AA 3977 then DL 4962 at Detroit
Chicago O'Hare → Detroit → Omaha
Timetable, Detroit time
13:00AA 3977 from Chicago O'Hare at the gate
12:15DL 4962 to Omaha leaves the gate
23 h 15 apart on the timetable, overnight
DL 4962 leaves 23 h 15 after AA 3977 arrives on the timetable: more than half a day, so not a connection we count.