Is it really worth it to try and save this relationship?

My now ex-girlfriend and I got into a fairly major argument this last week. We'd been together for a year and a half, and she was everything to me, but this last argument was basically an extension of things I had brought up in the past, and had only gotten worse.

I'm so tired or arguing about the same things over and over, and being told that they will work to correct the problem, only to have it come back worse than before a few months later. After arguing for the better part of a week and not getting anywhere I decided to end the relationship.

Now over the weekend she's come back and said that she's willing to work harder on these issues and wants us to restart our relationship, but she doesn't trust me anymore because I ended the relationship. This is understandable since I'm the one that ended things, but I'm not sure if I want to invest any more time into this if I can't trust that she is really going to work on these issues like she's said.

My question is, should I put the time and energy into gaining her trust again if I'm having trouble trusting her too? I've brought it up to her that I'm having trouble believing that she's really willing to work the issues that have been the center of most of our arguments, but she remains firm that I'm the one that has something to prove to her.
Is it really worth it to try and save this relationship?
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