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For every finitely generated free group we construct an explicit left orderextending the lexicographic order on the free monoid generated by the positiveletters. The order is defined by a left, free action on the orbit of 0 of afree group of piecewise linear homeomorphisms of the line. The membership inthe positive cone is decidable in linear time in the length of the input word.The positive cone forms a context-free language closed under word reversal.

Explicit left orders on free groups extending the lexicographic order on free monoids