Modular Termination of Basic Narrowing -- Linear-algebraic ?-calculus: higher-order, encodings, and confluence. -- Term-Graph Rewriting Via Explicit Paths -- Finer Is Better: Abstraction Refinement for Rewriting Approximations -- A Needed Rewriting Strategy for Data-Structures with Pointers -- Effectively Checking the Finite Variant Property -- Dependency Pairs for Rewriting with Built-In Numbers and Semantic Data Structures -- Maximal Termination -- Usable Rules for Context-Sensitive Rewrite Systems -- Combining Equational Tree Automata over AC and ACI Theories -- Closure of Hedge-Automata Languages by Hedge Rewriting -- On Normalisation of Infinitary Combinatory Reduction Systems -- Innermost Reachability and Context Sensitive Reachability Properties Are Decidable for Linear Right-Shallow Term Rewriting Systems -- Arctic Termination ...Below Zero -- Logics and Automata for Totally Ordered Trees -- Diagram Rewriting for Orthogonal Matrices: A Study of Critical Peaks -- Nominal Unification from a Higher-Order Perspective -- Functional-Logic Graph Parser Combinators -- Proving Quadratic Derivational Complexities Using Context Dependent Interpretations -- Tree Automata for Non-linear Arithmetic -- Confluence by Decreasing Diagrams -- A Finite Simulation Method in a Non-deterministic Call-by-Need Lambda-Calculus with Letrec, Constructors, and Case -- Root-Labeling -- Combining Rewriting with Noetherian Induction to Reason on Non-orientable Equalities -- Deciding Innermost Loops -- Termination Proof of S-Expression Rewriting Systems with Recursive Path Relations -- Encoding the Pure Lambda Calculus into Hierarchical Graph Rewriting -- Revisiting Cut-Elimination: One Difficult Proof Is Really a Proof -- Reduction Under Substitution -- Normalization of Infinite Terms.

This book constitutes the refereed proceedings of the 19th International Conference on Rewriting Techniques and Applications, RTA 2008, held in Hagenberg, Austria, July 15-17, in June 2008 as part of the RISC Summer 2008. The 30 revised full papers presented were carefully reviewed and selected from 57 initial submissions. The papers cover current research on all aspects of rewriting including typical areas of interest such as applications, foundational issues, frameworks, implementations, and semantics.