Global transformations form a categorical framework adapting graph\ntransformations to describe fully synchronous rule systems on a given data\nstructure.In this work we focus on data structures that can be captured as\npresheaves and study the computational aspects of such synchronous rule\nsystems.To obtain an online algorithm, a complete study of the sub-steps within\neach synchronous step is done at the semantic level.This leads to the\ndefinition of accretive rule systems and a local criterion to characterize\nthese systems.Finally an online computation algorithm for theses systems is\ngiven.\n