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In this paper we use the operadic framework to find Gr\"obner-Shirshov basesfor the free quadri-algebra. We perform computations using the representationof the nonsymmetric operad by planar rooted trees in a very intuitive way.Gr\"obner-Shirshov bases for the free dendriform algebra are also found withthis technique, simplifying the work by Chen and Wang in 2010.

Gr\"obner-Shirshov bases for the non-symmetric operads of dendriform algebras and quadri-algebras (unabridged version)