<human>: Summarize the given text in a few sentences.

Throwaway for obvious reasons.  I met my girlfriend in Europe 2.5 years ago, as I travel a lot for work.  We hit it off right away and began dating.  About a year ago, I started questioning things as I was going to be spending more time in the US again and we discussed briefly ending the relationship.  I actually thought it might be a reasonable choice to start an open relationship rather than ending it.  After a few discussions, we decided to do that, we had an open relationship for one year.

I then met someone while I was at work in the US and we started a semi casual sexual relationship.  As per our agreement, I didn't tell my girlfriend as she did not want to know if I met someone or had a sexual relationship.  As I was getting ready to head back to Europe, I ended the relationship in the US and my girlfriend and I decided an open relationship was not for us anymore.  I disclosed to her my sexual relationship and she had one as well.

Things were going great, I was going back and forth between the US and Europe and I thought our relationship was going great.  I felt really bad defriending the  other girl on facebook and decided to add her again behind my girlfriend's back and without her approval.  She found out and blew up on me and I then removed her as a friend again.

A few weeks later I caught her talking to another guy via text message and suspiciously deleting their previous conversations.  I confronted her and she promised to block him right away.  I then caught her continuing to talk to the guy, but she changed his name to a girl's name in order to get away with it.  She uses my friending of the other girl as her rationale for this behavior.  She insists to me nothing happened with the guy, but how am I to know for sure?

I do really like her, I'm just at a lost as to what do from this point.  I'm considering leaving her or talking to her again about having an open relationship.  Am I a fool for considering staying with her?
<bot>: GF and I have had an exclusive/open/exclusive relationship but I'm not sure if she respects the exclusive part, where do I go from here?