YES(?,ELEMENTARY)

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

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

and precedence

 + > - .

Following symbols are considered recursive:

 {+, -}

The recursion depth is 2.

For your convenience, here are the satisfied ordering constraints:

        +(0(),  y;) > y             
                                    
     +(s(; x),  y;) > s(; +(x,  y;))
                                    
          -(0(); x) > x             
                                    
          -(y; 0()) > 0()           
                                    
  -(s(; y); s(; x)) > -(y; x)       
                                    

Hurray, we answered YES(?,ELEMENTARY)