2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224300We discuss the time complexity of the word and conjugacy search problems for free products $G = A \star_C B$ of groups $A$ and $B$ with amalgamation over a subgroup $C$. We stratify the set of elements of $G$ with respect to the complexity of the word and conjugacy problems and show that for the generic stratum the conjugacy search problem is decidable under some reasonable assumptions about groups $A,B,C$.Group Theory20F10 (Primary), 20P05 (Secondary)text