Geodesic
Equations with endomorphisms in free semigroups
Diskretnaya Matematika, Tome 4 (1992) no. 2, pp. 136-141.

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For equations in free semigroups with three generators, three theorems are proved on the impossibility of constructing an algorithm allowing one to establish existence of solutions with constraints formulated in algebraic terms. 
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     author = {V. G. Durnev},
     title = {Equations with endomorphisms in free semigroups},
     journal = {Diskretnaya Matematika},
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     volume = {4},
     number = {2},
     year = {1992},
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     url = {http://geodesic.mathdoc.fr/item/DM_1992_4_2_a15/}
}
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V. G. Durnev. Equations with endomorphisms in free semigroups. Diskretnaya Matematika, Tome 4 (1992) no. 2, pp. 136-141. http://geodesic.mathdoc.fr/item/DM_1992_4_2_a15/