Yes. I don't think we will ever be able to truly figure out the interaction between God and our cooperation - how one effects the other. After a certain point, we can only speculate. We do know that prayer is effective, and we do know that God has predestined the saved, so go figure...!
Regards
After a certain point, we can only speculate [jo]
Jo, read 2 Kings 20:1-6 or, for that matter, look at the word "repent." The Bible is full of references that show that God is moved to divine mercy by our prayers. That is not speculation. It has a lot to do with our intent. Remember, our salvation does not depend on how much we do and what we do, but how Christ-like we are when we do it, how empty we are of pride.
But most importantly, we may not ask for forgiveness and mercy unless we have forgiven those who trespassed against us, unless we have shown mercy. "Blessed are the merciful, for they will be shown mercy" (Mat 5:7), says the Lord, and "Be merciful, just as your Father is merciful." (Lk 6:36), always remembering that "judgment without mercy will be shown to anyone who has not been merciful. Mercy triumphs over judgment!" (Ja 2:13)