First, you must determine that it is a pass not a shot. If it is a shot attempt, regardless of whether or not it hits rim, it is still a shot attempt and there is no violation even if the same player catches it.
If it is clearly a pass, then you have one of three scenarios.
1)A1 has not used dribble, tosses ball in air, runs to where ball has hit the floor, and starts a dribble with one hand off the bounce - Legal - the toss becomes the start of the dribble.
2)A1 has used dribble, picked ball up, and then did the same thing as in 1. Violation - double dribble, as A1's toss started a dribble again and he had used his dribble.
3)A1 has or has not used his dribble, tosses ball in air, takes two or more steps to retrieve, catches ball. Travel. A1 has moved both feet without dribbling or shooting the ball. I could also make a travel out of taking 1 1/2 steps and catching then dribbling, but that's another unlikely scenario that I don't want to explore right now
