Modularity of Convergence and Strong Convergence in Infinitary Rewriting

Properties of Term Rewriting Systems are called modular iff they arepreserved under (and reflected by) disjoint union, i.e. when combining two TermRewriting Systems with disjoint signatures. Convergence is the property ofInfinitary Term Rewriting Systems that all reduction sequences converge to alimit. Strong Convergence requires in addition that redex positions in areduction sequence move arbitrarily deep. In this paper it is shown that bothConvergence and Strong Convergence are modular properties of non-collapsingInfinitary Term Rewriting Systems, provided (for convergence) that the termmetrics are granular. This generalises known modularity results beyond metric\infty