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Ashleigh Barty, of Australia, serves to Sofia Kenin, of the U.S., during round one of the Rogers Cup women's tennis tournament in Toronto, on Aug. 6, 2019.MARK BLINCH/The Canadian Press

Ashleigh Barty of Australia is in danger of losing her world No. 1 ranking after falling 6-7, 6-3, 6-4 to American Sofia Kenin in second-round play Tuesday at the Rogers Cup.

Barty wasn’t thinking about that during the match, though. And the reigning French Open champion certainly didn’t seem too concerned about it afterward.

“I couldn’t tell you from a bar of soap what’s going on with the rankings,” Barty said, prompting laughter from reporters in her postmatch press conference. “It’s not something that I worry about or focus on. I try and do the best that I can every single day, and that’s all it is.”

Current world No. 2 Naomi Osaka of Japan could overtake Barty for the top ranking by winning her first match on Wednesday. The 21-year-old opens her Rogers Cup against Germany’s Tatjana Maria.

Barty had points defend at the tournament after a semi-final appearance at the Rogers Cup in Montreal last year. Osaka, meanwhile, lost her first-round matchup at the 2018 event.

As the second seed in Toronto, Osaka earned a bye to the second round. Any points she gains at the tournament is a bonus.

“I don’t have much say for the rest of the week,” said Barty, who added she didn’t know who was in position to overtake her in the standings. “I came here and tried to do my best and, you know, it wasn’t enough today … Whoever it is, if they play well enough and, they haven’t given up points or whatever it is, they deserve to take the ranking.”

Barty had beaten the 29th-ranked Kenin three times this year. But the 20-year-old got the better of the Aussie on centre court at Aviva Centre to earn the fourth top-10 win of her career.

Kenin broke Barty six times over the match, which lasted one hour 58 minutes.

Tuesday was Barty’s first time in a live match since her fourth-round exit from Wimbledon four weeks ago. She admitted that rust may have played a factor.

“I think, all in all, I didn’t adjust well enough or quick enough or adapt to the conditions how I needed to,” she said. “I have no idea how I was able to get out of that first set and probably should have been bagelled in the second and done pretty quickly in the third, as well.

“So I think I was able to find a way to hang in there and make it tricky, but the polish wasn’t there and Sofia was the better player in big moments today.”

Kenin will play either Dayana Yastremska, who upset No. 13 seed Johanna Konta on Monday, or former world No. 1 Victoria Azarenka, who rolled to a 6-2, 6-2 win over Camila Giorgi of Italy earlier Tuesday, in the third round.

Seven-time Grand Slam champion Venus Williams also made an early exit at the Rogers Cup. The 39-year-old American lost 6-4, 6-2 to Spain’s Carla Suarez Navarro in the first match of the day on centre court.

Suarez Navarro, ranked 26th in the world, snapped a five-match losing streak against the 56th-ranked Williams.

“She was just extra sharp,” Williams said of her opponent. “I played a lot of great points but just didn’t put enough in a row. You know, play two great points and then some points not as well.

“And she just really played sharp off every shot.”

Williams has now lost four matches in a row over all, including a first-rounder at Wimbledon against 15-year-old American Cori Gauff.

Suarez Navarro will face No. 16 seed Anett Kontaveit of Estonia in the second round. Kontaveit beat former world No. 1 Maria Sharapova of Russia in a three-setter on Monday.

Alison Riske, Katerina Siniakova, Shuai Zhang, Iga Swiatek and Ekaterina Alexandrova advanced to the second round with wins Tuesday.

Canadian teenager Leylah Annie Fernandez and Wimbledon champion Simona Halep lost their first-round doubles match 1-6, 6-3, 10-5 to Nicole Melichar and Kveta Peschke on one of the smaller courts Tuesday afternoon.

Fernandez had lost her main-draw singles debut Monday and was partnering with Halep for the first time.

“For me it was great to play with a very young player, and she played really well today,” the No. 4-ranked Halep said.

The pairing came together when Halep picked Fernandez’s name from a list of potential doubles partners given to her by tournament director Karl Hale.

The 26-year-old Halep said she chose Fernandez in part because the Laval, Que., native had won the French Open girls title this year, something Halep had done herself 10 years ago.

Fernandez said she was nervous before the match, but Halep did a good job calming her down.

“I think just her presence has just motivated me a lot,” the teen said.

“I have to learn how I calmed down her, because I need to calm down myself sometimes,” Halep interjected with a laugh. “So I will take a look [at] that.”

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