AA 4038 then UA 3376 at O'Hare
Madison → Chicago → St Louis
Timetable, Chicago time
16:44AA 4038 from Madison at the gate
11:00UA 3376 to St Louis leaves the gate
18 h 16 apart on the timetable, overnight
UA 3376 leaves 18 h 16 after AA 4038 arrives on the timetable: more than half a day, so not a connection we count.