DOHA: Serbia's Jelena Jankovic crushed leg-weary Caroline Wozniacki to reach the semi-finals of the WTA Championships while American holder Venus Williams reached the last four without hitting a ball.

On a day when calculators were needed to work out the various permutations in the two groups of four, Wozniacki deservedly also survived for the weekend.

The Dane progressed after Belarussian Victoria Azarenka's hopes ended in tears when she retired injured in the third set of her match against stand-in Agnieszka Radwanska of Poland.

In Saturday's semi-finals, world number one Serena Williams, a class apart so far this week, will face White Group runner-up Wozniacki while sister Venus, who is through despite two defeats in three matches in the Maroon Group, plays Jankovic.

Venus crept in on a sets countback after already eliminated Svetlana Kuznetsova beat fellow Russian Elena Dementieva 6-3 6-2 to leave three players tied on one win each.

FEISTY DANE

The feisty Wozniacki, a surprise U.S. Open finalist last month, has gone through the full range of emotions on her first appearance at the WTA's showpiece finale.

After spending a total of almost six hours on court in winning her first two round-robin matches against Azarenka and first alternate Vera Zvonareva, she crumbled against Jankovic, losing 6-2 6-2 as she battled fatigue and an abdominal strain.

"I didn't have anything left. I couldn't play like I wanted to. I had some pain in my stomach muscle so I couldn't serve," the 19-year-old, who the day before had writhed in agony with cramp late on against against Zvonareva, told reporters.

Quite what shape she will be in on Saturday against the formidable power of Serena, in what will be her fourth match in as many day, is debatable.

"It's still the hamstring. I also have my stomach iced," she said. "My body is just tired now. I was hoping for a couple more matches here but after this I'm ready for a vacation."