Seaman Staynes....
While not with Delta, I was with a comparable company flying 777's. The schedule for that was this...
Anything over 8 hours required 3rd crew. Over 12 hours required 4th crew.
Their schedule was quite nice actually. They flew 2 six day trips per month for about 76 hours of flying. That means 12 days flying and 18 off. One of the best rosters I've ever seen at an airline. Needless to say I was envious!!
Crew rest for that type flying was keen as well.... Bunk was right behind the flight deck and crew also had reserved first class seat blocked off for use if he chose not to use bunk during rest break.
Doesn't seem EK has quite that nice a roster, eh?
K