"Peace is proportional to the number of enemy killed" Total peace comes when they are all dead (or, these days, when they realise that they could all be dead in a few minutes.) However, (potential) genocide has a bad name and few are willing to have their name associated with it, even as a solution to an intractable problem. We know from the Bible that genocide was seen as good and Godly and created a peace, but people even tend to get upset with God for this pragmatic solution.
The alternative is education that will lead to understanding. This usually takes 3 or 4 generations and event then there is always a small minority who hanker after the "good old days".
The compromise is a mixture of the two - a slaughter of as many combatants as possible and that will unfortunately have to include a few innocents. This has the effect of reducing the base numbers of fanatics and dispiriting to population. Whilst you have them by the balls, you express regret and shake your head and say such things as "Well, of course if the rebels were not fighting, there would be no need for all this... those rebels are wrong you know they are bound to loose... what a waste of life... I don't think any sane person can support them... Here's why they are wrong.... Oh, listen, there's another bomb - got the orphanage this time but those rebels had set up a position there - what bastards, eh?"
On top of this, you try to be the sole supplier of what the people need. They have to be loyal to you to get food/medicine/housing, etc. And you educate everyone under 21, and you fill the airwaves with your propaganda - particularly radio and TV comedy shows that show the enemy and their ideas as hysterically funny idiots. And you execute a few suspected troublemakers as examples and bribe officials.
(This also offers a brilliant opportunity for a few "show trials" of anyone who can be made out to be a leader of some sort.)
Surrounding an area is good. You can starve them out pretty quickly if you go about it well. As they come to surrender, you have the opportunity of shooting any of them who look as if they might have raised a gun in anger or might have failed to get the message. Those who fight to the death are self-selecting candidates for Darwin Awards and their wish to dies as martyrs and heroes should be honoured.
There should be an aid program too - water, food, infrastructure, medicine, housing, employment - this is all expensive but, if you play your cards right, this moeny can be recouped in trade, reparations, etc., later.
As the same time as the above is going on, your best brains are hacking all the phones, websites, and bank accounts of anyone who you suspect of having anything to do with the rebels. Again there will be a few whining innocents whose lives are ruined, but Hey - at least they weren't bombed.
None of this should obscure the prime objective which is to secure the oil/natural resources of the region.
The British had a wonderful method of execution for rebellious Moslems: they would wrap them up in a pigskin and have them trampled to death by an elephant - apparently this put the fear of Allah into them as they would die and not go to Paradise.
I'm not saying that all the above will work every time but the original maxim is pretty solid and it at least cuts down the numbers.
Anything less than this is abnegating the responsibility of government which is to facilitate trade and secure the best for its own people.
A thought to bear in mind is that most of those who are prominent in advocating "Peace and love" end up being killed.