The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(2^n, INF).

(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

empty(nil) → true
empty(cons(x, l)) → false
head(cons(x, l)) → x
tail(nil) → nil
tail(cons(x, l)) → l
rev(nil) → nil
rev(cons(x, l)) → cons(rev1(x, l), rev2(x, l))
last(x, l) → if(empty(l), x, l)
if(true, x, l) → x
if(false, x, l) → last(head(l), tail(l))
rev2(x, nil) → nil
rev2(x, cons(y, l)) → rev(cons(x, rev2(y, l)))

Rewrite Strategy: FULL

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(2ⁿ):
The rewrite sequence
rev2(x, cons(y, l)) →⁺ cons(rev1(x, rev2(y, l)), rev2(x, rev2(y, l)))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0,1].
The pumping substitution is [l / cons(y, l)].
The result substitution is [x / y].

The rewrite sequence
rev2(x, cons(y, l)) →⁺ cons(rev1(x, rev2(y, l)), rev2(x, rev2(y, l)))
gives rise to a decreasing loop by considering the right hand sides subterm at position [1,1].
The pumping substitution is [l / cons(y, l)].
The result substitution is [x / y].

(2) BOUNDS(2^n, INF)