Dehn algorithm
= Dehn algorithm
{c}
{wiki}
For a <Dehn presentation>, repeatedly freely reduce a word or replace a <relator> segment longer than half its perimeter by its shorter complementary segment. Length decreases strictly. A word represents the identity exactly when the procedure reaches the empty word: any nonempty terminal null word would contradict the defining Dehn property. The finite list of <relators> makes each search effective.