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

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

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) > +(x; s(; y))
                             
  +(s(; x); y) > s(; +(x; y))
                             

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