Zero, One, or Two

I Two wiener dogs and their owners so proud Approached each other right there on the green. Then, the hounds commenced at yapping so loud. But that wasn’t the dangdest thing I’d seen. One of them’s front bit the other one’s butt. At once, the other one’s front did the same. This baffling case was not open and shut. Those who saw it didn’t know who to blame. I can’t believe what I saw on the lawn, Because it all happened there so neatly. In an instant, both yaps and dogs were gone - They had devoured each other completely. II Don’t listen to that fool - I’m his brother. I saw the wieners who had no muzzle. He tells the wrong stumper, there’s another - Quite a different confounding puzzle. One ‘et t’other, while t’other et the one. Which was out, which was in, no man could tell, But there remained but one, not two or none. One endured; one, a sadder fate befell. III Don’t listen to them, I’s little sister. I saw what really happened, if you please. There warn’t none, nor one, but two left, mister, But uncommon strange, they switched identities.