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Cited article:

RATIONAL SUBSETS IN HNN-EXTENSIONS AND AMALGAMATED PRODUCTS

MARKUS LOHREY and GÉRAUD SÉNIZERGUES
International Journal of Algebra and Computation 18 (01) 111 (2008)
https://doi.org/10.1142/S021819670800438X

Mathematical Foundations of Computer Science 1986

Jean Berstel and Jacques Sakarovitch
Lecture Notes in Computer Science, Mathematical Foundations of Computer Science 1986 233 15 (1986)
https://doi.org/10.1007/BFb0016231