Should I give up on my wife?

A month ago a busted my wife spending time with another man, I promptly left. We started talking again and we are slowly trying to work things out. A friend of mine told me on her facebook page her status was in a relationship with the guy I busted her with. She claims he is out of the picture but I do not believe her. Should I just let this run its course and see if it can work or should I just file the papers and move on with my life? My heart says one thing but my head says the other.