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)),
              p(s(x)) -> x,
         f(x, y, 0()) -> max(x, y),
         f(x, 0(), z) -> max(x, z),
         f(0(), y, z) -> max(y, z),
  f(s(x), s(y), s(z)) ->
  f(
   max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))),
   min(s(x), min(s(y), s(z)))
  )
 }
 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)),
                p(s(x)) -> x,
           f(x, y, 0()) -> max(x, y),
           f(x, 0(), z) -> max(x, z),
           f(0(), y, z) -> max(y, z),
    f(s(x), s(y), s(z)) ->
    f(
     max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))),
     min(s(x), min(s(y), s(z)))
    )
   }
  Fail