I suspect our heavily doctrinal approach to sequential phases for operations causes us to mirror image that onto Mao's three phases. The key is to understand the fundamental principles of insurgent warfare, but to always remember that there are no rules, no timelines, no movement sequentially through phases. Success can occur in any phase for the insurgent, and he is always seeking success, not the next phase.
The phase just helps understand what he is doing to succeed, not what he must do next to succeed.
Good COIN is like good yard work. No matter how great your yard looks on Saturday afternoon when you've just "finished" and put your tools away, it will start to look ragged in a few days without constant maintenance. It is not a failure of the yard that causes this to occur, it is the nature of things. One can blame the sun, the rain or invading insects, but they too are part of the natural process that one is attempting to "control" through their gardening efforts. Virtually every Gardener understands this, yet virtually every politician for some reason does not.
Here is a chart I've put together that tries to capture the essence of what I believe to be the essence of insurgency:
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