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Pure associative unification is equivalel~t to the resolution of word equations. We give a short survey of known results and algorithms in this field and describe the central algorithm of Makanin. T e r m i n o l o g y and N o t a t i o n s Pure associative unification is better known in literature as the resolution problem of word equations. An algebra equipped with a single associative law is a semigroup. It is a m o n o i d when it has a unit. The free monoid generated by the set A (alsodoi:10.1016/s0747-7171(89)80056-2 fatcat:lqsxwqa3ijhr5h3eaioyh3l4me