AA 4669 then UA 4405 at O'Hare
Madison → Chicago → Springfield Branson National
Timetable, Chicago time
08:00AA 4669 from Madison at the gate
21:20UA 4405 to Springfield Branson National leaves the gate
13 h 20 apart on the timetable
UA 4405 leaves 13 h 20 after AA 4669 arrives on the timetable: more than half a day, so not a connection we count.