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Modularity of Termination for Disjoint Term Graph Rewrite Systems: A Simple Proof
 Bulletin of the European Association for Theoretical Computer Science
, 1998
"... Introduction It is wellknown 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 nonterminating system because there ..."
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Introduction It is wellknown 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 nonterminating 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 noncollapsing and nonduplicat
A Uniform Framework for Term and Graph Rewriting Applied to Combined Systems
"... This paper will bridge this gap by presenting a uniform framework, called marked rewriting. The advantage of this new approach is that both term rewriting and graph rewriting can be viewed as instances of marked rewriting. With such a method it is possible to prove statements in the framework of mar ..."
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This paper will bridge this gap by presenting a uniform framework, called marked rewriting. The advantage of this new approach is that both term rewriting and graph rewriting can be viewed as instances of marked rewriting. With such a method it is possible to prove statements in the framework of marked rewriting and to obtain results for term and graph rewriting as corollaries thereof. This will be demonstrated by proving different modularity results from both areas in one framework. 2 The Uniform Framework