Thanks to Andrei, from the latest Tool Army newsletter:

Something that might be encouraging to some Tool enthusiasts is that while riding with Danny to Chili John’s yesterday, I heard a lot of new Tool music (sans Maynard). This was the most new material that I’ve heard so far, although a few of the riffs and arrangements were familiar. So, what did I think? Dare I say that it sounded like… Tool (some of it reminiscent to earlier Tool stuff, with other parts pushing the envelope), and I assume that it will sound even more like Tool once the vocal melodies, etc. have been added. To answer your next question, I cannot say how far along in the writing process the band is. If I had to GUESS, I would say more than half way (and keep in mind that in the past, at least, the writing went faster once the first few [more complex] songs were finished).