2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106274The original version of the paper was published in Contemporary Mathematics 378 ``Groups, Languages, Algorithms''; 2005, pp. 319-348. This is a modified version with Appendix that holds a corrected formulation of Proposition 4.1.43 pages, Appendix includedGroup Theory20E06; 20F05; 20F10Divisibility Theory and Complexity of Algorithms in Free Partially Commutative Groupstext