Moot point. North Korea is indulging in some saber-rattling, but a new full-scale war on the Korean Peninsula would be absurd. (North Korea would be utterly destroyed in short order, for one thing.)
North Korea is saber rattling, for sure. I'm reminded of World War 1 though when Austro Hungary was basically saber rattling against Serbia. Then the Russians mobilized because they were basically saber rattling. Then the Germans mobilized to face Russia. Then a month later we had World War 1. Which everyone had been preparing for but which no one really wanted to fight. Escalation sometimes happens in spite of best intentions.
I'm not quite so sure I believe the "utterly destroyed" part unless we were to go massively nuclear. We would probably have air superiority, but maybe not if North Korea can damage runways in the South consistently and keep our aircraft carriers backed off to less efficient ranges. Iraq 2 showed us that air campaign alone won't defeat an enemy.
North Korea probably wouldn't invade unless it had nuked a major part of the South Korean/US military, or popped a nuclear weapon off above South Korea and destroyed military electronics with EMP to "level the playing field". But I don't think South Korea and the US would be keen on invading North Korea either. It's a small country, but also densely packed. You either drive up the right side of coast line, or the left side coast line. The mountains will hinder most other movement thru the center. Other than walking of course. Also we don't know what China would do if we invade North Korea. They don't want a US and South Korean base on the Yalu River. We, I know, don't want to go toe to toe with China. If they say they can hit a US city with a nuclear weapon, they aren't blowing smoke.
I think it would mostly stay conventional as a war, unless N.K. get desperate and decides to launch one after getting pounded for a while. Because it would be conventional though I think that it could last for a few months at a minimum. Iraq 1 took over six months to get ready but was over quickly. Iraq 2 took less time to get ready but took 3 weeks to fight. I would think North Korea would take at least a couple of months if not longer to fight. More if China supplies it with material to keep the war going. Frankly, if I were Chinese, I'd fight to my last North Korean to defend China's border.
During this whole time though I think we'd be shipping US ammo production to South Korea, Japan, and US forces.