TRS:
 {  sum(0()) -> 0(),
   sum(s(x)) -> +(sum(x), s(x)),
   sum1(0()) -> 0(),
  sum1(s(x)) -> s(+(sum1(x), +(x, x)))}
 MPO:
  Prec:
   sum > +, 
   sum1 > s, 
   sum1 > +
   empty
  Strict:
   {}
   Weak:
    {}
  Qed