MELBOURNE (Reuters) - Since her invites to the White House are likely to dry up once outgoing U.S. President Barack Obama vacates the premises this week, Caroline Wozniacki was relieved to snap her backward sliding run at the Australian Open on Tuesday.

After tweeting a picture of herself with Obama with the message "Thank you Mr President!... I'll miss playing tennis with you at the White House", the former world number one was relieved that she finally bucked a worrying trend at the Australian Open.

Since reaching the Australian Open semi-finals in 2011, Wozniacki had fallen one round earlier in each subsequent visit to Melbourne Park - which meant her journey to this season's opening grand slam was full of trepidation.

"My trend has been semis, quarters, fourth, third, second, first round, and then, according to my trend, I should have

been in the third-round quallies (this year)," the bubbly Dane, whose ranking has slipped to 20th, quipped on Tuesday following her 6-1 6-2 first-round rout of local hope Arina Rodionova.

"Thankfully that did not happen and I'm going the right direction."

The 26-year-old had been tipped as a future grand slam champion when she reached the U.S. Open final as a teenager in 2009.

But despite reaching the ranking summit a year later, Wozniacki remains a bona fide member of a WTA club which boasts only two other members -- players who failed to win a major despite being ranked world number one.

Breaking free from that club -- which also includes Russia's Dinara Safina and Serbia's Jelena Jankovic -- remains the number one goal for Wozniacki.

"Lifting trophies and competing is what I love," said Wozniacki, who completed the New York City marathon just a few weeks after finishing runner-up at the U.S. Open in 2014.

"Obviously, training, you've hit a million balls over my life.

"But I think the competing is what drives me. I love to win, so... That's what I train for."

(Reporting by Pritha Sarkar, editing by Amlan Chakraborty)