MAYBE
Trs:
 {    min(0(), y) -> 0(),
  min(s(x), s(y)) -> s(min(x, y)),
      min(x, 0()) -> 0(),
        +(0(), y) -> y,
       +(s(x), y) -> s(+(x, y)),
        *(x, 0()) -> 0(),
       *(x, s(y)) -> +(x, *(x, y)),
      max(0(), y) -> y,
  max(s(x), s(y)) -> s(max(x, y)),
      max(x, 0()) -> x,
    -(s(x), s(y)) -> -(x, y),
        -(x, 0()) -> x,
          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()))))))))}
 Comment:
  We consider a duplicating trs.
  FAIL:
   Open