Bernhard Gramlich

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We investigate the modularity behaviour of termination and connuence properties of conditional term rewriting systems. In particular , we show how to obtain suucient conditions for the modularity of weak termination, weak innermost termination, (strong) innermost termination , (strong) termination, connuence and completeness of conditional rewrite systems.
For a complete, i.e., connuent and terminating term rewriting system (TRS) it is well-known that simpliication (also called interreduction) into an equivalent canonical, i.e., complete and interreduced TRS is easily possible. This can be achieved by rst normalizing all right-hand sides of the TRS and then deleting all rules with a reducible left-hand side.(More)
A terminating term rewriting system is called simply terminating if its termination can be shown by means of a simpliication ordering, an ordering with the property that a term is always bigger than its proper subterms. Almost all methods for proving termination yield, when applicable, simple termination. We show that simple termination is an undecidable(More)