Mirror, mirror on the wall, who is the nicest terrorist of them all (or the worst)?  The world is witnessing the riveting spectacle of terrorist groups in Syria and Iraq feuding and grading each other in terms of their brutality, lack of collegial behavior, and ultimate objectives.  Watching the skirmish becomes even more tantalizing as it coincides with ostensible peace talks over Syria taking place in Geneva.

There are now three wars occurring in Syria: one between the regime of President Bashar Assad and the rebels, the second between the regime and the Kurds in the northeast part of the country, and the third the confrontation and vicious fighting between al-Qaeda and other rebel groups in at least four provinces: Hama, Idlib, Aleppo, and Raqqa.

On a number of occasions, President Barack Obama has declared that al-Qaeda had been "decimated" or is "on the path to defeat."  We now know that in fact, it is alive and well.  It has mutated from a single terrorist organization into one with many branches, perhaps called by different names, but nevertheless linked to each other.  It is engaged in civil war among its own affiliates as well as with its proclaimed enemies.  That civil war has come to a height with the disowning by Ayman al-Zawahiri, the leader of al-Qaeda, of the rival group, the Islamic State of Iraq and al-Sham, normally referred to as ISIS, led by Abu Bakr al-Baghdadi.

The conflict between the groups has taken a number of forms, political and personal, including clashes ranging from ideological-religious disputes of an arcane nature about events that took place fourteen hundred years ago to complicated disagreements over the strategies of the fighting in Iraq.

ISIS in its original configuration dates back to 2003.  Abu Musab al-Zarqawi, the leader of one of the 16 extremist Sunni factions at that time, swore allegiance to Osama bin Laden.  He, a brutal gangster-like figure, was killed by U.S. forces in June 2006.  The present ISIS, established in April 2013, is a militant jihadist group active in Iraq and Syria, an outgrowth from al-Qaeda's affiliate group in Iraq.  It has become a major fighting force in Syria.  Though figures are imprecise, ISIS has some ten thousand fighters -- many, probably a majority, of whom are foreigners.

In addition  to its activities in Syria, ISIS is still operational in Iraq and has been responsible for a number of bomb attacks in Baghdad and other places, as well as seizing  control of part of the town of Fallujah.  Tensions have grown in Iraq as a result of the war in Syria.  In Syria, ISIS has acted independently of other rebel Islamist groups, including the Nusra Front and Ahrar al-Sham, and clashed with them in the coastal province of Lattakia and the provinces of Idlib and Aleppo.  It is paradoxical that ISIS was originally supposed to be the merger between the Islamic State of Iraq (ISI) and the Syrian Nusra Front.  But this amalgamation was rejected by the Nusra Front, which, although an al-Qaeda affiliate, is less brutal and more concerned with issues of Syria than is ISIS.  The merger was formally annulled by the al-Qaeda leader Ayman Zawahiri.  The latter claimed that al-Qaeda was never notified or consulted about the founding of ISIS.

The ISIS group is now recognized as the most belligerent and the most jihadist of the Islamist groups.  Its brutality, its killing and abducting of other activists, its use of torture, its exercise of strong monopoly rule in the areas it controls, its attempts to control supply routes from Turkey, and its imposition of its harsh version of Islam have disturbed even the other terrorist groups.  From being leader of a terrorist group, Baghdadi was appointed "emir of the faithful" and issues all domestic and foreign policies for the "state" he rules.  The animosity among the groups became intense, and fighting began in January 2014 after ISIS murdered and delivered the body of Abu Rayyan, a commander of the Ahrar al-Sham faction, one part of the Islamic Front, who was widely respected and admired.

A number of other factions exist in the rebel camp fighting against the Assad regime.  Among them are the Green Battalion, founded by Saudi fighters; Jamaat Jund al-Sham, founded by Lebanese fighters; and other groups led by Saudi fighters (Suqour al-Izz) and Moroccan fighters (Harakat Sham al-Islam).  The issue is even more complicated because of the splits in these groups and the friction among them.

However, it is ISIS, well-financed and exercising control over a local network, that is the most vehement advocate of global jihad, and of its objective: world domination.  Fantasy though this objective may be, it has attracted thousands of foreign fighters to ISIS.  They make no secret of their intention to attack the Western world, to establish an Islamic state in Iraq and Syria, and to create a caliphate in the Muslim world.  Syria is regarded as a training ground for developing the skills to mount such attacks.

It is important to understand ISIS -- not only because of its extreme brutality and openly declared quest for world domination, but also because it undermines the ability of al-Qaeda to impose central control over its terrorist affiliates and thus destabilizes the terrorist forces even further.  Zawahiri does not consider Baghdadi to be a "ruling emir."  Zawahiri is emir of his own group, but unlike Baghdadi, he does not declare himself emir of a state.  But he is also eager for a global jihad and an Islamic world order.  His position, stated in a letter of 2005, is clear: "the two short term goals were removing the Americans and establishing an Islamic emirate in Iraq, or a caliphate if possible."  But at the same time he expressed his displeasure about the behavior of the al-Qaeda group in Iraq and criticized their daily slaughter of captives and civilians.  Zawahiri failed in his effort to assert control over that group, which in fact went on to increase its sectarian attacks on Shiite civilians.

Zawahiri is no longer attempting to establish authority over the ISIS group in Syria.  He is simply stating publicly that ISIS is not linked to or a branch of al-Qaeda.  Since there is no organizational relationship, al-Qaeda is not responsible for ISIS's actions and behavior.

For President Assad, the continuing fighting among the jihadists must be satisfying.  These jihadists, by their infighting and disarray, are losing the unifying power they need to unseat him.  The Arabs states are divided over which terrorist groups they favor.  For its part, the Western world should be embarrassed that a stinging rebuke of ISIS as a group that murders fellow Muslims, that is attempting to impose Muslim states based on an extremely repressive version of Islamic law, and that oppresses Muslims as well as non-Muslims comes from the leader of al-Qaeda and not from the democratic countries.

Michael Curtis is author of Jews, Antisemites, and the Middle East.