Well-behaved search and the Robbins problem.- Goal-Directed Completion using SOUR Graphs.- Shostak's congruence closure as completion.- Conditional equational specifications of data types with partial operations for inductive theorem proving.- Cross-sections for finitely presented monoids with decidable word problems.- New undecidability results for finitely presented monoids.- On the property of preserving regularity for string-rewriting systems.- Rewrite systems for natural, integral, and rational arithmetic.- D-bases for polynomial ideals over commutative noetherian rings.- On the word problem for free lattices.- A total, ground path ordering for proving termination of AC-rewrite systems.- Proving innermost normalisation automatically.- Termination of context-sensitive rewriting.- A new parallel closed condition for Church-Rosser of left-linear term rewriting systems.- Innocuous constructor-sharing combinations.- Scott's conjecture is true, position sensitive weights.- Two-dimensional rewriting.- A complete axiomatisation for the inclusion of series-parallel partial orders.- Undecidability of the first order theory of one-step right ground rewriting.- The first-order theory of one step rewriting in linear noetherian systems is undecidable.- Solving linear Diophantine equations using the geometric structure of the solution space.- A criterion for intractability of E-unification with free function symbols and its relevance for combination of unification algorithms.- Effective reduction and conversion strategies for combinators.- Finite family developments.- Prototyping combination of unification algorithms with the ELAN rule-based programming language.- The invariant package of MAS.- Opal: A system for computing noncommutative gröbner bases.- TRAM: An abstract machinefor order-sorted conditional term rewriting systems.