An almost-confluent congruential language which is not Church–Rosser congruential

It is fairly easy to show that every regular set is an almost-confluent congruential language (ACCL), and it is known [3] that every regular set is a Church–Rosser congruential language (CRCL). Whether there exists an ACCL, which is not a CRCL, seems to remain an open question. In this note we present one such ACCL.