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A term rewriting system is called growing if each variable occurring both the left-hand side and the right-hand side of a rewrite rule occurs at depth zero or one in the left-hand side. Jacquemard showed that the reachability and the sequentiality of linear (i.e., left-right-linear) growing term rewriting systems are decidable. In this paper we show that Jacquemard’s result can be extended to left-linear...
We present two new transformation techniques for proving termination of context-sensitive rewriting. Ourfirst method is simple, sound, and more powerful than previously suggested transformations. However, it is not complete, i.e., there are terminating context-sensitive rewrite systems that are transformed into non-terminating term rewrite systems. The second method that we present in this paper is...
Context-sensitive rewriting was introduced in [7] and consists of syntactical restrictions imposed on a Term Rewriting System indicating how reductions can be performed. So context-sensitive rewriting is a restriction of the usual rewrite relation which reduces the reduction space and allows for a finer control of the reductions of a term. In this paper we extend the concept of context-sensitive...
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