jump stop on catch

[hoopguy]

Player A1 receives pass from A2 with left foot on floor. A1 then jumps and lands on the floor with both feet simultaneously to to complete a legal jump stop. Now A1 decides to dribble but before dribbling he lifts one foot but the other foot remains on the floor until after the ball has been released from his hand. I believe this is legal since neither foot is the pivot foot on a jump stop. However, this seems to circumvent the traveling rule of lifting the pivot foot before releasing the ball from the hand on a dribble.

I believe the rule book should address this situation and clarify that this situation is legal or travel. Right now I believe it is legal but I feel like it is an unfair advantage to the dribbler. If not legal please explain.