where E is the 2-polygraph Com 2 (X) for a finite set X defined in 2.4.2. The 2-cell of the 2-polygraph Com 2 (X) are oriented with respect to a deglex order induced by a total order on X, hence Com 2 (X) is terminating ,
? is compatible with R because rewritings with respect to R do not make the dot 2-cell move around a cup or a cap, or create sources of isotopies ,
, This square extension is made of the ten elements given by the diagrams of the homotopy basis for the 3-polygraph of permutations from
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