As Zues said, what exactly does "giving up" look like?
The real kicker with this DB stuff is that no matter what, to move on from this in a healthy manner, you need to go through the same steps anyway.
So I'd recommend to detach emotionally as you can. Then move forward with how you want to live without focusing on him or R. If you want to burn the bridge behind you as Huddy suggested, fine... But I think you move forward with YOU. When he is interested in R, then you can deal with all the "stuff" going on now.
