There is a lot of discussion about the the wayward fighting for the marriage, more importantly, fighting for their spouse if R is to happen. What does that look like?
The seeds of your perception as to whether she is fighting for the marriage begin even before the initial discovery. Were you completely unaware and unsuspecting at the time of discovery? In my opinion, this would give your recovery a much better chance than if, for example, you had your suspicions prior to discovery, asked her about those suspicions, and were lied to. The more you were lied to before discovery about your later-confirmed suspicions, the harder it will be to believe her later, with a foundation of lies having already been built up by her.
Fighting for the marriage begins with the initial discovery. For one thing, right off the bat, it makes a huge difference in how you found out. Did she confess? And if so, was it out of wanting to repair the marriage (as opposed to, say, knowing that someone else was going to out her anyway)? If she confessed, it leaves less doubt that she does, in fact, want to save the marriage, as opposed to if you had to find out on your own, it leaves a lot of doubt that maybe she is just trying to reconcile because she has no better option at that time, that other man was not ready to take her on, that she was not financially ready, whatever.
If you did find out without her telling you, which seems to be the case here more often than not, was she immediately remorseful, did she immediately agree to do what was needed, did she immediately give you the whole truth? Did she try to blame you? Did she immediately and sincerely apologize? Someone who values the marriage and wants to stay in it, someone who truly loves you, will be honest and be accountable for their own actions, someone who is just looking out for their own interests may not be willing to immediately commit.
I'm not saying that these things can't be overcome later, but what I'm saying is that the longer it takes to get these things, the more doubt there will be, the less it will seem like she is fighting for the marriage, the more it will seem like she is just doing what she needs to do to preserve the marriage because the crumbs she gave you at first didn't work.
Did she willingly break off contact with other man or did you have to argue and insist and fight to get her to do it, if she did it at all? Did she come clean with all of the facts, or did you have to drag them out of her? It's best if she does it on her own without having to be asked, it's OK if you ask her to and she immediately agrees, it gets progressively worse the longer it takes and the more you have to argue with her about doing it with her resisting. THIS IS THE TIME that she can really show she wants to fight for the marriage. After this time frame, IF YOU ARE THE ONE WHO HAD TO FIGHT TO GET THIS FAR, in my opinion, it will be very difficult for her to show that she does, in fact, want to fight for the marriage. Because these are the main things that are important to you upon finding out about the affair.
To the extent that she continues to lie, minimize, and hide things from you, and you discover them or she finally confesses to them, these are signs of NOT FIGHTING for the marriage. How could you feel otherwise about still being lied to?
Also, to the extent that her story does not make sense, for example, a common story I hear is that it was sex "just one time" or "no sex, only a kiss" when the affair partners were together numerous times, this is not going to make sense, and it is going to feel like a lie (and it probably is a lie).
To the extent that she re-contacts the affair partner, or the affair partner re-contacts her and she doesn't tell you about it, and you find out on your own, it will feel like she is not fighting for the marriage.
To the extent that she tries to "protect" the affair partner, make excuses for the affair partner, continue to portray the affair partner as a "good" and "honorable" and "decent" person, it will feel that she is not fighting for the marriage.
All of this stuff is on a sliding scale. The more of it there is, and the worse she does it, the more you will have trouble believing ever that she is truly fighting for the marriage. The more she does willingly and voluntarily without being asked, or with being asked and not giving resistance, the faster you will heal.
In my opinion, a lot of this has to be done in the initial stages right after discovery. It can be made up for later, but the longer it takes, the more doubt there will be. I give anyone a lot of credit if they hang in and they are not getting these things, but I also question why they are willing to put up with it.
Assuming your wife had secret communications with the other man, did she offer you all passwords and access to all devices? Did she block him on Facebook and on her phone and on her email? Try to let you know where she is, especially at times of day she used for hookups with other man? Did she offer to combine her email account into yours so you could see all messages? Did she do what you needed to re-establish trust? My wife offered to delete Facebook entirely and to get a cell phone with no texting. I have kids and those are avenues of communication that are used for school and activity related communications, so it was not practical for us, but I appreciated that my wife offered and took that as a good sign that she wanted to make me feel safe in the relationship, it showed me that SHE was actually actively thinking of ways to fix things, and it wasn't all just me.
After this initial phase, where all the truth is out, contact has ended, accountability for the affair has been accepted, then it just comes down to doing things that will help you heal.
I am over two years out and consider myself reconciled. Here are some things my wife did, either on her own, or with me asking just once with no resistance: Got rid of anything that I said reminded me of the affair, for example, there were "songs" she and other man had, she owned the CDs and liked this music prior to the affair, used to listen to this stuff all the time prior to the affair but also especially during the affair. Since the affair was discovered and I mentioned how those songs were a trigger to me, she took all of those CDs and threw them in the trash in front of me. If that music comes on the radio in the car, she changes the channel, if I say it's OK I'm over it you can listen to that stuff again, she says no, the thoughts of those songs disgust me now. That's just one example, but whatever my triggers were, if she could, she took some actions to alleviate them, usually unprompted by me.
I used to tell her during the first year or so afterward things like, "I don't trust you" and "Whatever you're doing it's not enough, I've got one foot out the door, you better step it up." She would only reply with something like "I'm sorry I hurt you and I will never forgive myself and I will spend the rest of our marriage making it up to you."
There was another thread on here somewhere about financial restitution for money spent on other man, personally, it's not something that would help me, but if she spent money on other man and is willing to downsize her car or sacrifice something else she normally would spend money on for herself in order to make amends, that is something else to consider as a way of fighting for the marriage.