By the time the United States withdrew from its long, bloody encounter with Iraq in 2010, it thought it had declawed a once fearsome enemy: the Islamic State of Iraq and Syria, which had many names and incarnations but at the time was neither fearsome nor a state. Beaten back by the American troop surge and Sunni tribal fighters, it was considered such a diminished threat that the bounty the United States put on one of its leaders had dropped from $5 million to $100,000.