AA 4441 then UA 4789 at O'Hare
Madison → Chicago → Fargo
Timetable, Chicago time
20:30AA 4441 from Madison at the gate
19:45UA 4789 to Fargo leaves the gate
23 h 15 apart on the timetable, overnight
UA 4789 leaves 23 h 15 after AA 4441 arrives on the timetable: more than half a day, so not a connection we count.