Moreover, chemical reactions may have multiple potential AAM solution candidates. In such ambiguous cases, the chemically correct mapping based on the actual reaction mechanism is typically determined through experiments, such as isotope labeling. Therefore, an exhaustive enumeration of potential candidate mappings is an effective approach to identifying all probable reaction patterns in unknown reactions. Based on these candidates, experimental chemists can clarify a mechanism by a designed experiment to distinguish these candidates. It is important to note that such multiple candidate mappings frequently include chemically "equivalent" transformations, which arise due to molecular symmetries in the reaction. Thus, to effectively identify all distinct reaction patterns represented by "nonequivalent" mappings, a symmetry reduction method is required.