Journal of Symbolic Computation
Term rewriting and all that
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
Applicable Algebra in Engineering, Communication and Computing
Mechanically Proving Termination Using Polynomial Interpretations
Journal of Automated Reasoning
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
Matrix Interpretations for Proving Termination of Term Rewriting
Journal of Automated Reasoning
Search Techniques for Rational Polynomial Orders
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Solving Non-linear Polynomial Arithmetic via SAT Modulo Linear Arithmetic
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Orderings and constraints: theory and practice of proving termination
Rewriting Computation and Proof
On the domain and dimension hierarchy of matrix interpretations
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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Matrix interpretations generalize linear polynomial interpretations and have been proved useful in the implementation of tools for automatically proving termination of Term Rewriting Systems. In view of the successful use of rational coefficients in polynomial interpretations, we have recently generalized traditional matrix interpretations (using natural numbers in the matrix entries) to incorporate real numbers. However, existing results which formally prove that polynomials over the reals are more powerful than polynomials over the naturals for proving termination of rewrite systems failed to be extended to matrix interpretations. In this paper we get deeper into this problem. We show that, under some conditions, it is possible to transform a matrix interpretation over the rationals satisfying a set of symbolic constraints into a matrix interpretation over the naturals (using bigger matrices) which still satisfies the constraints.