We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).

Strict Trs:
  { f(0()) -> s(0())
  , f(s(0())) -> s(0())
  , f(s(s(x))) -> f(f(s(x))) }
Obligation:
  runtime complexity
Answer:
  YES(?,O(n^1))

The input is overlay and right-linear. Switching to innermost
rewriting.

We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).

Strict Trs:
  { f(0()) -> s(0())
  , f(s(0())) -> s(0())
  , f(s(s(x))) -> f(f(s(x))) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(n^1))

The problem is match-bounded by 2. The enriched problem is
compatible with the following automaton.
{ f_0(2) -> 1
, f_1(4) -> 1
, f_1(4) -> 4
, f_1(5) -> 4
, 0_0() -> 2
, 0_1() -> 3
, 0_2() -> 6
, s_0(2) -> 2
, s_1(2) -> 5
, s_1(3) -> 1
, s_1(3) -> 4
, s_2(6) -> 1
, s_2(6) -> 4 }

Hurray, we answered YES(?,O(n^1))