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Modular properties of term rewriting systems, i.e. properties which are preserved under disjoint unions, have attracted an increasing attention within the last few years. Whereas confluence is modular this does not hold true in general for termination. By means of a careful analysis of potential counterexamples we prove the following abstract result.… (More)
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.
Modular properties of term rewriting systems, i.e. properties which are preserved under disjoint unions, have attracted an increasing attention within the last few years. Whereas connuence is modular this does not hold true in general for termination. By means of a careful analysis of potential counterexamples we prove the following abstract result.… (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)
The automated analysis of termination of term rewriting systems (TRSs) has drawn a lot of attention in the scientific community during the last decades and many different methods and approaches have been developed for this purpose. We present VMTL (Vienna Modular Termination Laboratory), a tool implementing some of the most recent and powerful algorithms… (More)
We present a new criterion for connuence of (possibly) non-terminating left-linear term rewriting systems. The criterion is based on certain strong joinabil-ity properties of parallel critical pairs. We show how this criterion relates to other well-known results, consider some special cases and discuss some possible extensions.
We consider the problem of verifying connuence and termination of conditional term rewriting systems. Recently we have obtained some interesting results for unconditional term rewriting systems (TRSs) which are non-overlapping or, more generally, locally connuent overlay systems. These results provide suucient criteria for termination plus connuence in… (More)
We revisit (un)soundness of transformations of conditional into unconditional rewrite systems. The focus here is on so-called unravelings, the most simple and natural kind of such transformations, for the class of normal conditional systems without extra variables. By a systematic and thorough study of existing counterexamples and of the potential sources… (More)
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)