Reminds me very much of Braid! The concept of controlling two "lives" at once and having one work in tandem with a real-time "recording" of the other is pretty cool, though it does get confusing when one of the "lives" I was in control of duplicates itself, runs forward just as I did before and grabs a key before I can!
Also, since it takes a while to figure things out and execute on plans as the duplicated player recording plays out, this means a lot of waiting for events to play out before the other "life" can execute the second part of the intended plan (i.e. one "life" waiting to catch the key that's eventually going to be thrown from above by the other "life")
Hope my description doesn't tie your brain in knots! (Though then again, that's the good hallmark of a promising puzzle game imo)