UA 3874 then AA 4038 at O'Hare
Chicago Rockford → Chicago → Madison
Timetable, Chicago time
01:21UA 3874 from Chicago Rockford at the gate
13:49AA 4038 to Madison leaves the gate
12 h 28 apart on the timetable
AA 4038 leaves 12 h 28 after UA 3874 arrives on the timetable: more than half a day, so not a connection we count.