The class of Church-Rosser congruential languages has been introduced by
McNaughton, Narendran, and Otto in 1988. A language L is Church-Rosser
congruential (belongs to CRCL), if there is a finite, confluent, and
length-reducing semi-Thue system S such that L is a finite union of congruence
classes modulo S. To date, it is still open whether every regular language is
in CRCL. In this paper, we show that every star-free language is in CRCL. In
fact, we prove a stronger statement: For every star-free language L there
exists a finite, confluent, and subword-reducing semi-Thue system S such that
the total number of congruence classes modulo S is finite and such that L is a
union of congruence classes modulo S. The construction turns out to be
effective