Turkish military strategy in Syria is fraught with contradictions. Last week it began a cross-border raid targeting Daesh (the self-proclaimed IS) in response to the terrorists' continuing attacks in Turkey itself. But the assault on the border IS-held town of Jarablus was conducted in cooperation with units of the Free Syrian Army, at a time when, at Russian prompting, President Recep Tayyip Erdogan is working to improve relations with the Assad dictatorship. Moreover, once the Turks had overrun Jarablus, they advanced south and began to bombard the town of Manbij which, however, is not held by Daesh but by Syrian Kurds, who have also been fighting Daesh in nominal cooperation with the FSA. The concerning factor here is that for Ankara, the Syrian Kurds are supporters of Turkey's domestic Kurdish rebels, the PKK, designated by the US and Europe as a terrorist organization. Syrian Kurds have little reason to like the Turkish military after it stood by for weeks while its Syrian Democratic Forces fighters withstood a vicious Daesh assault in the border town of Kobane. The contradictions become even deeper because the SDF is being backed by US advisers on the ground and American warplanes. Washington is supporting these Syrian Kurds since they have proven they are the most effective opponents of Daesh in Syria. It was thus entirely possible that the assaults on the SDF by NATO member Turkey were also targeting fellow-NATO member, the United States. Washington has been appalled at this development and over the weekend, urgent high-level contacts were made with the Erdogan administration. According to the Americans, a "loose agreement" has been reached to stop further Turkish assaults on the Kurds. However SDF sources are suggesting that they are still under attack. There is a clear danger here for Turkey. The Syrian Kurds had denied that they were giving any sustenance to the PKK. Whether true or not, they now have absolutely no reason to hold back in support for their fellow Kurds across the border. That being the case, whether it likes it or not, Washington is further embroiled in PKK rebellion. It is already supporting the autonomous Kurdish region in Iraq which is widely believed to be also offering the PKK clandestine support and has done nothing to clean out PKK bases in its territory. Coming on top of Erdogan's assertion - hotly denied by the Obama administration - that it was behind the failed July coup and is protecting its alleged instigator Fethullah Gulen by refusing to extradite him from his US exile, Ankara's relations with Washington look in danger of heading for the shredder. Russia's Vladimir Putin can be feeling nothing but satisfaction as two NATO allies find themselves confronting each other on a foreign battlefield. In addition, the Turkish army's plunging into the Syrian ground conflict it likely to produce yet further bloody complications in a carnage that is a shameful monument to international refusal to intervene against the country's brutal dictatorship. While it undoubtedly increases the pressure on Daesh, it is likely to ease the difficulties facing Assad because the SDF's fighters have proven themselves a potent government enemy to the north of the besieged city of Aleppo. It is hard to know who wins most from Turkey's ground incursion, but it is not difficult to believe that Turkey is likely to end up a loser.