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

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

The input is overlay and right-linear. Switching to innermost
rewriting.

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

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(?,O(n^1))

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

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

and precedence

 empty .

Following symbols are considered recursive:

 {+, -}

The recursion depth is 1.

For your convenience, here are the satisfied ordering constraints:

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

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