TRS:
 {                  ge(x, 0()) -> true(),
                 ge(0(), s(y)) -> false(),
                ge(s(x), s(y)) -> ge(x, y),
                 minus(x, 0()) -> x,
                 minus(0(), y) -> 0(),
             minus(s(x), s(y)) -> minus(x, y),
                     id_inc(x) -> x,
                     id_inc(x) -> s(x),
                    quot(x, y) -> div(x, y, 0()),
                  div(x, y, z) -> if(ge(y, s(0())), ge(x, y), x, y, z),
       if(false(), b, x, y, z) -> div_by_zero(),
  if(true(), false(), x, y, z) -> z,
   if(true(), true(), x, y, z) -> div(minus(x, y), y, id_inc(z))}
 Fail