Geodesic
Decidability of the positive theory of a~free countably generated semigroup
Sbornik. Mathematics, Tome 44 (1983) no. 1, pp. 109-116

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A decision procedure for the positive theory of a free countably generated semigroup is constructed, with a bound on the number of steps, obtained by modifying an algorithm from work of G. S. Makanin (see Matem. Sb. (N.S.), 103(145) (1977), 147–236). Bibliography: 7 titles. 
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     title = {Decidability of the positive theory of a~free countably generated semigroup},
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Yu. M. Vazhenin; B. V. Rozenblat. Decidability of the positive theory of a~free countably generated semigroup. Sbornik. Mathematics, Tome 44 (1983) no. 1, pp. 109-116. http://geodesic.mathdoc.fr/item/SM_1983_44_1_a5/