I recently returned to HP! *confetti*

And as I sorted through my fourth generation GSP lines, I began wondering if I'd accidentally bred the wrong lines together, causing some inbreeding, but I'm not totally sure. :P

So I figured I'd ask.

My first generation pair had two puppies, that produced beasts of no nation and in cold blood (so I have siblings)

As I initially began training them I purchased two dogs from the store to pair with them for the next breeding, therefore the store dogs have no connection to the first generation lines. 

I breed the first pair (beasts of no nation x store) and got a boy, then I bred the second pair (in cold blood x store) and got a girl. Now I realize I've bred the girl pup and that boy pup from both lines together. They have the same grandparents, but not the same parents, is that inbreeding?

Welcome back! :).

Technically I would say yes, because the grandparents in the line are the same. However, it's not inbreeding that is direct enough to be caught by the game's inbreeding filters. I would have to know their ID's and check to be sure, though. I'm pre-coffee over here! Haha.

 most people would consider it inbreeding because the same parents show up more than once in the pedigree http://horsephenomena.com/dogs.php?id=92634&lineage=true

★ Like a drum, baby, don't stop beating★

what Tera said. if they have the same lines anywhere most people consider it inbred but it does happen sometimes. especially with say AQHs they are shared so much you lose track and you get some same horses going far down the line.  

And with Arabians, too! The linebreeding in some of the strains is insane

And this is a pretty tame example...