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We show that for the family of Church-Rosser languages the Higman-Haines sets, which are the sets of all scattered subwords of a given language and the sets of all words that contain some word of a given language as a scattered subword, cannot be effectively constructed, although both these sets are regular for any language. This nicely contrasts the result on the effectiveness of the Higman-Haines sets for the family of context-free languages. The non-effectiveness is based on a non-recursivedoi:10.1016/j.tcs.2007.07.036 fatcat:pj5zmp5dfvhuvjridivq7l4zia