## 105 Citations

T E R M I N a T I O N *

- Mathematics
- 1995

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…

Proving termination of (conditional) rewrite systems

- Computer ScienceActa Informatica
- 2005

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

- Computer Science
- 1991

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

- Computer ScienceHandbook of Theoretical Computer Science, Volume B: Formal Models and Sematics
- 1990

Basics of Term Rewriting

- Computer ScienceHandbook of Formal Languages
- 1997

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

- Mathematics, Computer ScienceApplicable 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.

On the Modularity of Termination of Term Rewriting Systems

- Computer Science, MathematicsTheor. Comput. Sci.
- 1994

## References

SHOWING 1-5 OF 5 REFERENCES

Proving termination with multiset orderings

- Computer ScienceCACM
- 1979

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

- Mathematics
- 1951

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

- Mathematics
- 1963

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…