When I take the feat Greater Bull Rush (http://www.d20pfsrd.com/feats/combat-feats/greater-bull-rush-combat---fina l) and Bull Rush an opponent out of an ally's threatened square, do I have to push my opponent more than 5 feet (beat his CMD by 5) for the opponent to provoke an attack of opportunity for my ally? It seems unclear to me whether or not that would count as a 5-foot step for my opponent, thus avoiding the attack of opporunity. Let me illustrate:
P=Player (the one doing the Bull Rush with Greater Bull Rush feat)
A=Ally
O=Opponent
X=Empty square
a) Bull Rushing opponent 5 feet
XXX -> XXX
XAX -> XAO
XXO -> XXX
XXP -> XXP
Would this trigger an attack of opportunity from my ally? Or would I have to:
b) Bull Rushing opponent 10 feet (beating opponent's CMD by 5)
XXX -> XXO
XAX -> XAX
XXO -> XXX
XXP -> XXP
Does only this trigger the attack of opportunity from my ally?
I haven't found any sources on whether or not one can make a 5-foot step on someone else's turn, as the opponent would do in case a) for the attack of opportunity not to trigger. I think this also raises another question: is all 5-feet movement 5-foot steps, or is the 5-foot step a specific action that you can only do on your own turn?
Also, if case a) doesn't provoke AoOs, has the opponent spent 5 feet of his movement that round?
In addition, it would seem to me that if case a) doesn't provoke attacks of opportunity, that the Greater Bull Rush feat is quite weak, as you would have to beat the opponent's CMD by 5 every time to get the attacks of opportunity off (especially considering that the player doing the Bull Rush does not get an AoO himself).
What do you think? Please link sources.