Counterexamples to termination for the direct sum of term rewriting systems
Information Processing Letters
Theories of computational complexity
Theories of computational complexity
Modular proofs for completeness of hierarchical term rewriting systems
Selected papers of the thirteenth conference on Foundations of software technology and theoretical computer science
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
Hierarchical termination revisited
Information Processing Letters
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
On Proving Termination by Innermost Termination
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Complete Monotonic Semantic Path Orderings
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
The Higher-Order Recursive Path Ordering
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Relaxing monotonicity for innermost termination
Information Processing Letters
On proving C E-termination of rewriting by size-change termination
Information Processing Letters
Size-change termination for term rewriting
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Orderings for innermost termination
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Termination of abstract reduction systems
CATS '07 Proceedings of the thirteenth Australasian symposium on Theory of computing - Volume 65
An extension of the Knuth-Bendix ordering with LPO-like properties
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
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In this paper the Recursive Path Ordering is adapted for proving termination of rewriting incrementally. The new ordering, called Recursive Path Ordering with Modules, has as ingredients not only a precedence but also an underlying ordering $\sqsupset_{B}$. It can be used for incremental (innermost) termination proofs of hierarchical unions by defining $\sqsupset_{B}$as an extension of the termination proof obtained for the base system. Furthermore, there are practical situations in which such proofs can be done modularly.