Lord Trimble, the former leader of the Ulster Unionist Party and one of the architects of the Good Friday accords, which were the cornerstone of the Irish peace process, characterized the current situation in the region as "unstable" and called for the imposition of direct rule.
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He called for May to stop "pussyfooting around" and not to submit to Sinn Fein's provocation.
Trimble's statement comes after the Democratic Unionist Party (DUP) refused to come to an agreement with Sinn Fein and declared that there was "no prospect" for a deal.
The DUP and Sinn Fein have been struggling to strike a power-sharing deal since the snap assembly election in March 2017. The latest round of talks between the governing parties began in January, however, Northern Ireland still has no executive.
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The apple of discord between the parties appears to be the bill on the official status of the Irish language, which is being vehemently advanced by Sinn Fein. The DUP, though trying to meet Sinn Fein's demands, suggested culture legislation that embraced Irish and Ulster Scots, which fell short of what Sinn Feins tries to achieve.