YES(?,O(n^1))

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

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

and precedence

 empty .

Following symbols are considered recursive:

 {add}

The recursion depth is 1.

For your convenience, here are the satisfied ordering constraints:

     add(0(),  x;) > x               
                                     
  add(s(; x),  y;) > s(; add(x,  y;))
                                     

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