  Sch\"utzenberger's jeu de taquin is an algorithm on the structure of
tableaux, which transforms a skew tableau into a Young one by local
transformation rules on the columns of the tableaux. This algorithm defines an
equivalence relation on tableaux compatible with the plactic congruence, and
gives a proof of the Littlewood-Richardson rule on Schur polynomials. In this
article, we introduce the notion of string of columns rewriting system as
mechanism of transformations of glued sequences of columns. We describe the
execution of the jeu de taquin algorithm as rewriting paths of a string of
columns rewriting. We deduce algebraic properties on the plastic congruence and
we relate the jeu de taquin to insertion algorithms on tableaux.
