AA 4441 then UA 5609 at O'Hare
Madison → Chicago → Appleton
Timetable, Chicago time
20:30AA 4441 from Madison at the gate
20:15UA 5609 to Appleton leaves the gate
23 h 45 apart on the timetable, overnight
UA 5609 leaves 23 h 45 after AA 4441 arrives on the timetable: more than half a day, so not a connection we count.