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