World number one Novak Djokovic and Andy Murray reached the last four at the ATP World Tour Finals on Friday after slicing through the various permutations of their round-robin group with matching wins at the O2 Arena.
A day that began with all four Group A players in contention for the top two spots ended without the need for calculators as Djokovic beat Czech Tomas Berdych 6-2, 7-6 and Murray later overcame Frenchman Jo-Wilfried Tsonga by the same score.
Djokovic finished the group stage with an unblemished record to top the standings although the make-up of the semi-finals will not be known until Group B concludes on Saturday.
Swiss world number two Roger Federer is already assured of reaching the last four and will top the group and set up a clash with Murray if he beats Argentina's Juan Martin del Potro.
Djokovic's victory eliminated Berdych, who was left to rue three squandered set points in the second set tie-break.
It also meant Murray only had to win a set against Tsonga in the evening to progress, a fact his coach Ivan Lendl inadvertently gave away before the match although the Scot was still not quite sure of all the mathematics.
As it was, he rattled through the first set in 33 minutes.
"I didn't know exactly what I needed to do," Murray told reporters. "I asked the umpire at the change of ends after the first set whether I was through. He said I was. That was it."
Djokovic, whose thoughts have been with his father who has been suffering with a serious illness, dominated the first set with precision hitting and then showed his mettle to fend off a Berdych fightback in front of another sell-out crowd.
"I didn't want to think about scenarios or calculations, I'll leave that to other people," said the 25-year-old, who is looking to win the season-ending showpiece for the second time having won it in Shanghai in 2008.
"I try to do my job. I played a really good match. I was fortunate to come back and win in straight sets.
"This is the first time I've won all my matches in the group stage so that's encouraging for me, so I will try to focus on the semi-final now."
Fifth seed Berdych can now prepare for the Czech Republic's Davis Cup final against holders Spain in Prague.
"Next week, it's another week, another event, another big thing," Berdych told reporters. "I hope the best moment (of my year)
Djokovic, the year-end No.1 for a second successive season, boasted a 10-1 record against Berdych and it was easy to see why in the first set as he consistently outmanoeuvred his opponent.
Berdych likes nothing better than to dictate rallies with his clubbing forehand but Djokovic's superior movement and variety kept the Czech powerhouse off balance.
Two service breaks saw Djokovic cruise through the opening set and when he broke again early in the second there looked no way back for Berdych, whose sole win in their previous matches was at Wimbledon in 2010 when he was runner-up to Rafa Nadal.
To his credit Berdych did eventually make Djokovic sweat.
After breaking back he pushed the Serb into a tiebreak and surged 5-1 and then 6-3 ahead.
Typically, the warrior-like Djokovic did not flinch.
He won the next two points on serve and then a stunning service return forced a lumbering Berdych to net.
Djokovic completed victory on his first match point when his opponent ballooned a forehand long after one hour 37 minutes.
Murray also had to save a set point in the second set of his match against Tsonga, although by that stage the U.S. Open champion's place in the semi-finals was assured.
Tsonga, despite losing his opening two round-robin matches, could have reached the semis at Murray's expense with a straight sets knockout but a loose start scuppered any hopes he had.
Murray surged into a 4-0 lead as a languid Tsonga gifted the Scot two service breaks with a rash of unforced errors.
Tsonga finally got off the mark in the fifth game but it did little to alter the flow of the match as Murray quickly wrapped up the opening set.
Two double faults from Tsonga helped the world number three break serve at the start of the second. Murray then appeared to lose focus when he was broken to love and pegged back to 4-4.
The Frenchman wasted a set point on Murray's serve at 6-5 but with nothing to lose he at least treated the 17,000 crowd to a few glimpses of his eye-catching brand of tennis.
Murray avoided using up any extra energy ahead of the semi-finals when he claimed the second set tiebreak 7-3 to the delight of the noisy home fans.
In the doubles, fifth seeds Mahesh Bhupathi and Rohan Bopanna reached the semi-finals as Group B runners-up after beating second seeds and holders Max Mirnyi and Daniel Nestor lost to 7-6, 6-7, 10-5 (match tie-break).