Daisy is not above chasing any cat that will run, but Tweedle Dum was not about to give her the satisfaction. He was, however, quite wary of her attentiveness.
Aw! That's a good picture. I had a cat who my dogs would only chase if she ran. They would sit on the sofa together or in the garden, but the minute she ran or jumped the fence, the dog would bark and chase. She lived to ripe old age so no stress caused to her!