One thing I have noticed about greyhounds, is that they often have very distinctive and different rituals around the evacuation of their bowels. All three that we have owned had their own unique quirks.
Oliver, our first greyhound, needed a difficulty factor. Preferably a steep slope, and some loose gravel. I assume that he was going for both the toughness of getting in position and then for the potential for his stools to roll downhill. But he was maniacal about it.
Garrett, has to find the right spot. He gets a special gait to his walk so we know that he is getting close, then it will be back and forth 4 or 5 times to find the right location and he does the butt scrunchies.
Tate on the other hand, has to find shrubbery or bushes to stick his head into. He will search (and hold his colon) all walk long until he finds the right kind of bushes. Then he has to try several before the right combination of head in the bush is found, and he defecates.
The other dogs I have owned? No such oddities. They did their business when they needed to do their business, no drama.