YES(?,O(n^2))

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

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

and precedence

 double > + .

Following symbols are considered recursive:

 {double, +}

The recursion depth is 2.

For your convenience, here are the satisfied ordering constraints:

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

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