-Tim Cocks is a Reuters correspondent based in Baghdad.-

For the U.S. military, it’s the million dollar question — or rather the $687 billion question, according to a recent estimate of the Iraq war’s total cost. Is Iraq now stable enough for them to take a permanent back seat?

The short answer is no one knows. The only way they were ever going to find out was to leave Iraq’s own forces to it and hope the whole thing doesn’t come tumbling down. They started doing that on Tuesday when they pulled out of Iraqi cities.

It’s been an encouraging start. A big bomb in Kirkuk cast a shadow over Iraq’s celebrations of its new-found sovereignty, but since then things have been relatively quiet. Militants might try to take advantage by stepping up attacks, but for the moment they seem content with celebrating a “victory” over the occupation — and setting off the odd bomb, of course.

The United States’ coalition partners have for the most part long since departed. British forces handed over southern Iraq to the Americans in April, but since 2007 their 4,000 odd troops left had been largely confined to Basra airport anyway.

And one thing the crystal ball gazers have learned about Iraq’s hugely complicated, many-sided conflict is that the past is rarely a reliable guide to the future.

When optimists thought Iraq was poised to enjoy democracy after the fall of Saddam, it spiralled into years of bloody insurgency and sectarian killing. Later, just when it seemed all hope was lost and Iraq would have to be partitioned, things starting getting dramatically better.

The idea that Iraqi forces aren’t ready to take on the country’s security usually centre on claims that they are untested, not well trained or infiltrated with militiamen.

But few deny they look more professional and integrated now than anyone would have thought possible two years ago. They might still be full of militiamen, but those militiamen are no longer kidnapping or killing political rivals, as in the past.

And there are clearly some things the Iraqis do better. For one thing, they know the language and understand the culture.

When I was on a U.S. patrol in Iraq’s troubled Diyala province, a U.S. unit nearby accidentallly shot and wounded a civilian in Jalawla town, forcing them to vacate it because a public outcry would put other soldiers at risk of attack.

What they had done is fire a warning shot at a vehicle after the driver failed to heed a command — in English — to stay back. But few Iraqis in rural areas speak basic English.

The real test will be when U.S. pulls all combat forces out, under President Barack Obama’s orders, by September next year.

Many Iraqis I’ve spoken too seem convinced the insurgents are just biding their time, sharpening their knives and stockpiling explosives waiting to reignite the conflict.

But whether or not Iraq can look after itself, at some point the Americans have to say: Look, we’ve done our best to get the lid back on Pandora’s Box. Now it’s over to you.