I wonder if the logic breaks down here:
The American Indian knew they were outnumbered by the white population. "White man is like the buffalo -- endless numbers".
The Islamist believes Muslims outnumber (or soon shall, "god" willing)the Infidels. They will fight on.
No strategy will defeat the Islamists. All we can do is hope to manage them. Even a "scorched earth", "glass parking lot" policy won't defeat them. They are with us until the end times.
In the line of work I do, I have said that "I'm in this fight until the last terrorist is reduced to a puff of pink mist". And I know I'll still be saying that when I'm 89, should the Lord tarry.
They can be defeated. They have been defeated before. If they are not defeated this time, it will be because Western Christendom surrendered.
General Crook's historical example has some application against hostile Pashtuns in Afghanistan and Waziristan. Success there will not end the Global War On Terror, but it wouldn't suck.
We defeated Islamic extremists in the Moro War (see #7), even though it took a long time. Although almost forgotten, the Moro War, which lasted from 1902 to 1917, was America's longest.
All war ultimately comes down to logistics and will. Seizing the oil fields will shut off their supplies. Right now they have nothing else to do except fight us because we give them everything that they need. Ultimately they will lose their will to fight, simply through attrition.
Any nation that declares war on the US either through words or actions should lose their resources.