DL 499 then DL 3876 at Denver
Boston → Denver → Austin
Timetable, Denver time
10:26DL 499 from Boston at the gate
09:42DL 3876 to Austin leaves the gate
23 h 16 apart on the timetable, overnight
DL 3876 leaves 23 h 16 after DL 499 arrives on the timetable: more than half a day, so not a connection we count.