A320
Flight Crew Air Transport Pilot (ATP)
ATC Issue All Types; Conflict Ground Conflict; Less Severe
General None Reported / Taken
Human Factors
When departing on Runway XX it is required to back taxi from Taxiway X. When approaching the runway on Taxiway X there was an aircraft that was not finished with a run up in front of us. The ground controller then instructed the aircraft to cross Runway XX and hold on Taxiway Y to complete the run up. We were then instructed to back taxi full length for Runway XX. When reaching the end I performed a 180 degree turn and we were then cleared for takeoff. When making the turn we cleared the area including having the aircraft in sight sitting on Taxiway Y. Once we were about to rotate; we passed and noticed that the entire aircraft was over the hold short line on the runway side. We continued the departure without incident. The ground and tower controllers should have noticed that the aircraft was on the runway before we were cleared for takeoff.
[Report narrative contained no additional information.]
A320 crew reported that a general aviation aircraft completing their run up was completely over the hold short line for the runway and they should not have been cleared to takeoff.