c, l) → help(s(c), l, x, z)
help(c, l, cons(x, y), z) → if(append(y, cons(x, nil)), ge(c, l), cons(x, z), c, l)
append(nil, y) → y
append(cons(x, y), z) → cons(x, append(y, z))
length(nil) → 0
length(cons(x, y)) → s(length(y))

Rewrite Strategy: INNERMOST

(1) DecreasingLoopProof (EQUIVALENT transformation)

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

(2) BOUNDS(n^1, INF)