|ATP World Tour Finals, O2 Arena London, 9-16 November|
|Coverage: Afternoon sessions (14:00 GMT) and first semi-final (14:00 GMT) on BBC Two & BBC website, final on BBC Three & BBC website (19:00 GMT); live commentary of each match on 5 live sports extra, live text commentary on BBC website|
Roger Federer thrashed Andy Murray 6-0 6-1 to end the Briton's ATP World Tour Finals hopes in humiliating fashion.
The 17-time Grand Slam champion needed just 56 minutes to win his third Group B match and reach the semi-finals.
Murray required a straight-sets win to qualify but won only eight points in the first set and did not win a game until 6-0 5-0 down.
The result is Murray's worst since he lost 6-1 6-0 to Novak Djokovic in Miami seven years ago.
"Clearly, I'm very happy to play a good match today," Federer said. "I knew I was qualified so maybe I went in a bit more relaxed.
"It's not the way I thought it was going to go, but there's always next year for Andy and hopefully he can have a good season.
"At the end I was happy I didn't win the second to last game to be quite honest."
|Jeremy Bates, former British number one|
|"Everyone who watches a lot of matches knows that is as close to perfection as you can possibly get. Everyone is in shock at that scoreline."|
After 24 minutes, Murray's progress in the tournament was over as he suffered his first 6-0 set loss in four years.
"It was a tough night," Murray said.
"I've lost Grand Slam finals, which have been very tough, but in terms of the way the match went it was not ideal from my side of the court - far from it.
"He played exceptionally well, that's for sure. I can say I'm disappointed with my level tonight but if I played well, he probably still would have won anyway."
A tight, tense encounter had been anticipated with the Scot needing a fast start, and Federer keen to win the group and so probably avoid top seed Novak Djokovic in the semi-finals.
In the event, only one player brought anything like his best game.
The 17,000 spectators packed into the O2 must have thought they were in a for classic when Murray won the opening two points on Federer's serve, before the Swiss won an epic 34-stroke rally on the third.
From that moment on it was one-way traffic as Murray struggled to find first serves and Federer produced some sublime tennis.
As the games rolled by, he even threatened to inflict the dreaded 'double bagel' on Murray, whose ambition became drastically reduced.
|BBC Tennis correspondent Russell Fuller|
|Murray spoke of cutting short his holiday and making technical changes to his game in the immediate aftermath of a defeat that will come as a major shock to his system. Even in the face of what coach Stefan Edberg described as the best tennis Federer has played all year, Murray was simply steamrollered. He has lost all nine of this year's matches against Djokovic, Nadal and Federer: a gulf in form and belief has opened up between Murray and the players he's used to rubbing shoulders with in Grand Slam finals.|
"Just try and win the point," he said. "Try and set a target of winning points. Try and win two points in a row rather than trying to focus on, 'OK, I want to get this game.'
"You just try and set smaller goals than that. That's basically it."
Federer moves on to the semi-finals and keeps his outside hopes of ending the year as world number one alive, although Djokovic can end that race should he beat Tomas Berdych on Friday.