You're not cheating. You're not the one in the relationship. In all fairness, you are not to blame or culpable in sharing blame with a cheater. It's not your fault that she's cheating.
However....
That doesn't mean that what you're doing doesn't make you a dick, or possibly even an asshole. That's not a dig, it's just an honest appraisal of the situation.
As far as morals go, that's a personal decision. Consider how you'll feel about it when it's all over.
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