TRS:
 {  sum(0()) -> 0(),
   sum(s(x)) -> +(sum(x), s(x)),
   +(x, 0()) -> x,
  +(x, s(y)) -> s(+(x, y))}
 LMPO:
  Quasi-Precedence:
  sum > +
  empty
  
Normal:
   pi(+) = [2], pi(sum) = [1]
  
Safe:
   pi(+) = [1]
  
Predicative System:
   {  sum(0();) -> 0(),
    sum(s(x;);) -> +(s(x;);sum(x;)),
       +(0();x) -> x,
     +(s(y;);x) -> s(+(y;x);)}
  

   
  

  Qed