Soluble word problem in finite cyclic amalgams

An amalgamated free product of finite cyclic groups has an effective normal form theorem for an amalgamated free product: multiplication, subgroup membership and subgroup identifications are finite table operations. Replacing an amalgamated syllable by its image in the neighbouring factor and combining adjacent syllables from one factor strictly decreases syllable count. A remaining alternating product outside the amalgamated subgroup is nonidentity. This supplies a terminating word problem for a group algorithm.