Order doesn't matter really. The first ability to take place is the one that is not cancelled.
ab: +2 damage // bo: stop ability ----- vs, ----- ab: stop bonus // bo: nothing
+2 damage takes effect, as the stop bonus get canceled by stop ability
ab: +2 damage // bo: stop bonus ----- vs, ----- ab: stop ability // bo: stop bonus
+2 damage doesn't take effect, as right's stop ability cancels left's, thus right's stop bonus can take effect
Here's the thing, primarily, everything ios placed on a table, where it is reviewed which one is stopped.
Momento Mori(took me a while to remember that Stand alone complex episode) displayed the process.
the thing is, if you have an Ability, stop bonus, and your opponent has a bonus, stop ability, then it doesn't matter which one goes first. but if you have a bonus, stop ability, and your opponent has a bonus stop bonus, then the table shows...
A = +2 life per damage
B = Stop Opp bonus
A = -2 damage min 1
B = Stop opp Ability
then it is accessed, and it marks off an X where abilities are canceled.
so, even if initially, the Card one Ability is canceled due to the computer reading card two first, it is re activated once card one is read, canceling card two bonus, then card two is read again, and card one is reactivated.
yargh, the question gets posed a whole lot... but the truth is, it works, whatever way they have it set up, so therefore this question is pointless.