Greene (24) is the top-ranked women's athlete in the CrossFit Games, at the head of a leaderboard of more than 30,000 athletes.
She has one more workout to go in a very long process to be crowned the champion woman in CrossFit.
CrossFit is a type of fitness developed in 2000, is described as a a strength and conditioning programme consisting mainly of a mix of aerobic exercise, calisthenics - which is body weight exercises - and Olympic weightlifting.
It has its share of critics but has gained plenty of popularity.
Greene, who was brought up in Dunedin, works at a CrossFit gym in Abu Dhabi in the Middle East.
Last year, she was voted best in the discipline in the Middle East and African region.
She is leading this year's worldwide competition after four workouts out of the five required.
The workouts are sent out to each competitor in their own gym and they have to complete the workout in a certain time and send it back.
Greene is likely to do her fifth and final workout in the next couple of days.
So far Greene has finished third twice, been placed sixth and an 11th in the open grade.
After the open part of the competition is finished, a regional competition will take place over three weekends in May across different parts of the world.
Only the top five from selected regions qualify to go to the culmination of the event, the CrossFit Games, in California, in July.
Only 40 men and 40 women compete at that event. If Greene, who previously played rugby for Otago on the wing, can keep up this form she would appear certain to go to California.
