Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Testing Positiveness of Polynomials
Journal of Automated Reasoning
Mechanically Proving Termination Using Polynomial Interpretations
Journal of Automated Reasoning
Tyrolean termination tool: Techniques and features
Information and Computation
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Automating the dependency pair method
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
SAT solving for termination analysis with polynomial interpretations
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Ordinals and knuth-bendix orders
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
| Hi-index | 0.00 |
Polynomial interpretations are a useful technique for proving termination of term rewrite systems. In an automated setting, termination tools are concerned with parametric polynomials whose coefficients (i.e., the parameters) are initially unknown and have to be instantiated suitably such that the resulting concrete polynomials satisfy certain conditions. We focus on monotonicity and well-definedness, the two main conditions that are independent of the respective term rewrite system considered, and provide constraints on the abstract coefficients for linear, quadratic and cubic parametric polynomials such that monotonicity and well-definedness of the resulting concrete polynomials are guaranteed whenever the constraints are satisfied. Our approach subsumes the absolute positiveness approach, which is currently used in many termination tools. In particular, it allows for negative numbers in certain coefficients. We also give an example of a term rewrite system whose termination proof relies on the use of negative coefficients, thus showing that our approach is more powerful.