The reduction is computed by one word RAM program, the compilation of the IMP+ program that reads the word into an array, using its own structure, and then writes the word of the multicoloured graph: the number of vertices, the number of edges, the offsets, the targets and the colours, each computed by a pass over all ordered pairs of copies. The program runs within $c (k + 1)² (|x| + 1)$ instructions, and every value it computes is below the value bound that the fitting conditions on the word and on its image provide.