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Is forgiving someone who doesn't regret beneficial for you?
Yes, forgiving someone gives closure and you'll stop thinking about the unpleasant situation.
Sometimes you also need to forgive yourself for past mistakes. In this sense, forgiving the other person allows you to take a step forwards and start forgiving yourself.
As long as someone isn't forgiven, whatever transgression was made will be considered unresolved subconsciously, leading people to uncontrollably obsess about it.
If there are situations in your daily life that trigger bad memories, you will still be unwittingly reminded of the situation.