  We study rewriting properties of the column presentation of plactic monoid
for any semisimple Lie algebra such as termination and confluence. Littelmann
described this presentation using L-S paths generators. Thanks to the shapes of
tableaux, we show that this presentation is finite and convergent. We obtain as
a corollary that plactic monoids for any semisimple Lie algebra satisfy
homological finiteness properties.
