] Is there an example of a
] non-state terrorist organization that has lost and gone away?

not that I know of

Actually yes the Baader-Meinhof / Red Army Faction they were either captured or killed. I am not too familiar with the details. However the important difference between them and Al'Q is that at the time communism was a living social experiment. Yet it was a dying meme (intentional pun, a social experiment that cost millions of lives). West German democracy survived and defeated them although how much physical support they had from the Soviet bloc I honestly don't know. Radical Islamism is very much a thriving meme. Al'Q as it's military wing, the symbiosis of extreme violence as a meme and radical Islamism as a meme, must be decommissioned.

In Northern Ireland we have had long discussions about decommissioning, the IICD (Independent International Commission on Decommissioning) led by General John de Chastelain has worked long and hard to the find agreement and monitor the process of destroying the IRA's guns and bombs.
I heard what I regard as one of the most intelligent observations about the whole issue of decommissioning. Physically destroying the IRA's semtex and guns isn't the point because they can always get more. What you must decommission is the will to use those weapons in the first place. An IRA bomber will always know how to build a bomb but if they have no desire to build bombs and kill, then voila. It is like the NRA's argument guns don't kill people, people kill people and it has the same flaws (a terrorist who only has access to knives can kill people but a terrorist who has access to nuclear weapons!).
Decommissioning
1 You can kill them with the danger that they become martyrs for the cause.
2 You can capture them, put them in prison and make them political prisoners. They might go on hunger strike like Bobby Sands and become martys ( he ran for Parliament, was elected and died. You can execute them (see 1).
3 You stop them wanting to bomb and destroy. You decommission their will to do so.

Al'Q - I do not believe that 3 is a realistic option for the senior hierarchy of Al'Q. They must be captured or killed. I believe this war will last at least a generation and I believe the secret of success is through 3. Stopping the agressive and war like posturing of the US administration which creates militants on both sides. In civil wars it is the collapse of the center ground which is one of the key stages. Look at the French revolution or the events which led to the English Civil war. It was the collapse of the center and the rise of the militants; the creation of two armed camps.

We will win this war. We have a working model of how to run a society and a civilisation which is far more credible than Al'Qs. They offer only medievalism, tyranny and oppression.
The key is to win the hearts and minds of the Muslim World by demonstrating the moral, political and economic superiority of the Western liberal model.
By reverting to a trench mentality we only increase the dichotomy in the Muslim world between the radical Islamists and the pro-Western elements, which can be seen so clearly in Bin Laden's own family.

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