MAYBE
MAYBE
TRS:
 {
      min(x, 0()) -> 0(),
      min(0(), y) -> 0(),
  min(s(x), s(y)) -> s(min(x, y)),
      max(x, 0()) -> x,
      max(0(), y) -> y,
  max(s(x), s(y)) -> s(max(x, y)),
        +(0(), y) -> y,
       +(s(x), y) -> s(+(x, y)),
        -(x, 0()) -> x,
    -(s(x), s(y)) -> -(x, y),
        *(x, 0()) -> 0(),
       *(x, s(y)) -> +(x, *(x, y)),
          f(s(x)) ->
  f(
   -(
    max(*(s(x), s(x)), +(s(x), s(s(s(0()))))),
    max(s(*(s(x), s(x))), +(s(x), s(s(s(s(0()))))))
   )
  )
 }
 DUP: We consider a duplicating system.
  Trs:
   {
        min(x, 0()) -> 0(),
        min(0(), y) -> 0(),
    min(s(x), s(y)) -> s(min(x, y)),
        max(x, 0()) -> x,
        max(0(), y) -> y,
    max(s(x), s(y)) -> s(max(x, y)),
          +(0(), y) -> y,
         +(s(x), y) -> s(+(x, y)),
          -(x, 0()) -> x,
      -(s(x), s(y)) -> -(x, y),
          *(x, 0()) -> 0(),
         *(x, s(y)) -> +(x, *(x, y)),
            f(s(x)) ->
    f(
     -(
      max(*(s(x), s(x)), +(s(x), s(s(s(0()))))),
      max(s(*(s(x), s(x))), +(s(x), s(s(s(s(0()))))))
     )
    )
   }
  Fail