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