# Generalized Sufficient Conditions for Modular Termination of Rewriting

@inproceedings{Gramlich1992GeneralizedSC,
title={Generalized Sufficient Conditions for Modular Termination of Rewriting},
author={Bernhard Gramlich},
booktitle={ALP},
year={1992}
}
• B. Gramlich
• Published in ALP 2 September 1992
• Mathematics, Computer Science
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. Whenever the disjoint union $$\mathcal{R}_1 \oplus \mathcal{R}_2$$ of two (finite) terminating term rewriting systems \(\mathcal{R}_1 ,\mathcal{R…
Generalized sufficient conditions for modular termination of rewriting
• B. Gramlich
• Mathematics, Computer Science
Applicable Algebra in Engineering, Communication and Computing
• 2005
The main results are generalized to some restricted form of non-disjoint combinations of term rewriting systems, namely for ‘combined systems with shared constructors’ and it is proved that the minimal rank of potential counterexamples in disjoint unions may be arbitrarily high which shows that interaction of systems in such disj joints may be very subtle.
Sufficient Conditions for Modular Termination of Conditional Term Rewriting Systems
This work derived sufficient criteria for modularity of termination to the case of conditional term rewriting systems (CTRSs) and related various definitions of notions related to termination of CTRSs to each other and discusses some subtleties and problems concerning extra variables in the rules.
Suucient Conditions for Modular Termination of Conditional Term Rewriting Systems
This result generalizes known suucient syntactical criteria for modular termination of rewriting to the case of conditional term rewriting systems (CTRSs) and relates various deenitions of notions related to termination of CTRSs to each other and discusses some subtleties and problems concerning extra variables in the rules.
On the Modularity of Termination of Term Rewriting Systems
• E. Ohlebusch
• Computer Science, Mathematics
Theor. Comput. Sci.
• 1994
Relating Innermost, Weak, Uniform and Modular Termination of Term Rewriting Systems
It is shown that termination is modular for locally confluent overlay systems and a simplified proof of the fact that completeness is a decomposable property of so-called constructor systems is obtained.
Completeness of Combinations of Conditional Constructor Systems 1 , 2
A property of term rewriting systems is modular if it is preserved under disjoint union. In the past few years the modularity of properties of term rewriting systems has been extensively studied. The
Termination of Narrowing: Automated Proofs and Modularity Properties
This method generalizes the current state-of-the-art, enabling the study of termination of logic programs in terms of the termination of narrowing, something which was not possible previously.
Abstract Relations between Restricted Termination and Confluence Properties of Rewrite Systems
It is shown that termination is modular for some classes of innermost terminating and locally confluent term rewriting systems, namely for non-overlapping and even for overlay systems, by means of a proof technique which itself constitutes a modular approach.

## References

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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 connuence is modular
Sufficient Conditions for Modular Termination of Conditional Term Rewriting Systems
This work derived sufficient criteria for modularity of termination to the case of conditional term rewriting systems (CTRSs) and related various definitions of notions related to termination of CTRSs to each other and discusses some subtleties and problems concerning extra variables in the rules.
Suucient Conditions for Modular Termination of Conditional Term Rewriting Systems
This result generalizes known suucient syntactical criteria for modular termination of rewriting to the case of conditional term rewriting systems (CTRSs) and relates various deenitions of notions related to termination of CTRSs to each other and discusses some subtleties and problems concerning extra variables in the rules.
Relating Innermost, Weak, Uniform and Modular Termination of Term Rewriting Systems
It is shown that termination is modular for locally confluent overlay systems and a simplified proof of the fact that completeness is a decomposable property of so-called constructor systems is obtained.
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