This paper continues the study of decision problems for finite complete rewriting systems [1]. The authors show that the problem of cyclic equality is undecidable for length-reducing finite complete rewriting systems. Their complicated proof, a combination of a construction and a characterization method, applies only to nonmonadic rewriting systems. The decidability of cyclic equality for finite monadic complete rewriting systems remains an open problem. Furthermore, whereas the left conjugacy problem and the conjugacy problem are decidable for length-reducing finite complete rewriting systems [2], the authors prove that these two problems are undecidable for general finite complete rewriting systems; the system T in the proof of Lemma 3.6 does not resolve this question.