We present a new approach for proving termination of rewrite systems by innermost termination. From the resulting abstract criterion we derive concrete conditions, based on critical peak properties, under which innermost termination implies termination (and connuence). Finally , we show how to apply the main results for providing new suucient conditions for the modularity of termination.

We report the atomic-scale imaging with concurrent transport measurements of the breakdown of individual multiwall carbon nanotubes inside a transmission electron microscope equipped with a piezomanipulator. We found unexpectedly three distinct breakdown sequences: namely, from the outermost wall inward, from the innermost wall outward, and alternatively between the innermost and the outmost wa...

We introduce a technique to facilitate termination proofs for term rewriting systems. We especially focus on innermost termination. The main features of this technique lie in its simplicity and e ectiveness in practice. This work can be regarded as an application of the general notion termination through transformation to both termination and innermost termination proofs.

variable, 66algebra, 16weakly monotone, 16well-founded, 16argument filtering, 26reverse, 71arity, 10assignment, 16 carrier, 16collapsing, 13compatible, 50constant, 10context, 11closed under, 12cycle, 21 defined symbol, 12dependency graph, 21approximation, 37estimated, 37estimated*, 38dependency pair, 20symbol, 20dom...

Time complexity in rewriting is naturally understood as the number of steps needed to reduce terms normal forms. Establishing bounds this measure a well-known problem community. A vast majority techniques find such consist modifying termination proofs order recover information. This has been done for instance with semantic interpretations, recursive path orders, and dependency pairs. In paper, ...

We investigate the modularity behaviour of termination and connuence properties of conditional term rewriting systems. In particular , we show how to obtain suucient conditions for the modularity of weak termination, weak innermost termination, (strong) innermost termination , (strong) termination, connuence and completeness of conditional rewrite systems.

BACKGROUND The invasive nature of surgery, with its increased exposure to blood, means that during surgery there is a high risk of transfer of pathogens. Pathogens can be transferred through contact between surgical patients and the surgical team, resulting in post-operative or blood borne infections in patients or blood borne infections in the surgical team. Both patients and the surgical team...

Preservation of regularity by a term rewrite system (TRS) states that the set of reachable terms from a tree automata (TA) language (aka regular term set) is also a TA language. It is an important and useful property, and there have been many works on identifying classes of TRS ensuring it; unfortunately, regularity is not preserved for restricted classes of TRS like shallow TRS. Nevertheless, ...