Motivic fundamental group and motivic Galois group

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The Grothendieck-Teichmuller is the pro-algebraic group introduced by V. G. Drinfeld in 1990 as a deformation group of a certain type of quantum groups, which is defined by special three relations ; one pentagon equation and two hexagon equations. It is also worthy to note that in arithmetic geometry it is expected to coincide with the motivic Galois group of rational integers. I have found the unexpected fact that actually one pentagon equation implies the others, the two hexagon equations.Double shuffle relations and associators relations are two of the most known algebraic relations over rational numbers among multiple zeta values. Though actually both are conjectured to yield. the full set. of them, an interrelationship between these two relations was a mystery. P. Deligne and T. Terasoma posed a project(though incomplete) to deduce the former relations from the latter ones. One of my results is a final completion of their project. My method is quite different from theirs and actually it is based on really concise idea on K. T. Chen's bar construction calculus.