For MEB, forever.
As to the term "eradicateur" in the Algerian context, that is the subset of the ruling Algerian elite that concluded after fighting the civil war in the nineties with the Islamic Salvation Front, the FIS, that literally eradicating such people was the only policy.
That "eradicateur" approach was as opposed to the "dialogistes," whose meaning is obvious from the French. It's almost sort of laughable at one level, dialogue, like some PC "we need to dialogue with the terrorists," except that sometimes you can bring things to a more expedient end by negotiations, usually though by having a decent to superior military hand first.
In fact, all Counter-Insurgency campaigns, in which terrorism is a form of insugency, and therefore its control a subset of Counter-Insurgency (COIN), involves more eradication than some COIN theorists like to admit at the garden party in polite company, if there is usually dialogue at the conclusion of sucessful COIN campaigns too, killing and talking not being mutually exclusive, per Clausewitz, a continuation of politics by other means.
COIN theorists may have made what they advocate sound too good to be true, and if COIN is ideal when applying multiple instruments of power, it still sometimes is the most violent of strategies of all when properly executed, precisely because its killing features when done are so focused and discriminate, ideally speaking of course.
As to why that terminology matters now, eradicateur and dialogiste, a lot of hostages died in Algeria last week after the Al Qaeda attack, which raises questions as to this question: was that necessary?
Well, the hostage takers demanded the release of the Blind Sheikh, Omar Abdel Rahman.
This is the man who was the founder of Maktab al Khadimat al Afgahni with Bin Laden and Al Zawahari, the "Afghan Sevices Bureau" that was the predecessor of Al Qaeda. Granted, we thought they were harmless back then fighting the Soviets, but we lost that idea pretty quickly after the Soviets left Afghanistan too. Fortunately, certain Russian experiences since then make them reasonably tractable on that issue, as to resisting certain temptations enough for our tastes.
But as to any criticism of the Algerians in that matter, ask youself the question at hand, realistically speaking: "Should we release Bin Laden and al Zawahari's main partner, the Blind Sheikh, or should we ask why is he still alive instead?"
What does it tell you when the people taking the hostages asked for the Blind Sheikh?
As to the defense of the eradicationist tactics used by the Algerians, most hostages lived, many militants died, and again, what exactly would there have been to talk about?
Nothing, since they wanted the Blind Sheikh, who it would be dangerous to release, just as it is obvious that he is a dangerous to some extent to keep alive, even very sequestered.
The only reason to have talked to the militants would be tactical, perhaps to lure them into thinking the Sheikh was on his way, and then throw him to them from a great height as the signal to launch the last assault, in order to strike with maximum fear, to terrorize as the Russians say the terrorists.
There was no other basis of negotiation that was acceptable, and tossing his body like that, if harsh, also would have both solved that ongoing problem, and made a statement, if a harsh one some shrink from, if that shrinking some think a little risky too.
Fear and awe (they don't care if the crazies we are afraid of riot?) are a part of life at times, if one would rather the Rodney King Theory always applied.
Again, when you read the allegedly peaceful innocent Sheikh's resume, it's Al Qaeda before there was al Qaeda, with fatwas on killing Sadat for making peace with Israel before, fatwas after al Qaeda took off on Meir Kahane in New York (not the poster child of peace in our time himself of course), and of course a fatwa on World Trade Center I for sure, plus the spiritual inspiration and targeting selection for World Trade Center II, fatwa or no fatwa.
The Blind Sheikh was never a good "catch and release" candidate, if a good candidate for the eradicationist approach some would argue, e.g. release him, from a helicopter 200 meters over the Egyptian desert, and see if he grows wings. Maybe pitch him into international waters, for our legalistes. What does legality really have to do with dealing with such people?
Not much, if hypocrisy is the tribute vice pays to virtue too.
As to the narrower question, any criticism of the Algerians in eradicating the assailants at the Al Amenas gas facility this week, who demanded the release of the Blind Sheikh, just think about that: Could one do that, and then potentially have him come back to Egypt a hero freed by jihadists, maybe even claim to be a "Mahdi" like figure, or even be perceived as such?
Not really, so there was nothing to "dialogue" about, which is why in that case, the theory of the Algerians, known as eradicateurs, best understood as "Kill all the Militants and Let Allah sort it out," was totally defensible, even if as a hostage, that's not what you want to hear personally.
That's the downside of the eradicatuer strategy, and why it can't be the only strategy in general, if sometimes, that's all there is in a particular instance, or then you just surrender to what other people want, like releasing the Blind Sheikh.
As a pure demonstration of resolve to never give in to such threats, and thereby discourage people from trying that, there is much to be said for that eradicatuer theory, because that theory raises the question: How many more people are going to die before someone takes the Blind Sheik out?
Sending him back to Egypt after short but not very pleasant flight by helicopter is the purest application of that Algerian erradicateur theory, and is what the Russians often have done, especially if President Morsi of Egypt wants to keep insisting on his release, as that tells you something important about either him, or some subset of his followers who pressure him.
Or he can announce that he's had a revelation on that point.
Even being willing to hint to President Morsi that the Sheikh is a lawful target of war, eligible for summary execution by pitching him out of a helicopter into the desert, the latter for having a deliberately garrish quality that is its point as to modality, somewhat more provocative than just stuffing Bin Laden to the fishes, is to that way of thinking potentially functional from the point of view of dealing with hard facts as they sometimes must, if some would worry about other consequences, e.g. riots in Cairo.
To the eradicationist point of view, maybe they riot in Cairo because they fear America not, and need to relearn that lesson, as if one must chose between being loved and being feared, it is safer to be feared, and it's not like all the foreign aid we have given Egyptians over the years, including constructing Cairo's water supply, and feeding millions of Egyptians has gotten us much gratitude.
Moreover, the worry about other consequences of pitching a seemingly harmless blind old man out of a helicopter into the desert like a dangerous vermin in a real way does show a slight hint of fear, the one thing that the eradicationist theory doesn't show, and in fact directs the other way, on the Algerian and Russian theory that the best way to fight terrorists is in fact to "terrorize the terrorists."
If that makes you somewhat more like your enemy, that is a concern, if to not be willing to do that is to that kind of enemy also potentially seen as weakness, not a consideration many Americans particularly like, if that doesn't change who are enemies are either.