The 2015 UC PPS dog on your side is a fair swap for a 2015 UC chicken on their side.
A 2013 UC is worth about 16 2015 commons (this is my way of doing rarity math, so this is based off of my opinion).
They have enough commons for one of your 2013 UC. The two 2016 C chickens is fair for your 2015 C dog. 4 2014 C + the 2014 UC on their side is enough for the other 2013 UC on your side. The two 2014 C on their side is equal to a 2013 common on your side.
They ran out of pets to equal to your side.
So they are unfair.
Unfair to you.
2 2015 rares = 1 2014 rare
2 2016 rares = 1 2015 rare
They aren't adding up to a 2013 rare even with the unknown rarity