WASHINGTON (AP) — The United States, Russia, Saudi Arabia and Iran haven't agreed on much throughout Syria's bloody four-and-a-half year-old civil war.

But for the sake of peace, they will try this weekend to decide which of Syria's fighting forces are common enemies and which can be included in a transition government with President Bashar Assad, their intractable enemy.

Failure to reach an agreement could leave international peace efforts in tatters.

As diplomats return to Vienna for another round of Syria talks on Saturday, they're grappling with questions that have scuttled all previous attempts to forge a ceasefire and usher in a political transition.

Other than the Islamic State group, who are the extremists? Who from Syria's government and opposition should do the negotiating? How long can Assad remain in power?

"We face an environment now that bears little resemblance to the kind of black-white scenarios that make decisions relatively easy," U.S. Secretary of State John Kerry said in a speech on Syria Thursday. "Put simply, there are bad guys all around and good guys who are not accustomed to working with each other."

Kerry departed Thursday for Tunisia, which he'll visit before traveling to Vienna, the capital of Austria. He left just hours after the latest demonstration that Syria's civil war was spiraling out of control: A twin suicide bombing in neighboring Lebanon that killed 37 people in a Hezbollah stronghold. The Islamic State took claim for the attack.

Throughout Syria's conflict, world and regional powers have waged bitter public relations battles over defining the extremists and the freedom fighters, providing military equipment and even directly intervening to support Syria's opposing camps.

Assad's army is now backed by Iran's hardline Quds Force and its proxy, Hezbollah, along with Russia. The rebels include Western-backed "moderates" and Arab-supported Islamist groups, as well as al-Qaida-linked militias. In the mix is the Islamic State, opposed by all, in principle.

Over the last couple of weeks, countries have been trading lists of who they consider terrorists. No common understanding has been reached, but some movement has occurred.

Kerry and other U.S. officials have tamped down demands for Assad's quick departure and allowed Iran — whom they call the world's leading state sponsor of terrorism — to join the mediation process.

By doing so, Washington has accepted that Tehran can continue wielding influence in Syria, which has helped Iran for decades to project power throughout the Middle East through groups such as Hamas and Hezbollah, which the U.S. considers terrorist organizations. The shift has occurred although the Obama administration vowed to "redouble" efforts to counter Iran's regional ambitions.

It's unclear what the U.S. and Saudi Arabia, Iran's Mideast rival, are getting in return. A draft Russian settlement leaked this week says the U.N. Security Council would endorse the fight against the Islamic State, but that nations must still "agree on the additional list of terrorist groups." These groups wouldn't be covered by a ceasefire.

That could be the rub. Assad has bombed militants and civilians alike, labelling almost anyone who opposes him a terrorist. Western nations say the Russians have mainly bombed moderate forces as part of its "counterterrorism" campaign. Even the U.S. and its allies disagree: Whereas Washington avoids the more Islamist opposition militias like Ahrar ash-Sham, Arab states such as Saudi Arabia and Qatar readily back them.

More than 250,000 people have been killed in the Syrian war. Eleven million have been uprooted from their homes. The conflict has allowed Islamic State militants to carve out significant parts of Syria and Iraq for their would-be caliphate and commit atrocities, particularly against women and minorities, that some human rights groups consider genocide. Europe, meanwhile, is struggling to cope with the worst migrant crisis since World War II.

History augurs poorly for a quick understanding — even among just the would-be mediators.

The U.S. says Assad forfeited the ability to lead Syria in the long term, while the Sunni monarchy of Saudi Arabia wants him toppled as part of a proxy war with Shiite Iran. Russia is ambiguous about Assad's long-term future, carefully safeguarding its longstanding security relationship.

Just getting all countries to the table is proving difficult. On Thursday, Russia's Foreign Ministry angrily criticized the composition of a set of working groups designed to hammer out agreements on fighting terrorism, bless opposition figures for inclusion in transition talks and ease Syria's dire humanitarian situation.

The U.N.'s Syria envoy, Staffan de Mistura, has told colleagues that one idea involves avoiding the "terrorist" label for groups agreeing to the truce; holdouts would be fair game.

Such a formula puts a far greater onus on the U.S. and its partners. Russia and Iran would only need to convince Assad to stop fighting. The United States and allies would have to contend with a multitude of fighting forces with competing ideologies and interests, all jockeying for position in a post-conflict Syria. The prospect of "terrorist" and "non-terrorist" forces embedded with one another complicates the matter.