Introduction It is well-known that termination is not modular for disjoint term rewriting systems (TRSs). In Toyama's counterexample the combination of the terminating systems R 1 = fF (0; 1; x) ! F (x; x; x)g, and R 2 = fg(x; y) ! x; g(x; y) ! yg yields a non-terminating system because there is the cyclic rewrite derivation 0 1 g 1 0 + 0 1 g 0 1 g g 0 1 0 1 g 0 1 g g 0 1 F F F In the last decade, many sufficient criteria for the modularity of termination have been given; see [Mid90, Ohl94, Gra96] for an overview. For instance, termination is modular for the classes of non-collapsing and non-duplicat