Resumen de Termination of rewriting with mon-monotonic ordering

Mirtha Lina Fernandez Venero

• This thesis is intended to provide a first step on the study of the monotonicity property with the aim of increasing the orderings to be used in practice for proving termination, In this light, we will show that the need of monotonic orderings for termination is closely related to the kind of rewriting under consideration as well as to the method that is applied. Within the context of the use of non-monotonic orderings, we will also focus on obtaining modularity results at the level of proofs (i.e. orderings) rather than at the level of the rewriting systems. It turns out that relaxing the monotonicity property is also important in order to provide suitable orderings for building incremental termination proofs. By suitable, we mean imposing few properties on these orderings which, in turn, means imposing few properties on the base systems and the proofs which are reused.

  In order to achieve our goals, we have divided our research in two main parts. The first part is devoted to study non-monotonic orderings for proving inner-most termination. The second part studies non-monotonic orderings for proving CE-termination.