TRS:
 { 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)),
     double(x) -> +(x, x)}
 POP*:
  Precedence:
  double > +, 
  double > s, 
  + > s
  empty
  
Normal:
   pi(+) = [1,2], pi(double) = [1]
  
Safe:
   pi(s) = [1]
  
Predicative System:
   {  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;)),
        double(x;) -> +(x,x;)}
  Qed