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 growing rewriting systems that may have right-non-linear rewriterules.This implies that the reachability and the joinability of some class of right-linear term rewriting systems are decidable,which improves the results for right-ground term rewriting systems by Oyamaguchi.Our result extends the class of left-linear term rewriting systems having a decidable call-by-need normalizing strategy.Moreover,we prove that the termination property is decidable for almost orthogonal growing term rewriting systems.
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