An exercise in universal algebra for process axiomatisations

This (unpublished) 8 page manuscript note was written in 1989 by me, site author,
as a subroutine to establish completeness of various axiom systems in process algebra, as needed at that time in our study (with Jan Bergstra and Ernst Olderog) of ready and failure semantics and their axiomatisations, reported in SIAM J. COMPUT. 1988, Readies and failures in the algebra of communicating processes (p. 1134-1177). See for a condensed version of this note’s content there Section 4.2.1, General Intermezzo, p.p.1152-1156.