Semigroup presentation
= Semigroup presentation
{title2=$\langle X\mid u_i=v_i\rangle$}
A semigroup presentation specifies generators $X$ and equalities between nonempty words. The resulting <semigroup> is the quotient of the free semigroup $X^+$ by the smallest congruence containing these equalities. Two words are equal precisely when one can be transformed into the other by finitely many replacements in contexts, using the defining equalities in either direction.