Special monoids and special Thue systems (Q1089108)

A special monoid is a monoid with defining relations of the form \(w=1\). The authors prove in the context of Thue systems that for two special monoids \(M_ 1\) and \(M_ 2\) with a bijective correspondence of their generators the following holds: If any congruence class \([x]_{M_ 1}\) equals the congruence class \([x]_{M_ 2}\) for \(M_ 2\) then the two congruences of \(M_ 1\) and \(M_ 2\) are equal.