Turkey says the United States is legally bound by a treaty to immediately hand over Fethullah Gulen, the U.S.-based Muslim cleric it accuses of plotting to overthrow Turkey's government.

The U.S. government says it can't comply until Turkey can convince a judge its allegations against Gulen are legitimate.

Any solution lies in the murky world of extradition, where the U.S. criminal justice system overlaps with diplomacy and international law.

Unable to agree about the process, Turkey and the U.S. are feuding over Gulen, who denies involvement in the thwarted July 15 coup attempt. It's become the biggest irritant between the two strategic partners just as they struggle to reconcile their approaches to fighting the Islamic State group across Turkey's border in Syria.

During Vice President Joe Biden's visit to Ankara this week, the disagreement played out in unusually sharp and open fashion. Both Turkey's prime minister and president publicly badgered Biden and said the U.S. was harboring a terrorist, while Biden tried simultaneously to show sympathy and defend U.S. legal traditions.

"It's never understood that the wheels of justice move deliberately and slowly," Biden said.

A look at the case against Gulen and how extradition works:

Q: Why does Turkey want Gulen extradited?

A: Once an ally of President Recep Tayyip Erdogan, Gulen now lives in self-imposed exile in Pennsylvania. He's associated with Sufism, or Islamic mysticism, and a founder of a movement known as Hizmet — "Service" in Turkish — that first expanded outside Turkey in the early 1990s after the Soviet Union fell. Gulen's followers have established a network of schools around the world, and Turkey accuses Gulen of surreptitiously grooming students to eventually overthrow Turkey's government. But U.S. officials say privately they're skeptical about claims that Gulen was involved in the failed coup.

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Q. Has Turkey provided evidence that Gulen should be returned?

A: Yes and no. Turkey has submitted extradition requests for Gulen, but senior Obama administration officials say those requests were based on alleged crimes prior to the coup attempt. Turkey's justice minister says more evidence relating specifically to the failed coup will be submitted next week.

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Q: How does extradition ordinarily work?

A: Foreign countries seeking to prosecute individuals in the United States must submit a formal request to the U.S. government laying out evidence. The requirements are spelled out in a 1979 treaty between the U.S. and Turkey that allows for extradition for crimes recognized in both countries.

The State Department and the Justice Department both have a hand in processing requests. The U.S. Attorneys' Manual says after the State Department receives the requests, the Justice Department evaluates them. Those determined to be legally sufficient are forwarded to the court district where the person being sought lives so he or she can be detained and brought before a magistrate.

The process generally unfolds in secret, with countries inclined to avoid tipping off subjects of their extradition requests. By publicly broadcasting their intent to seize Gulen, Turkey is "playing to the public arena" rather than strict legal protocol, said former State Department legal adviser Ashley Deeks, who teaches national security law at the University of Virginia.

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Q: How does the U.S. decide whether Turkey's request moves forward?

A: This appears to be where the understanding between the U.S. and Turkey has broken down.

The treaty doesn't lay out in detail how much discretion the U.S. has to evaluate the merits of the allegation before turning the request over to a judge. So Turkey, having submitted a request, says Gulen should be turned over immediately — or "at least be detained, arrested and kept under surveillance" while the process plays out, Erdogan said on Wednesday.

But aside from the treaty, the U.S. government also has constitutional and domestic legal requirements to worry about. That includes making sure any arrest warrants issued in the U.S. meet the standard of probable cause.

"They're not going to just pick him up and put him on a plane to Istanbul. That's crazy," said Douglas McNabb, a Houston-based lawyer specializing in extradition. Added Andrew Levchuk, formerly an attorney in the Justice Department's Office of International Affairs: "It's entirely up to us what steps we take."

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Q: Let's say the U.S. decides the request is legitimate. What happens next?

A: Gulen would be brought before a magistrate in Pennsylvania. It's not a trial. The U.S. Attorney's Office wouldn't have to prove he's guilty, just that there's sufficient legal basis for him to be tried in Turkey.

If the judge recommends extradition, the request goes back to the State Department. That's where Gulen's attorneys could present other arguments against extradition, such as claims he'd be tortured if he were returned or that the health of Gulen, who is in his 70s, is too poor for him to travel.

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Q: Are there any exceptions in the treaty?

A: Yes, a big one.

The treaty says extradition may be refused if the crime is regarded to be of a "political character or an offense connected with such an offense." Turkey's longstanding gripes with Gulen could provide fodder for such an argument, though the treaty does say any offense committed against a head of state can't be classified as of a "political character."

"The defendant in this case is going to scream to the high heavens that this is politically motivated," predicted Frank Rubino, a lawyer who defends individuals facing extradition.

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