YES(?,O(n^2))

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

Strict Trs:
  { f(s(x), y) -> f(x, g(x, y))
  , f(0(), y) -> y
  , g(x, y) -> y }
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(f) = {2}, safe(s) = {1}, safe(g) = {1, 2}, safe(0) = {}

and precedence

 f > g .

Following symbols are considered recursive:

 {f, g}

The recursion depth is 2.

For your convenience, here are the satisfied ordering constraints:

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

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