(CNN) On December 19, President Trump declared: "We have defeated ISIS in Syria, my only reason for being there during the Trump Presidency." US troops there, he said in a video the same day, are "all coming back, and they're coming back now."

But in between both statements, his Defense Secretary James Mattis and the US special envoy on fighting ISIS, Brett McGurk, had resigned. Senior Republican Senators had openly criticized the abrupt withdrawal.

US Secretary of State Mike Pompeo said on Monday that "there is no change in our commitment to the defeat of the caliphate or of ISIS globally," but has also maintained that it can be done without the 2,000 US troops that currently support the Kurdish-led Syrian Democratic Forces in northern-eastern Syria.

For its part, the US Defense Department says the withdrawal is conditions-based and not subject to "an arbitrary timeline."

The rest of this article could be spent trying to divine the US policy in Syria. But it's easier to ask whether ISIS is defeated or not.

For sure, it's a shadow of what is was at the zenith of the self-declared Caliphate, when it controlled territory the size of Hungary. But it is far from vanquished, either as a fighting force or an ideology.

Beyond Syria, there are signs that it's regenerating in Iraq. A UN report in August estimated that some 20,000 to 30,000 ISIS fighters were still at large in the two countries.

And ISIS affiliates -- from West Africa to Indonesia -- show no sign of folding their tents.

The "Hajin Pocket"

Several hundred ISIS fighters still control territory along the Syria-Iraq border. It was there last weekend that two British soldiers were reportedly wounded by a rocket or missile attack during clashes in the "Hajin pocket", an area of some 20 square kilometers where networks of caves and tunnels enable ISIS fighters to survive.

Kurdish forces on the ground, supported by western special forces and airstrikes, have battled to eliminate the ISIS presence in Hajin for months. Between December 9 and 15 alone, the US-led coalition conducted 208 airstrikes against ISIS in Syria, the vast majority around Hajin.

Hardly a sign of operations winding down, let alone the liquidation of ISIS in Syria.

ISIS has also been able to conduct offensive operations. It has exploited poor weather to attack Kurdish forces, killing dozens of them in one engagement in November and releasing videos of those it had captured.

There are also signs that ISIS cells are active around Raqqa, once the group's self-declared capital. ISIS claimed on Monday that it was responsible for a suicide attack in the city in which several people were killed or injured.

Recovering in Iraq

There are also indications that ISIS is regrouping in Iraq, albeit in small numbers. Iraqi officials and counter-terrorism analysts say ISIS cells have infiltrated the sparsely-populated Hamrin mountains south of Mosul, which was the last major city in Iraq occupied by the group.

They have exploited the fault line between the government in Baghdad and the Kurdish regional authorities -- and the fact that civilians have not returned to many villages because of poor security and infrastructure.

Security in Baghdad is much improved, symbolized by the reopening of the high-security Green Zone in December after 15 years. But ISIS, which regards Shia Muslims as apostates, targeted Shia neighborhoods of the Iraqi capital in simultaneous bomb attacks in October and November.

Elsewhere, it has assassinated security officials in Diyala province, Sunni tribal leaders in Nineveh province and carried out ambushes on the main highway linking Baghdad and Mosul. A car bomb near a restaurant in Mosul in November killed several people.

The pattern of coalition airstrikes in Iraq over the past few months also suggests that ISIS retains a presence in the deserts of western Iraq.

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Nor is ISIS short of money. It is believed to have stashed away hundreds of millions of dollars from oil revenues and taxes levied while it occupied large parts of Iraq and Syria. Long before the Caliphate was declared, ISIS ran sophisticated extortion rackets in Mosul. One source tells CNN some of its cash pile has been laundered through businesses in Turkey.

In October, the US Treasury imposed sanctions today on an Iraq-based money services business that had been moving money for ISIS, describing it as part of a "complex network of money services businesses, hawalas [informal money exchange businesses] and financial facilitators funding terrorism across the Middle East."

At the same time, Kurdish commandos in Iraq arrested eight men in a raid on an ISIS financial network in northern Iraq.

The ISIS diaspora

The appeal of ISIS' ideology -- which once drew hundreds of foreign fighters to Iraq and Syria -- has dimmed with the loss of the Caliphate -- but it has not died.

Affiliates pledging their allegiance, in West Africa, Libya, Yemen, the Philippines and Indonesia to name just a few places, are still active. A pro-ISIS group is suspected of bombing a shopping mall in the Philippines on New Year's Eve, an attack which killed two people.

ISIS may not be able to direct attacks in Europe any more, but radicalized individuals still aspire to carry out attacks in its name. Cherif Chekatt, who killed five people in Strasbourg in December before being shot dead, had recorded a video of support for ISIS. He had been radicalized in prison and was on France's security watchlist -- but so are 29,000 others.

According to security analysts Globsec , 97% of the jihadis responsible for terror attacks in France since 2012 were already known either for radicalization or by the police.

But the task of tracking militants who might move from word to deed is beyond security agencies -- in France or anywhere. Should ISIS show remarkable powers of recuperation despite the international efforts to destroy it, its appeal to would-be militants beyond the Middle East might grow again.

The future

The current situation in Syria and Iraq suggests that recuperation has begun. A vast stretch of territory either side of their border lacks governance and security. Rural and remote, it is ideal for an insurgency, especially one as deep-rooted and well-organized as ISIS.

Hassan Hassan, who has followed the group's evolution and is co-author of "ISIS: Inside the Army of Terror", sees the group's strategy as "sahraa, sahwat, sawlat" -- the Arabic words for the desert, opponents within the Sunni community, and hit-and-run attacks.

It has focused on attacking Sunni "collaborators" for over a decade and is now staging ambushes and "flying checkpoints" in Iraq to make its presence felt.

It may be helped by what is frequently an arbitrary campaign by the Iraqi state to punish alleged ISIS sympathizers. New research by Kristen Kao and Mara Revkin at the University of Gothenburg shows that this heavy-handed "victors' justice" may yet push some of the Sunni population back into the arms of ISIS.

Should the US withdrawal from Syria proceed without a deal between the Kurds and the Syrian regime and without assurances from Turkey that it will not attack the Kurds -- which it regards as a terrorist group -- the coalition stitched together to defeat ISIS will quickly unravel.

The idea that Turkey can pick up the slack against ISIS is unrealistic: it lacks the capacity and access to areas where ISIS is still active. And whatever guarantees it might offer, Ankara's prime target inside Syria would be not ISIS, but the Kurds.

As Hassan Hassan has written , if the US "simply leaves, new wars will almost certainly be reignited between Turkey and the YPG, the Arabs and the Kurds, and the opposition and the YPG."

And that would suit the remnants of ISIS fine.