AA 338 then UA 3876 at O'Hare
Phoenix → Chicago → Miami
Timetable, Chicago time
18:02AA 338 from Phoenix at the gate
07:00UA 3876 to Miami leaves the gate
12 h 58 apart on the timetable, overnight
UA 3876 leaves 12 h 58 after AA 338 arrives on the timetable: more than half a day, so not a connection we count.