For a group $G$ with a certain positive presentation, we provide a criterion for two tuples of generators of $G$ to be Hurwitz equivalent. Based on this criterion, we present an algorithmic approach to solve the Hurwitz equivalence and the Hurwitz search problems by using the word reversing method.
"An algorithmic approach to Hurwitz equivalences." Hiroshima Math. J. 43 (3) 335 - 350, November 2013. https://doi.org/10.32917/hmj/1389102579