Exact computation sequences are sequences of the form $$ \mathop - \limits^{S_1 } > \mathop - \limits^{S_2 } > ...\mathop - \limits^{S_n } > ,$$ , where L0 is a free algebra, A0 is a set of conditional equations over L0, Si is a "step function", L i =S i (L i −1), and A i =S i (A i −1). Each step function is the top-down reduction extension of a set of confluent and noetherian rewrite rules. These sequences are used in solving the word problem for free algebras, since for any pair of terms t1,t2 in L, $$t_1 = _{A_0 } t_2 iff S_n o...oS_1 \left( {t_1 } \right) = S_n o...oS_1 \left( {t_2 } \right).$$