Counterexamples to termination for the direct sum of term rewriting systems
Information Processing Letters
Journal of Symbolic Computation
Term rewriting and all that
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
The size-change principle for program termination
POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Modular termination proofs for rewriting using dependency pairs
Journal of Symbolic Computation
Argument Filtering Transformation
PPDP '99 Proceedings of the International Conference PPDP'99 on Principles and Practice of Declarative Programming
Complete Monotonic Semantic Path Orderings
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Relaxing monotonicity for innermost termination
Information Processing Letters
On proving C ε-termination of rewriting by size-change termination
Information Processing Letters
Fast narrowing-driven partial evaluation for inductively sequential programs
Proceedings of the tenth ACM SIGPLAN international conference on Functional programming
Program termination analysis in polynomial time
ACM Transactions on Programming Languages and Systems (TOPLAS)
Ranking functions for size-change termination
ACM Transactions on Programming Languages and Systems (TOPLAS)
Relaxing monotonicity for innermost termination
Information Processing Letters
On proving C E-termination of rewriting by size-change termination
Information Processing Letters
Testing for termination with monotonicity constraints
ICLP'05 Proceedings of the 21st international conference on Logic Programming
Resource analysis by sup-interpretation
FLOPS'06 Proceedings of the 8th international conference on Functional and Logic Programming
Recursive path orderings can also be incremental
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Orderings for innermost termination
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
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In [13], a new size-change principle was proposed to verify termination of functional programs automatically. We extend this principle in order to prove termination and innermost termination of arbitrary term rewrite systems (TRSs). Moreover, we compare this approach with existing techniques for termination analysis of TRSs (such as recursive path orderings or dependency pairs). It turns out that the size-change principle on its own fails for many examples that can be handled by standard techniques for rewriting, but there are also TRSs where it succeeds whereas existing rewriting techniques fail. In order to benefit from their respective advantages, we show how to combine the size-change principle with classical orderings and with dependency pairs. In this way, we obtain a new approach for automated termination proofs of TRSs which is more powerful than previous approaches.