NEW YORK – Their rivalry has taken an envious route, skipping from Argentina up to Monaco before flitting about Spain, France and Italy for seven matches in 13 months. It has included brief two-set bouts and rugged three-setters, with seven wins for the so-called “King of Clay,” and an admirable, tantalizing three victories for his presumed successor.

But for all their history, Rafael Nadal and Dominic Thiem have never played on hard court, and they’ve never played in New York. They’ll try it for the first time in the U.S. Open quarterfinals at Billie Jean King National Tennis Center on Tuesday and see how it goes.

“On clay, I think it’s one of the biggest challenges in sports to beat this guy or to compete with this guy,” Thiem said. “I hope that it’s a little bit more comfortable on hard court, but I’m not sure.”

It would do Thiem well to cling to that thought.

The change of scenery might even be good for the Austrian, who turns 25 on Monday and who defeated Wimbledon finalist Kevin Anderson on Sunday 7-5, 6-2, 7-6 (7-2) in a match so dominant that he only lost four points on his first serve.

The last time the burgeoning rivals met was in the French Open finals, when Nadal beat Thiem in straight sets to claim his 11th title in Paris. But Nadal is more vulnerable in New York than he is at Roland Garros: At the French Open, he has an 86-2 career record and 11 titles.

At the U.S. Open he’s a more modest 53-10. He’s only won it three times.

The 32-year-old has certainly been pushed in his last two matches, both of which have gone four sets. Top-seeded Nadal followed a thrilling upset bid from Karen Khachanov in the third round with a 6-3, 6-3, 6-7 (8-6), 6-4 win over Nikoloz Basilashvili in the fourth round on Sunday.

“Two matches in a row, very tough ones,” he said, understating his nearly eight hours of work.

His toiling was fruitful, however – this is the first year Nadal has made it to at least the quarterfinals of every Grand Slam since 2011.

Thiem has been tested too, requiring nine combined sets to defeat unseeded Americans Taylor Fritz and Steve Johnson en route to the fourth round. But this generally isn’t his best season – the best time to watch the young Austrian is on red clay in spring. He owns 10 career ATP Tour titles, eight of which have come on clay, two Grand Slam semifinals appearances and one finals appearance, all three of which have been at Roland Garros.

Tuesday will be his first quarterfinal appearance in a major tournament that’s not the French Open. It’s no wonder why the tennis world assumes as far as clay is concerned, Thiem is Nadal’s heir apparent. Even if it’s he’s not totally comfortable in the role.

“I grew up on the clay, so I think it’s natural that I feel most comfortable on this surface, but I like the hard court,” Thiem said. “I don’t really like to hear when somebody considers me a clay-court specialist, I don’t consider myself this way.”

Before he can inherit Nadal’s crown, Thiem knows he has a long way to go. When asked to describe his experience playing the 17-time Grand Slam champion, Thiem flashed a grin.

“Well, it was three very nice experiences and six horrible experiences,” he said, forgetting (or perhaps he’s blocked one out) that he has seven losses in the series.

Nadal was more generous in describing his matches against Thiem, the first of which came back in 2014.

He cited Thiem’s powerful, disciplined groundstrokes, which can do damage across multiple surfaces. He said he has a good off-court relationship with his fellow clay-court maven and that Thiem deserves to be here after losing a heartbreaking match to Juan Martin del Potro in the fourth round a year ago in which he held an early two-set advantage.

For Nadal, the surface hardly matters, and he doesn’t care if the match is in Barcelona or Queens. Against Thiem, he expects a challenge.

“Yeah, it’s a different kind of match than clay, but it’s still a tennis match,” Nadal said. “I know how he plays. He knows how I am playing. It’s going to be interesting one, tough one, hopefully for both of us. And hopefully who will play better, will have better chance. That’s all.”

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