What happens to cat & dog hair that got mixed into my Compost box?

Does pet hair decompose in a reasonable amount of time in a compost heap, or does it take five years ...

I did a bad thing - my compost pile needed more "brown" (it was all fruit and vegetable and coffee grounds, so it needed more leaves, dirt, cellulose - forget what-all else this is). Then I had just cleaned a heap of dirt and leaves from in front of our apartment (our landlord doesn't keep it tidy). I put that into the compost and then discovered it has some litter (I'll try to pick out the cigarette butts and plastic etc) and also A LOT OF PET HAIR!