Geodesic
An~algorithm for recognizing the solvability of equations in~one unknown over semigroups with overlap of less than~$1/3$ in the defining words
Sbornik. Mathematics, Tome 21 (1973) no. 1, pp. 1-32

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An algorithm is constructed for recognizing the solvability of systems of equations in one unknown over semigroups of the class $K_{1/3}$ in with overlap of less than $1/3$ in the defining words. Bibliography: 4 titles. 
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     title = {An~algorithm for recognizing the solvability of equations in~one unknown over semigroups with overlap of less than~$1/3$ in the defining words},
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V. A. Osipova. An~algorithm for recognizing the solvability of equations in~one unknown over semigroups with overlap of less than~$1/3$ in the defining words. Sbornik. Mathematics, Tome 21 (1973) no. 1, pp. 1-32. http://geodesic.mathdoc.fr/item/SM_1973_21_1_a0/