A Note on Simplification Orderings

@article{Dershowitz1979ANO,
  title={A Note on Simplification Orderings},
  author={Nachum Dershowitz},
  journal={Inf. Process. Lett.},
  year={1979},
  volume={9},
  pages={212-215}
}
  • N. Dershowitz
  • Published 16 December 1979
  • Philosophy
  • Inf. Process. Lett.
T E R M I N a T I O N *
A B S T R A C T This survey describes methods for proving that systems of rewrite rules terminate. Illustrations of the use of path orderings and other simplification orderings in termination proofs
Generating Polynomial Orderings
Simple Termination of Rewrite Systems
Proving termination of (conditional) rewrite systems
TLDR
This paper shows that in many applications, well-founded orderings on terms which only make use of syntactic information of a rewrite systemR, do not suffice for proving termination of R, and integrates a semantic interpretation of rewrite systems and terms into a well- founded ordering on terms: the notion of semantic ordering is the first main contribution of this paper.
A Structural Analysis of Modular Termination of Term Rewriting 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
Rewrite Systems
  • N. Dershowitz, J. Jouannaud
  • Computer Science
    Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics
  • 1990
Basics of Term Rewriting
  • M. Jantzen
  • Computer Science
    Handbook of Formal Languages
  • 1997
TLDR
Term rewriting can be seen as a generalization of string rewriting as studied early in this century by Axel Thue, and thereby introduced the idea of a universal algebra and the free algebra over sets of equations.
Generalized sufficient conditions for modular termination of rewriting
  • B. Gramlich
  • Mathematics, Computer Science
    Applicable Algebra in Engineering, Communication and Computing
  • 2005
TLDR
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.
On the Modularity of Termination of Term Rewriting Systems
  • E. Ohlebusch
  • Computer Science, Mathematics
    Theor. Comput. Sci.
  • 1994
Synthesis of sup-interpretations: A survey
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References

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Proving termination with multiset orderings
TLDR
The multiset ordering enables the use of relatively simple and intuitive termination functions in otherwise difficult termination proofs, and is used to prove the termination of production systems, programs defined in terms of sets of rewriting rules.
A Decision Method For Elementary Algebra And Geometry
By a decision method for a class K of sentence (or other expressions) is meant a method by means of which, given any sentence θ, one can always decide in a finite number of steps whether θ is in K;
On well-quasi-ordering finite trees
A new and simple proof is given of the known theorem that, if T 1 , T 2, … , is an infinite sequence of finite trees, then there exist i and j such that i < j and T i is homeomorphic to a subtree of