The \size-change termination" principle for a rst-order functional language with well-founded data is: a program terminates on all inputs if every innite call sequence (following program control ow) would cause an innite descent in some data values. Size-change analysis is based only on local approximations to parameter size changes derivable from program syntax. The set of innite call sequences that follow program ow and can be recognized as causing innite descent is an !-regular set, representable by a Buchi automaton. Algorithms for such automata can be used to decide size-change termination. We also give a direct algorithm operating on \size-change graphs" (without the passage to automata). Compared to other results in the literature, termination analysis based on the size-change principle is surprisingly simple and general: lexical orders (also called lexicographic orders), indirect function calls and permuted arguments (descent that is not in-situ) are all handled auto...

: We present here decidable approximations of sets of descendants and sets of normal forms of Term Rewriting Systems, based on specific tree automata techniques. In the context of rewriting logic, a Term Rewriting System is a program, and a normal form is a result of the program. Thus, approximations of sets of descendants and sets of normal forms provide tools for analysing a few properties of programs: we show how to compute a superset of results, to prove the sufficient completeness property, or to find a criterion for proving termination under a specific strategy, the sequential reduction strategy. Key-words: Term Rewriting, Program Verification, Normal Forms, Descendants, Tree Automata, Approximation, Sufficient Completeness, Reachability, Termination. (R'esum'e : tsvp) Email: Thomas.Genet@loria.fr, http://www.loria.fr/equipe/protheo.html Unite de recherche INRIA Lorraine Technopole de Nancy-Brabois, Campus scientifique, 615 rue de Jardin Botanique, BP 101, 54600 VILLERS L ES NA...

interpretation or constraint solving analyses may be used to detect both modalities of size-change behavior, and can be found in the literature [Chin and Khoo 2002; Hughes et al. 1996]. We develop analyses for the current context in Section 5, in the style of Jones et al. [1993, Section 14.3].

Recent research suggests that the goal of fully automatic and reliable program generation for a broad range of applications is coming nearer to feasibility. However, several interesting and challenging problems remain to be solved before it becomes a reality. Solving them is also necessary, if we hope ever to elevate software engineering from its current state (a highly-developed handiwork) into a successful branch of engineering, capable of solving a wide range of new problems by systematic, well-automated and well-founded methods.

A strategy of TRSs is said to be complete if all normal forms of a given term are reachable from the term. We show the innermost strategy is complete for terminating, right-linear and overlay TRSs. This strategy is fairly efficient to calculate all normal forms of a given term by searching reduction trees. We also discuss the possibilities for weakening the conditions. 1