Tennis might be fighting for its soul but Roger Federer remains its beating heart.

On a day when it was learned that a merger of the revamped 118-year-old Davis Cup and the new ATP Cup – which will be held within six weeks of each other at the end of next year and the beginning of 2020 – is one solution being considered to break the impasse that has gripped the sport for five years, the Swiss cruised into the semi-finals of the ATP Tour Finals for the 15th time.

He needed to win only five games against Kevin Anderson to move within two wins of lifting the trophy for a seventh time but he found another gear to win 6-4, 6-3 in an hour and a quarter. All of the matches in this tournament have been quick, some sadly so. This was a good match, but hardly memorable.

Federer might yet have to get past the world No 1 Novak Djokovic on Saturday to reach the final, knowing his old adversary has stopped him here three times in the past, but his game is in sound shape.

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He makes his mistakes elegantly, moving on from a slightly skewed backhand to a cool, crisp forehand thrash as if swatting flies. And there were enough of those to put away last night to get him over the line.

Victory put Federer top of group Guga Kuerten, so the only way he avoids a semi-final against Djokovic is if the Serb loses to Marin Cilic on Friday and John Isner beats Alexander Zverev.

“I’m very happy,” he said. When isn’t he? Perhaps when wrestling with self-doubt after struggling with a hand injury that struck at the start of the grasscourt season, but there was no sign of physical inconvenience here.

Other statistics will record that he made 14 unforced errors – 10 of them in a slightly nervy second set – but overall the performance had an air of flawlessness about it.

Federer broke Anderson to love for 4-3 after 24 minutes and again without conceding a point in the ninth game – yet in between dropped his own serve. He double-faulted in giving up three break points but still held to secure the set. This was carefree, get-out-of-gaol tennis, entertaining and full of rich, expansive strokes. No wonder there were occasional mistakes from both sides of the net.

He and Anderson were now in the semi-finals. All that needed to be determined was who would finish top of the group – and then the mathematical fun would start. As so often, it was Federer.

The match meandered to an almost mundane conclusion, pleasant and pretty enough but without the requisite tension to command serious attention. Federer squandered two match points before breaking the big serve of the South African for a second time in the set to close it out.

Elsewhere, there were waves on Planet Tennis. At an amicable meeting in London on Tuesday night, the Association of Tennis Professionals and the International Tennis Federation came closer than they have ever been to resolving their differences.

However, while a merger of their rival Cups would be hugely popular with players torn between loyalty to their national teams and the lure of another cash-rich tournament with ranking points, an insider at the meeting said: “It is a definite possibility down the line but there is a bit of work to do to get there.”

The stumbling block is the fact the ITF handed over stewardship of the Davis Cup to the Kosmos company run by Gerard Pique for $3bn (£2.35bn) over 25 years, so the ATP have to negotiate with the Barcelona star rather than the federation, and Pique is still learning about the internal politics of tennis.

It was striking at the ATP launch of their event here on Thursday that the new venture has the backing of all the world’s best players, while the future of the Davis Cup – played for national pride but no money or points – remains the game’s Brexit conundrum: to remain or to leave. So much tennis, so little time.