Tail reduction free term rewriting systems revisited

First we present various undecidability results on numerous subclasses of tail reduction free term rewriting systems which simply follow from the literature review on term rewriting. Then we show that the following problems are undecidable for linear tail reduction free term rewriting systems: the word problem, the existence of normal forms problem, the common ancestor problem, the joinability problem, the normalizing problem, the termination problem, the convergence problem, the reflexive transitive closure of reduction relation inclusion problem, the reflexive transitive closure of reduction relation equality problem, and the reflexive transitive closure of reduction relation proper inclusion problem. Finally, we show that the following problems are undecidable for right-linear trf TRSs: the inductive problem, the congruence relation inclusion problem, the congruence relation equality problem, and the congruence relation proper inclusion problem. In addition, we show that the restrictions of all the problems to ground terms are also undecidable.