Russian President Vladimir Putin. (Alexei Druzhinin/Associated Press)

When Donald Trump meets Vladimir Putin this Friday in Hamburg, the two presidents should have in the back of their minds the insignia worn by the Syrian Democratic Forces militia, which is the United States’ main ally here. The patch shows a map of Syria bisected by the sharp blue line of the Euphrates River.

The Euphrates marks the informal “deconfliction” line between the Russian-backed Syrian regime west of the river, and the U.S.-backed and Kurdish-led SDF to the east. In the past several weeks, the two powers negotiated a useful adjustment of the line — creating a roughly 80-mile arc that stretches south, from near this battlefront city on Lake Assad, to a town called Karama on the Euphrates.

U.S.-Russian agreement on this buffer zone is a promising sign. It allows, in effect, for the United States and its allies to clear the Islamic State’s capital, Raqqa, while Russia and the Syrian regime take the city of Deir al-Zour, to the southeast. The line keeps the combatants focused on the Islamic State, rather than sparring with each other.

What Trump and Putin should discuss at the Group of 20 summit is whether this recent agreement on the separation line is a model for wider U.S.-Russian cooperation in Syria. This broader effort would seek to defeat the Islamic State; stabilize a battered, fragmented Syria; and, eventually, discuss a political future. But is it practical?

Russian-American cooperation on Syria faces a huge obstacle right now. It would legitimize a Russian regime that invaded Ukraine and meddled in U.S. and European elections, in addition to its intervention in Syria. Putin’s very name is toxic in Congress and the U.S. media these days, and Trump is blasted for even considering compromise.

Against these negatives, there’s only one positive argument: Working with Russia may be the only way to reduce the level of violence in Syria and to create a foundation for a calmer, more decentralized nation that can eventually recover from its tragic war.

Secretary of State Rex Tillerson and Defense Secretary Jim Mattis are said to favor exploring options with Russia. “We see the potential for it,” a senior State Department official said Tuesday. “So far Russia is working in earnest with us on the effort.”

But there’s a contrary view among some hawkish National Security Council staffers and members of Congress. They argue that working with Russia would empower its allies, Iran and the Syrian regime of President Bashar al-Assad, and give a green light for their future role in Syria.

An extreme version of this view argues that the United States should mount a military campaign to block Iran and its Shiite militia allies in Iraq and Syria from obtaining a corridor across southeast Syria that would link Iran to Lebanon. This militant stance ignores two practical points: Iran already has such a corridor, but it doesn’t stop the United States or Israel from attacking dangerous arms shipments; and an assault on Shiite militias might draw the United States into a long, costly war that could spread across the Middle East.

It’s worth examining the process that established the Euphrates arc of deconfliction, because it shows how different Russia’s public and private actions have been. A Russian official initially suggested the Euphrates boundary about 18 months ago, according to a U.S. official. But it wasn’t formalized, so the two countries had been operating on an ad hoc basis.

This rough deconfliction system worked at three levels. There was daily phone consultation between colonels, supplemented by occasional contacts at the one-star level between the U.S. headquarters in Baghdad and Russian headquarters near Tartus, Syria. Big issues went to the U.S. commander, Lt. Gen. Stephen Townsend, and his Russian counterpart, Col. Gen. Sergei Surovikin.

A crisis arose last month when several Syrian tanks pushed north of what U.S. commanders believed was the informal line of separation. When this small Syrian force was backed by a Syrian Su-22 fighter jet, the United States shot down the plane. The Russians announced that they were suspending contacts, and “for a few hours, it looked pretty hairy,” recalls one U.S. official. But the Russians quietly resumed talking, and by late June, the two sides had agreed on the formal arc, with precisely delineated coordinates.

Similar U.S.-Russian cooperation has been calming tensions the past few weeks in southwest Syria. Those talks have been backed by Israel and Jordan, which border the zone. That, too, is a potential model for how de-escalation can work.

Cooperating with the Russians in Syria would be distasteful, given their past actions. But spurning them would keep this volatile country at the flash point and almost certainly make things worse rather than better for all sides.

Read more from David Ignatius’s archive, follow him on Twitter or subscribe to his updates on Facebook.