Yes, ARN can breed with IRN but it seems to me that you don't know enough about parrots in general and breeding in particular so I would highly recommend you don't. Breeding is not just a matter of putting a male with a female and 'allowing nature her course'. Nature does her own thing and does it very well but that is in the wild, not in captivity. When it comes to pet birds, breeding them is something that not only requires a lot of knowledge (about their physiology, calcium needs, problems that might happen to the babies even before they are hatched -humidity, temperature, parent feeding, etc- to handfeeding correctly -not as easy as people think! etc), it also prevents you from enjoying those birds as pets. All the psittacula species are aviary ones which require frequent and experienced handling to remain pets even when you have a single one so if you get the male to bond with the female and have babies, you will, pretty much, lose those two birds as pets because neither of them will ever like you again once they have each other.