If there is a Rest in Peace on the battlefield and I activate Helm of Obedience's ability with X=1, my opponent's entire library will be exiled.

And then what? Helm of Obedience's ability doesn't say to repeat the process until they become unable to mill any more cards, it says to repeat the process until a certain number of cards have been put into the graveyard. If the entire library is gone but still no card has been put into the graveyard, it doesn't mean the process can stop. It will keep going forever, causing the game to end in a draw, right?

Considering the way Helm of Obedience has been used in legacy tournaments since as far as I can remember, this has got to be wrong. But someone is going to have to explain to me why, exactly. There has got to be some rule I'm not finding that causes the process to stop, right?

Thanks in advance. :)