TRS:
 {       norm(nil()) -> 0(),
       norm(g(x, y)) -> s(norm(x)),
         f(x, nil()) -> g(nil(), x),
       f(x, g(y, z)) -> g(f(x, y), z),
       rem(nil(), y) -> nil(),
   rem(g(x, y), 0()) -> g(x, y),
  rem(g(x, y), s(z)) -> rem(x, z)}
 POP*:
  Precedence:
  norm > 0, 
  norm > s, 
  f > g
  empty
  
Normal:
   pi(rem) = [1,2], pi(f) = [1,2], pi(norm) = [1]
  
Safe:
   pi(g) = [1,2], pi(s) = [1]
  
Predicative System:
   {       norm(nil();) -> 0(),
         norm(g(;x,y);) -> s(;norm(x;)),
            f(x,nil();) -> g(;nil(),x),
          f(x,g(;y,z);) -> g(;f(x,y;),z),
          rem(nil(),y;) -> nil(),
      rem(g(;x,y),0();) -> g(;x,y),
    rem(g(;x,y),s(;z);) -> rem(x,z;)}
  Qed