MAYBE
Trs:
 {       plus(0(), y) -> y,
        plus(s(x), y) -> s(plus(x, y)),
         plus(x, 0()) -> x,
   quot(0(), s(y), z) -> 0(),
  quot(s(x), s(y), z) -> quot(x, y, z),
   quot(x, 0(), s(z)) -> s(div(x, s(z))),
        times(0(), y) -> 0(),
     times(s(0()), y) -> y,
       times(s(x), y) -> plus(y, times(x, y)),
          div(0(), y) -> 0(),
    div(div(x, y), z) -> div(x, times(y, z)),
            div(x, y) -> quot(x, y, y)}
 Comment:
  We consider a duplicating trs.
  FAIL:
   Open