Honestly, if you treated her bad enough that she cheated on you, she's probably not in a position where she wants to take you back. Has she ever contacted you and expressed her desire to get back together, possibly? If the answer is no, then she has likely moved on.

Unfortunately I know of a few guys in your situation. Screw things up with the best thing they ever had and don't realize it until later. I've not yet seen one of these guys get their ex gf back. Mostly because after you break up, the girl will usually realize how much better her life is without you. No offense.

All you can do in this situation is learn from your mistakes. If you're a good guy, you'll meet another nice girl at some point. When you do, just remind yourself of all the things you did to mess up the last one, and don't do it again.

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Live as if you were to die tomorrow. Learn as if you were to live forever. - Mohandas Gandhi