Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Generating Polynomial Orderings for Termination Proofs
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
Mechanically Proving Termination Using Polynomial Interpretations
Journal of Automated Reasoning
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Tyrolean termination tool: Techniques and features
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
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Constraint-Based Approach for Analysis of Hybrid Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
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
SAT solving for termination analysis with polynomial interpretations
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Polynomial interpretations as a basis for termination analysis of logic programs
ICLP'05 Proceedings of the 21st international conference on Logic Programming
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
AProVE 1.2: automatic termination proofs in the dependency pair framework
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
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
Proving termination properties with MU-TERM
AMAST'10 Proceedings of the 13th international conference on Algebraic methodology and software technology
Polytool: Polynomial interpretations as a basis for termination analysis of logic programs
Theory and Practice of Logic Programming
Integrating ICP and LRA solvers for deciding nonlinear real arithmetic problems
Proceedings of the 2010 Conference on Formal Methods in Computer-Aided Design
SAT Modulo Linear Arithmetic for Solving Polynomial Constraints
Journal of Automated Reasoning
Transcendental inductive invariants generation for non-linear differential and hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
SAT Solving for Termination Proofs with Recursive Path Orders and Dependency Pairs
Journal of Automated Reasoning
δ-complete decision procedures for satisfiability over the reals
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
SMT for Polynomial Constraints on Real Numbers
Electronic Notes in Theoretical Computer Science (ENTCS)
dReal: an SMT solver for nonlinear theories over the reals
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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Polynomial constraint-solving plays a prominent role in several areas of engineering and software verification. In particular, polynomial constraint solving has a long and successful history in the development of tools for proving termination of programs. Well-known and very efficient techniques, like SAT algorithms and tools, have been recently proposed and used for implementing polynomial constraint solving algorithms through appropriate encodings. However, powerful techniques like the ones provided by the SMT (SAT modulo theories) approach for linear arithmetic constraints (over the rationals) are underexplored to date. In this paper we show that the use of these techniques for developing polynomial constraint solvers outperforms the best existing solvers and provides a new and powerful approach for implementing better and more general solvers for termination provers.