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A proof of the conjecture of zantema on a persistent property of term rewriting systems

A property P of term rewriting system is persistent if for any many-sorted term rewriting system R, R has the property P i its underlying term rewriting system (R), which results from R by omitting its sort information, has the property P. It is shown that termination is a persistent property of many-sorted term rewriting systems that contain only variables of the same sorts. This is the positive solution to a problem of Zantema, which has been appeared as Rewriting Open Problem 60 in literature.