Geodesic
About the congruences of two-generated monoid
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 1, pp. 14-18

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The congruences of two-generated monoid which generated by pair of words of length 2 are considered over two-letter alphabet. It is shown that number of equivalence classes for words of length $n$ is equal to $n+1$. The number of words in each class is found. 
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L. A. Kudryavtseva. About the congruences of two-generated monoid. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 1, pp. 14-18. http://geodesic.mathdoc.fr/item/ISU_2010_10_1_a2/