Hi RA,
Pretty often you would get new "insurgencies". But I honestly don't see why you would expect anything else . Maliki is exercising the sovereignty inherent in his position, and the MNF doesn't have sovereignty in Iraq - nor are they under Maliki's command and/or control. In game theoretic terms, this is a multi-player version of the Prisoner's Dilemma with one player (the MNF) having a de facto "get out of jail free" card.
I don't see why you characterize them as "difficult to comprehend". Really, they stem from the structures imposed on Iraq. If a confederate system had been constructed - the tri-partite split - you would have had a different set of structures and different forms of insurgencies.
I think you do have a very valid point when you note that the government and the counter-insurgents (by which I assume you mean the MNF) goal are different. But I certainly don't find this surprising - it's totally predictable from the way the initial Phase IV was (mis-)handled. In the post-Westphalian construction of the state, a model that was an assumption of the architects of the invasion, such a conflict is inevitable since the MNF does not hold sovereignty.
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