Term rewriting and all that
Termination Proofs by Context-Dependent Interpretations
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Termination Proofs and the Length of Derivations (Preliminary Version)
RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
On tree automata that certify termination of left-linear term rewriting systems
Information and Computation
Matrix Interpretations for Proving Termination of Term Rewriting
Journal of Automated Reasoning
Arctic Termination ...Below Zero
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Satisfiability of non-linear (Ir)rational arithmetic
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Termination of string rewriting with matrix interpretations
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Joint spectral radius theory for automated complexity analysis of rewrite systems
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
A dependency pair framework for innermost complexity analysis of term rewrite systems
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Matrix interpretations for polynomial derivational complexity of rewrite systems
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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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Matrix interpretations can be used to bound the derivational complexity of term rewrite systems. In particular, triangular matrix interpretations over the natural numbers are known to induce polynomial upper bounds on the derivational complexity of (compatible) rewrite systems. Using techniques from linear algebra, we show how one can generalize the method to matrices that are not necessarily triangular but nevertheless polynomially bounded. Moreover, we show that our approach also applies to matrix interpretations over the real (algebraic) numbers. In particular, it allows triangular matrix interpretations to infer tighter bounds than the original approach.