YES(?,POLY)

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

Strict Trs:
  { add(0(), x) -> x
  , add(s(x), y) -> s(add(x, y)) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,POLY)

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

 safe(add) = {2}, 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(?,POLY)