AA 3232 then UA 4588 at Houston
Phoenix → Houston → Baton Rouge
Timetable, Houston time
23:54AA 3232 from Phoenix at the gate
20:34UA 4588 to Baton Rouge leaves the gate
20 h 40 apart on the timetable, overnight
UA 4588 leaves 20 h 40 after AA 3232 arrives on the timetable: more than half a day, so not a connection we count.