[stared]

IMHO you are absolutely right. I would add that also it mixes reading from left to right with from right to left (think: P(b|a) P(a)). Personally, I really dislike that it made the trend that we use:

v_after = A_3 A_2 A_1 v

not (what I would consider more straightforward)

v_after = v A_1 A_2 A_3