Maybe I just don't get the question. You do the first quarter move of A9 and get pure comm. Now you can figure out cycle direction and do the rest.
I do the pure version completely differently though.
UBL>DFL>DBL
A9: y U2 L2 U' R2 U L2 U' R2 U' y'
Pure w/ setup: U y x' R2 U' L' U R2 U' L U x y' U' making it a 10 mover.
With [U L2 U':R2] the pieces are moving in ways I'm not used to. Here's my logic/procedure for pure if it helps:
The 3 pieces are like a chain. With either 1 or 3 moves, corner 1 can swap with corner 2, and corner 2 can swap with corner 3. Corners 1 & 3 may or may not be able to swap, but it's irrelevant because there is no need to identify their connection. The position of the buffer in the chain determines what order to swap.
Buffer in position 1 (CP: move C first to Buffer, then move P to C)
Buffer in position 2 (IB: move B first to Buffer, then move I to Buffer)
Buffer in position 3 (PC: move P first to C, then move C to Buffer)
Basically, position 2 moves the second letter first, and the other cases are normal.
This is just the pattern I saw when learning Pures, and A9s don't fit into it. I can't tell based on the position of the buffer and the order of the letters whether to start with a quarter turn or a half turn. I presume I'm thinking about it all wrong and curious how others handle it.
