YES(?,O(n^2))

We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^2)).

Strict Trs:
  { g(0()) -> 0()
  , g(s(x)) -> f(g(x))
  , f(0()) -> 0() }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(n^2))

The input was oriented with the instance of 'Small Polynomial Path
Order (PS)' as induced by the safe mapping

 safe(g) = {}, safe(0) = {}, safe(s) = {1}, safe(f) = {1}

and precedence

 g > f .

Following symbols are considered recursive:

 {g, f}

The recursion depth is 2.

For your convenience, here are the satisfied ordering constraints:

     g(0();) > 0()       
                         
  g(s(; x);) > f(; g(x;))
                         
    f(; 0()) > 0()       
                         

Hurray, we answered YES(?,O(n^2))