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An [[Associative calculus|associative calculus]], named after A. Thue, who first formulated the problem of recognizing equality of words in associative systems (the Thue problem, see [[#References|[1]]]). If in a given Thue system the only admissible substitutions are taken to be substitutions of right-hand sides of relations into the left-hand sides (that is, the reverse substitutions are excluded), then one obtains a Thue semi-system (or semi-Thue system, or system of substitutions). These systems in fact coincide with local canonical Post systems. Every Thue system can be regarded as a Thue semi-system, but the converse is false.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A. Thue,   "Probleme über Veränderungen von Zeichenreihen nach gegebener Regeln"  ''Kra. Vidensk. Selsk. Skrifter.'' , '''10'''  (1914)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  A.I. Mal'tsev,   "Algorithms and recursive functions" , Wolters-Noordhoff  (1970)  (Translated from Russian)</TD></TR></table>