MAYBE
Trs:
 {          bits(x) -> bitIter(x, 0()),
          inc(s(x)) -> s(inc(x)),
           inc(0()) -> 0(),
         zero(s(x)) -> false(),
          zero(0()) -> true(),
            p(s(x)) -> x,
             p(0()) -> 0(),
   if(true(), x, y) -> p(y),
  if(false(), x, y) -> bitIter(half(x), y),
      half(s(s(x))) -> s(half(x)),
       half(s(0())) -> 0(),
          half(0()) -> 0(),
      bitIter(x, y) -> if(zero(x), x, inc(y))}
 Comment:
  We consider a duplicating trs.
  FAIL:
   Open