Present Perfect in reported speech

The Present Perfect (the other perfect tenses too) is a really confusing tense, on one hand there is not doubt that it belongs to the family of the present tenses, on the other it often refers to the past.

I have found my cat! It was on the tree.

That brings us to the question of how the sentence behaves when introduced by the Present Perfect in the reported speech.

• They said they wouldn't come to my party.
• They've said they _______ come to my party.

Do you know what the answer is?  The answer is: won't. So, it is the same way as it would be with a present tense!

• They say  they won't come to my party.

NOTE: It doesn't mean that present tenses and perfect tenses always behave the same because they are still affected by the reported speech.

"I haven't seen him for 20 years"

• He said he hadn't seen me for 20 years.

"I don't see anything wrong about it"

• He said he didn't see anything wrong about it.