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)
We present a new approach for proving termination of rewrite systems by innermost termination. From the resulting abstract criterion we derive concrete conditions, based on critical peak properties, under which innermost termination implies termination (and connuence). Finally , we show how to apply the main results for providing new suucient conditions for… (More)
A terminating term rewriting system is called simply terminating if its termination can be shown by means of a simplification 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)
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 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.
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)
Term rewriting systems play an important role in various areas, e.g. in abstract data type speciications, for automated theorem proving and as a basic computation model for functional programming languages. In theory and practice, one of the most important properties of term rewriting systems is the strong normalization or ((nite or uniform) termination… (More)