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

Strict Trs:
  { f(f(x)) -> f(x)
  , f(s(x)) -> f(x)
  , g(s(0())) -> g(f(s(0()))) }
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(2) -> 1
, f_1(4) -> 3
, f_2(5) -> 3
, s_0(2) -> 2
, s_1(5) -> 4
, g_0(2) -> 1
, g_1(3) -> 1
, 0_0() -> 2
, 0_1() -> 5 }

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