2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68540We present here a more general version of the balanced pair algorithm. This version works in the reducible case and terminates more often than the standard algorithm. We present examples to illustrate this point. Lastly, we discuss the features which lead to balanced pair algorithms not terminating and state several conjectures.Latex, 11 pages, no figures. Submitted to Topology ProceedingsDynamical SystemsMathematical PhysicsMetric GeometryPrimary 37A30; Secondary 37B10 52C23text