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Despite the fact that terrorists may have state sponsors, it is still best to deal with the problem by treating the terrorists themselves as criminals to be prosecuted in the courts, and their state sponsors as adversaries to be dealt with via diplomacy.
In cases where you have an actual insurrection over political grievances, like Northern Ireland or Palestine, the only solution is to negotiate.
al-Qaeda does not fall into that category - they will not negotiate. But they can be isolated via diplomacy with their state sponsors, and through good police work to hunt them down. This business of invading and bombing countries where terrorists reside, besides being immoral and criminal, is also counterproductive.