Introduction A term rewriting system (TRS for short) is a pair (F ; R) consisting of a signature F and a set R of rewrite rules [1, 4]. Every rewrite rule l ! r 2 R, where l; r are terms from T (F ; V), must satisfy the following two constraints: (i) l is not a variable, and (ii) variables occurring in r also occur in l. Two TRSs are disjoint if their signatures are disjoint. A property P of TRSs is called modular, if for all disjoint TRSs (F 1 ; R 1 ) and (F 2 ; R 2 ) their disjoint union (F 1 ]F 2 ; R 1 ] R 2 ) has the property P if and only if both (F 1 ;<F3
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