MAYBE
Trs:
 {    -(s(x), s(y)) -> -(x, y),
       -(0(), s(y)) -> 0(),
          -(x, 0()) -> x,
    div(s(x), s(y)) -> if(lt(x, y), 0(), s(div(-(x, y), s(y)))),
        div(0(), y) -> 0(),
        div(x, 0()) -> 0(),
     lt(s(x), s(y)) -> lt(x, y),
      lt(0(), s(y)) -> true(),
         lt(x, 0()) -> false(),
   if(true(), x, y) -> x,
  if(false(), x, y) -> y}
 Comment:
  We consider a duplicating trs.
  FAIL:
   Open