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