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Sch\"utzenberger's jeu de taquin is an algorithm on the structure oftableaux, which transforms a skew tableau into a Young one by localtransformation rules on the columns of the tableaux. This algorithm defines anequivalence relation on tableaux compatible with the plactic congruence, andgives a proof of the Littlewood-Richardson rule on Schur polynomials. In thisarticle, we introduce the notion of string of columns rewriting system asmechanism of transformations of glued sequences of columns. We describe theexecution of the jeu de taquin algorithm as rewriting paths of a string ofcolumns rewriting. We deduce algebraic properties on the plastic congruence andwe relate the jeu de taquin to insertion algorithms on tableaux.

String of columns rewriting and confluence of the jeu de taquin