Introduction: Formalin injection induces nociceptive bahaviour in phase I and II, with a quiescent phase between them. While active inhibitory mechanisms are proposed to be responsible for initiation of interphase, the exact mechanisms which lead to termination of nociceptive response in phase II are not clear yet. Phase II is a consequence of peripheral and central sensitization processes, whi...

The dependency pair approach is one of the most powerful techniques for automated termination proofs of term rewrite systems. Up to now, it was regarded as one of several possible methods to prove termination. We show that dependency pairs can instead be used as a general concept to integrate arbitrary techniques for termination analysis. In this way, the benefits of different techniques can be...

mu-term is a tool which can be used to verify a number of termination properties of (variants of) Term Rewriting Systems (TRSs): termination of rewriting, termination of innermost rewriting, termination of order-sorted rewriting, termination of context-sensitive rewriting, termination of innermost context-sensitive rewriting and termination of rewriting modulo specific axioms. Such termination ...

1 I n t r o d u c t i o n A fundamental problem in the theory of term rewriting is the detection of termination: for a fixed system of rewrite rules, determine whether there are infinite rewrite sequences. Besides termination a number of related properties are of interest, linearly ordered by implication: polynomial termination ~ w-termination ~ total termination simple termination ~ non-self-e...

The dependency pair approach is one of the most powerful techniques for automated (innermost) termination proofs of term rewrite systems (TRSs). For any TRS, it generates inequality constraints that have to be satisfied by well-founded orders. However, proving innermost termination is considerably easier than termination, since the constraints for innermost termination are a subset of those for...

"Relative termination" is a property that generalizes both termination and "termination modulo". In order to prove that a term rewrite Systemrelatively termmates, one may reuse the common termination quasiordenngs. Further proof methods become available by the Cooperation property. Relative termination sets up new proof techniques for termination and confluence. The usefulness of the notion of ...

In ACP-style process algebra, the interpretation of a constant atomic action combines action execution with termination. In a setting with timing, different forms of termination can be distinguished: some time termination, current time slice termination, urgent termination, termination in a virtual state. In a setting with the silent action τ , we also have silent termination. This leads to pro...

To prove termination of Java Bytecode (JBC) automatically, we transform JBC to finite termination graphs which represent all possible runs of the program. Afterwards, the graph can be translated into “simple” formalisms like term rewriting and existing tools can be used to prove termination of the resulting term rewrite system (TRS). In this paper we show that termination graphs indeed capture ...