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The French Open and Wimbledon champion dropped the first set 6-7 (3-7), but rallied to finish the second 6-1, forcing a decider after getting two vital breaks.

However, Machac pulled up in the opening game of the third set with cramp and was unable to carry on after one hour and 41 minutes on the court.

It followed Roberto Bautista's flying start in their opening singles match in Group B as he cruised past Jiri Lehecka 7-6 (7-1) 6-4, with the Czech making 27 unforced errors as he failed to find an edge.

In the doubles, Alcaraz and Marcel Granollers then had to dig deep, coming from behind to beat Adam Pavlasek and Jakub Mensik in three sets to give Spain a 3-0 victory and take them top of the group. 

Meanwhile, Great Britain made a bright start to its campaign in Group D, despite US Open semi-finalist Jack Draper sitting out.

Dan Evans got it started in Manchester with a hard-earned 7-6 (7-3) 6-2 victory over Eero Vasa of Finland, converting both of his break points in the second set.

Billy Harris followed that up with an impressive tournament debut, looking unflappable as he earned the hosts an unattainable lead with his 6-4 7-6 (7-4) win over Otto Virtanen.

Finland got on the board in the doubles though, with Evans and Neal Skupski unable to get the better of Harri Heliovaara and Virtanen ensuring it was only a 2-1 loss. 

Elsewhere, United States joined Germany at the top of Group C with a 3-0 win over Chile and Italy's Matteo Arnaldi held off a spirited Thiago Monteiro to put it in control against Brazil in Group A after Matteo Berrettini's earlier victory.