Geodesic
On the word and divisibility problems in semigroups with a~single defining relation
Izvestiya. Mathematics , Tome 12 (1978) no. 2, pp. 207-212.

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It is proved that the word problem and left (right) divisibility problem in an arbitrary semigroup with a single defining relation can be reduced to the respective problems for a single relation which is left (or right) noncancellative. Bibliography: 2 titles. 
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S. I. Adian; G. U. Oganesyan. On the word and divisibility problems in semigroups with a~single defining relation. Izvestiya. Mathematics , Tome 12 (1978) no. 2, pp. 207-212. http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a0/

[1] Adyan S. I., “Opredelyayuschie sootnosheniya i algoritmicheskie problemy dlya grupp i polugrupp”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 85, 1966, 1–124 | MR | Zbl

[2] Adyan S. I., “O preobrazovaniyakh slov v polugruppe, zadannoi sistemoi opredelyayuschikh sootnoshenii”, Algebra i logika, 15:6 (1976), 611–621 | MR | Zbl