The book covers all current aspects of rewriting including rewriting systems, term rewriting, string rewriting, theorem proving, resolution, normalization, unification, equational logics, lambda calculus, constraint solving, and functional programming.

Origin tracking in term rewriting.- Simultaneous critical pairs and Church-Rosser property.- Church-Rosser theorems for abstract reduction modulo an equivalence relation.- Automatic monoids versus monoids with finite convergent presentations.- Decidable and undecidable second-order unification problems.- On the exponent of periodicity of minimal solutions of context equations.- Unification in extensions of shallow equational theories.- Unification and matching in process algebras.- E-unification for subsystems of S4.- Solving disequations modulo some class of rewrite systems.- About proofs by consistency.- Normalization of S-terms is decidable.- Decidable approximations of sets of descendants and sets of normal forms.- Algorithms and reductions for rewriting problems.- The decidability of simultaneous rigid E-unification with one variable.- Ordering constraints over feature trees expressed in second-order monadic logic.- Co-definite set constraints.- Modularity of termination using dependency pairs.- Termination of associative-commutative rewriting by dependency pairs.- Termination transformation by tree lifting ordering.- Towards automated termination proofs through “freezing”.- Higher-order rewriting and partial evaluation.- SN combinators and partial combinatory algebras.- Coupling saturation-based provers by exchanging positive/negative information.- An on-line problem database.

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