YES(?,ELEMENTARY)

We are left with following problem, upon which TcT provides the
certificate YES(?,ELEMENTARY).

Strict Trs:
  { f(0()) -> 1()
  , f(s(x)) -> g(f(x))
  , f(s(x)) -> +(f(x), s(f(x)))
  , g(x) -> +(x, s(x)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,ELEMENTARY)

The input was oriented with the instance of 'Lightweight Multiset
Path Order' as induced by the safe mapping

 safe(f) = {}, safe(0) = {}, safe(1) = {}, safe(s) = {1},
 safe(g) = {1}, safe(+) = {1, 2}

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(0();) > 1()                    
                                      
  f(s(; x);) > g(; f(x;))             
                                      
  f(s(; x);) > +(; f(x;),  s(; f(x;)))
                                      
      g(; x) > +(; x,  s(; x))        
                                      

Hurray, we answered YES(?,ELEMENTARY)