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

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

The problem is match-bounded by 1. The enriched problem is
compatible with the following automaton.
{ f_0(2, 2, 2) -> 1
, g_0(2) -> 1
, g_1(2) -> 3
, s_0(2) -> 2
, s_1(3) -> 1
, s_1(3) -> 3
, 0_0() -> 2
, 0_1() -> 1
, 0_1() -> 3 }

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