With unit processing times, a fair schedule exists exactly when a bipartite graph has a matching that saturates its left side. The left vertices of the graph are the jobs, one for every day and client. The right vertices are the pairs of a day and a client, of which the first client of a day with a given due date stands for that due date, and, for every client, the $k$ days that the client must be served on being taken out of the $m$ days, $m - k$ rejection vertices. The graph is written as a flat table of zeros and ones by a word RAM program on the zeros and ones of the word of the instance, in time polynomial in the size of the word; a second word RAM program converts the table into the compressed sparse row word of the graph, in time polynomial in the size of the table; and the cited decider of $lax-817977$ ($ramPolytime_saturating$) decides whether the graph has such a matching in time polynomial in the size of that word. A word that encodes no instance with unit processing times is sent to a graph with one left vertex and no right vertex.