Modularity of Convergence in Infinitary Rewriting

Properties of Term Rewriting Systems are called Modular iff they are preserved tinder disjoint union, i.e. when combining two Term Rewriting Systems with disjoint signatures. Convergence is the property of Infinitary Term Rewriting Systems that all reduction Sequences converge to a limit. Strong Convergence requires in addition that no redex position in a reduction sequence is used infinitely often.

In this paper it is shown that Strong Convergence is it modular property, lifting a restriction from a known result by Simonsen, and that Convergence is modular for non-collapsing Infinitary Term Rewriting Systems