Geodesic
Systems of equations in a~free group.~II
Izvestiya. Mathematics , Tome 6 (1972) no. 1, pp. 109-180.

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An algorithm for solving a class of systems of equations in a free group is constructed, and the structure of the general solution is studied. 
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     author = {Yu. I. Khmelevskii},
     title = {Systems of equations in a~free {group.~II}},
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Yu. I. Khmelevskii. Systems of equations in a~free group.~II. Izvestiya. Mathematics , Tome 6 (1972) no. 1, pp. 109-180. http://geodesic.mathdoc.fr/item/IM2_1972_6_1_a3/