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 both Convergence and Strong Convergence aremodular properties of non-collapsing Infinitary Term Rewriting Systems,provided (for convergence) that the term metrics are granular. This generalisesknown modularity results beyond metric ∞.
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