  For every finitely generated free group we construct an explicit left order
extending the lexicographic order on the free monoid generated by the positive
letters. The order is defined by a left, free action on the orbit of 0 of a
free group of piecewise linear homeomorphisms of the line. The membership in
the 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.
