Does Slow Running Count?

When you run really slowly, does that count as running? Before answering, I want to clarify my query. I'm talking about running at 13:00 minute per mile pace. And that's the actual "running" part of the session. I may walk some hills and also walk the beginning and end of the "run" too. Overall the pace might be more like 14:00 or 15:00 minute miles. I suppose it technically is still a run since both feet are off the ground during the running gait cycle (is that the definition of running?). In walking, one foot is always on the ground. Hmmmm....my heart rate the last two days during these very slow jogs has been about 110. That's a pretty easy "run." Coach Jeff says these count just like any other run or hike or sprint. Of course, Jeff is the one I'm "running" with on these easy jogs! What do you think?

I'm all in favor of slow distance running...like the Arthur Lydiard or Phil Maffetone or Ernst Van Aaken training methods of the past. Usually during those Lydiard easy runs my heart rate is still elevated into the 120-150 range. My pace might be slow, but it's still what I would consider "running." Maybe a 9:00 pace or so on the trails. At some point my slow jogging heart rate may be the same as sitting on a couch watching an exciting soccer match (yes, there is such a thing!). Does that count as running?