Rafael Nadal's hopes of a first ATP Finals title are over after he was knocked out of the tournament in the group stage.

The 36-year-old's exit means Spanish compatriot Carlos Alcaraz finishes 2022 as world number one.

Norway's Casper Ruud needed to win just one set against Fritz on Tuesday to eliminate Nadal.

Ruud, who had already beaten Auger-Aliassime, edged out Fritz 6-3 4-6 7-6 (8-6) in a tight encounter and is now top of the Green Group with two wins from two.

"I mean, I don't think I forget how to play tennis, how to be strong enough mentally," said Nadal.

"I just need to recover all these positive feelings and all this confidence and all this strong mentality that I need to be at the level that I want to be.

"I don't know if I am going to reach that level again. But what I don't have any doubt [about], is that I'm going to die for it."

The 19-year-old Alcaraz, who won the US Open in September, is the youngest ever year-end world number one but is not competing in Turin because of injury.

Nadal has now lost four matches in a row, going back to the US Open.

Meanwhile, Britain's Joe Salisbury and American Rajeev Ram, who successfully defended their US Open title this year, beat Lloyd Glasspool and his Finnish partner Harri Heliovaara in the men's doubles 7-5 6-4.

On Wednesday Novak Djokovic, who won his opening match against Stefanos Tsitsipas, will take on Andrey Rublev in his second match of the Finals while Tsitsipas will face Daniil Medvedev.