Termination of rewriting systems by polynomial interpretations and its implementation
Science of Computer Programming
Journal of Symbolic Computation
POPL '87 Proceedings of the 14th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Term rewriting and all that
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Testing Positiveness of Polynomials
Journal of Automated Reasoning
Termination of Rewrite Systems by Elementary Interpretations
Proceedings of the Third International Conference on Algebraic and Logic Programming
Mechanically Proving Termination Using Polynomial Interpretations
Journal of Automated Reasoning
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Proving termination of context-sensitive rewriting by transformation
Information and Computation
Practical use of polynomials over the reals in proofs of termination
Proceedings of the 9th ACM SIGPLAN international conference on Principles and practice of declarative programming
Context-sensitive dependency pairs
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Orderings and constraints: theory and practice of proving termination
Rewriting Computation and Proof
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Symbolic constraints arising in proofs of termination of programs are often translated into numeric constraints before checking them for satisfiability. In this setting, polynomial interpretations are a simple and popular choice. In the nineties, Lescanne introduced the elementary algebraic interpretations as a suitable alternative to polynomial interpretations in proofs of termination of term rewriting. Here, not only addition and product but also exponential expressions are allowed. Lescanne investigated the use of elementary interpretations for witnessing satisfiability of a given set of symbolic constraints. He also motivated the usefulness of elementary interpretations in proofs of termination by means of several examples. Unfortunately, he did not consider the automatic generation of such interpretations for a given termination problem. This is an important drawback for using these interpretations in practice. In this paper we show how to solve this problem by using a combination of rewriting, CLP, and CSP techniques for handling the elementary constraints which are obtained when giving the symbols parametric elementary interpretations.