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Titlebook: Rewriting Techniques and Applications; 7th International Co Harald Ganzinger Conference proceedings 1996 Springer-Verlag Berlin Heidelberg

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On proving termination by innermost termination,e conditions, based on critical peak properties, under which innermost termination implies termination (and confluence). Finally, we show how to apply the main results for providing new sufficient conditions for the modularity of termination.
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Higher-order superposition for dependent types,y-typed case, though substantial modifications and some additional theoretical machinery are needed to ensure well-typedness of rewriting in this richer type system. We conclude the paper presenting some significant applications of the theory.
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Higher-order narrowing with definitional trees, only incomparable solutions. Thus, it is the first calculus for higher-order functional logic programming which provides for such an optimality result. Since we allow higher-order logical variables denoting λ-terms, applications go beyond current functional and logic programming languages.
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Fine-grained concurrent completion,s asynchronous, there is no need for a global memory or global control, equations are stored in a SOUR graph with maximal structure sharing, and each vertex is a process, representing a term. Therefore, the parallelism is at the term level. Each edge is a communication link, representing a (subterm,
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