But Puigdemont's Belgian lawyer, Paul Bekaert, said that the Catalan separatist leader wasn't planning an immediate return.
Over a dozen Catalan leaders are facing possible charges of sedition, misuse of public funds and rebellion in Spain, over their roles in October's illegal independence referendum and the subsequent unilateral declaration of independence. The withdrawal of the arrest warrant would leave him without an worldwide legal platform to pursue his independence campaign.
Puigdemont fled to Belgium after declaring his region independent from Spain in a referendum that saw voters in Catalonia vote overwhelmingly to secede from Madrid's control - although the ballot was not sanctioned by Madrid and less than half of the electorate turned out to vote.
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In the appeal, lawyers for Turner argue their client was denied due process during his trial and called it "fundamentally unfair". The case received worldwide attention after Turner's victim delivered a heartbreaking 12-page statement detailing her experience.
The decision does not mean that Puigdemont, who faces charges of rebellion, would not be arrested if he returned to Spain, where he is still wanted by judicial authorities.
Puidgemont's former deputy Oriol Junqueras, another cabinet member and two independence activists have already been jailed in Spain.
Puigdemont and his associates were due to appear in a Belgian court on December 14, coincidentally, when Spanish Prime Minister Mariano Rajoy is in Brussels for a meeting of European Union (EU) leaders.
Catalans remain deeply split on independence, and several polls suggest pro-secession parties might struggle to win enough seats to form a new regional government.
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Official campaigning for a 21 December regional election, which was called after Puigdemont's government was dissolved, started on Tuesday.
The Spanish government called the early elections in a bid to find a democratic way out of the nation's worst crisis in almost four decades. Puigdement is running as the candidate for the Junts Per Catalunya party, despite his exile.
Llarena said that Puigdemont and the Catalan cabinet members in Belgium showed a willingness to return to Spain while withdrawing the warrants prevented more than one European jurisdiction overseeing the case.
The judge's decision follows mounting concerns among Spanish legal experts that the Belgian judiciary could in effect limit the range of crimes for which Mr. Puigdemont and the others could be put on trial if brought back to Madrid from Brussels.
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Rickie Fowler closed with a blistering 61 to finish at 18-under 270 for the weekend to claim the Hero World Challenge title. Woods, who stated post-round that he was happiest about his driving this week, played his final 45 holes in level-par.