We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^2)).

Strict Trs:
  { exp(x, 0()) -> s(0())
  , exp(x, s(y)) -> *(x, exp(x, y))
  , *(0(), y) -> 0()
  , *(s(x), y) -> +(y, *(x, y))
  , -(x, 0()) -> x
  , -(0(), y) -> 0()
  , -(s(x), s(y)) -> -(x, y) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(n^2))

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

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

and precedence

 exp > * .

Following symbols are considered recursive:

 {exp, *, -}

The recursion depth is 2.

For your convenience, here are the satisfied ordering constraints:

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

Hurray, we answered YES(?,O(n^2))