Mercedes' two official protests over the Abu Dhabi Grand Prix have been rejected.
Red Bull's Max Verstappen moved ahead of Lewis Hamilton, who had led for most of the contest, to clinch the race and his maiden world title.
Mercedes alleged a breach after the late decision regarding lapped cars, and against Verstappen for overtaking Hamilton under the Safety Car.
The Safety Car wiped out Hamilton's considerable advantage and allowed Verstappen to pit for fresh soft tyres but still stay second in the title decider.
There were five lapped cars between Verstappen and Hamilton in Lap 57 of 58.
F1 Race Control then allowed those cars to un-lap themselves before signalling an end of the Safety Car period, leading to one final lap of the race and championship.
This was then effectively a straight shoot-out between the two drivers.
Verstappen of course now had a tyre advantage and overtook Hamilton, who was going for a historic eighth title, in the sprint finish.
Mercedes protested "against the classification established at the end of the competition."
They said a breach occurred of Article 48.12 of the FIA Sporting Regulations which states that "any cars that have been lapped by the leader will be required to pass the cars on the lead lap and the safety car."
Daniel Ricciardo, Lance Stroll and Mick Schumacher, who had been lapped but were not in between Hamilton and Verstappen like the other five cars, did not un-lap themselves.
They also raised concern over Verstappen's conduct under the Safety Car.
Article 48.8 of the same regulations says "No driver may overtake another car on the track, including the safety car, until he passes the line for the first time after the safety car has returned to the pits."
Both of these protests were dismissed with Max Verstappen confirmed as Formula One World Champion.