But knitting together the country’s torn sectarian fabric is an even bigger job. Every round of conflict tears it a little bit more, and since 2003, the periods of respite have rarely been long enough.

Many believe Prime Minister Abadi has a less sectarian agenda than his predecessor, Nouri al-Maliki.

But he has rejected accusations of human rights violations by members of the PMF.

In August, he dismissed a call from the powerful Shia cleric and former militia leader, Moqtada al-Sadr, to disband the PMF.

The caliphate, declared by IS with such violence and ferocious enthusiasm three years ago, is vanishing.

The militants have been picked off in one city after another.

But even when the last stronghold has fallen, few people think the struggle is over.

You can destroy a caliphate, kill its self-proclaimed leaders, restore borders and, if there’s any money left, rebuild cities.

But the conflicts in Iraq and Syria have so many drivers – sectarian, political, criminal and regional – that both countries will remain breeding grounds for violent opposition until this toxic mix is addressed.

A recent spate of IS bombings in Baghdad suggested that the group’s loss of territory is unlikely to kill off its ability to cause mayhem elsewhere.

When do you think the war will end, I ask an officer over tea and our own protracted wait to pass through the Suqoor checkpoint

“It’s never going to end,” he replies.

Hardly surprising, then, that Anas al-Janabi’s customers keep a wary look out, under the bright lights of his shiny new Falluja fairground.