AZ 58 then AA 37 at Madrid
Rome → Madrid → Dallas-Fort Worth
Timetable, Madrid time
10:50AZ 58 from Rome at the gate
10:00AA 37 to Dallas-Fort Worth leaves the gatealso BA 1513, AY 3743, IB 4608
23 h 10 apart on the timetable, overnight
AA 37 leaves 23 h 10 after AZ 58 arrives on the timetable: more than half a day, so not a connection we count.