I agree with Rat. Once a cheater....you know the rest of that mantra. The truth is anyone can change, but she has showed that after years of dedication, that she could turn her back on you in the worst way. You try to win her back like it's your fault, it's NOT! YOU should've been the one to walk away and kick that cheater to the curb. Anyone who does that to you does not respect you at all! If there's issues in the relationship, someone who cares/loves you will take the time to talk/council/TRY to work things out. A mature partner who decides that things have to end, WILL end it before being with someone else when she so obviously didn't.
Now she realizes the error of her ways, (or perhaps whoever she was with backstabbed her so she knows how it feels) and is asking you to take her back. She's basically saying "I know I f*'d you over, but let's try it again. The worst that can happen is I f*k you over twice." What do you want?
3 out of 2 people have problems with fractions.