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The defending champion looked the stronger of the two from the start as he claimed a break in the opening game of the match, before wrapping up the set 6-1.
The world number five doubled his lead by claiming the second by the same scoreline as he cruised towards a place in round three.
Rola had few chances against the Scot's serve. He did have the opportunity to break back a couple of times, but the third seed was able to up his game each time.
While 4-0 down in the third set, Rola tried to get back into contention with some big serves, but a double fault allowed Murray to break again and serve for the match after less than 90 minutes on court.