TRS:
 { not(true()) -> false(),
  not(false()) -> true(),
      odd(0()) -> false(),
     odd(s(x)) -> not(odd(x)),
     +(x, 0()) -> x,
    +(x, s(y)) -> s(+(x, y)),
    +(s(x), y) -> s(+(x, y))}
 POP*:
  Precedence:
  not > true, 
  not > false, 
  odd > not, 
  odd > false, 
  + > s
  empty
  
Normal:
   pi(+) = [1,2], pi(odd) = [1]
  
Safe:
   pi(s) = [1], pi(not) = [1]
  
Predicative System:
   { not(;true()) -> false(),
    not(;false()) -> true(),
        odd(0();) -> false(),
      odd(s(;x);) -> not(;odd(x;)),
        +(x,0();) -> x,
      +(x,s(;y);) -> s(;+(x,y;)),
      +(s(;x),y;) -> s(;+(x,y;))}
  Qed