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
Proving Termination of Context-Sensitive Rewriting with MU-TERM
Electronic Notes in Theoretical Computer Science (ENTCS)
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
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
From matrix interpretations over the rationals to matrix interpretations over the naturals
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
Satisfiability of non-linear (Ir)rational arithmetic
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Complexity invariance of real interpretations
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
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
Synthesis of sup-interpretations: A survey
Theoretical Computer Science
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In the seventies, Manna and Ness, Lankford, and Dershowitz pionneered the use of polynomial interpretations with integer and real coefficients in proofs of termination of rewriting. More than twenty five years after these works were published, however, the absence of true examples in the literature has given rise to some doubts about the possible benefits of using polynomials with real or rational coefficients. In this paper we prove that there are, in fact, rewriting systems that can be proved polynomially terminating by using polynomial interpretations with (algebraic) real coefficients; however, the proof cannot be achieved if polynomials only contain rational coefficients. We prove a similar statement with respect to the use of rational coefficients versus integer coefficients.