Can a rooster eat a dog?

This is a personal dilema that you need to figure out yourself. However, here are some questions that you should think about -

• Will the dog continue to eat my livestock/pets?

If so, you should take measures to prevent this. You don't have to put the dog down, but you can sell him, get rid of him, etc

• Is the dog a threat to other peoples livestock/pets?

If so, you need to take preventive measures so your dog cant ruin other peoples lives by destroying livestock or killing pets. Get a fence, keep him inside, use a leash, etc.

Also, remember that is natural to a dog to chase/kill small prey animals such as chickens. He is doing what seems right or natural to him.