As I understand it, the war between Iraq and the United States, begun in 1991, has not yet ended.
As I understand, the US and Iraq war has not ended, but today few troops remain in Iraq. 
mnli hypothesis: As I understand, the US and Iraq war has not ended, but today few troops remain in Iraq.  premise: As I understand it, the war between Iraq and the United States, begun in 1991, has not yet ended.