Today I noticed that the last relator in the 27-relator presentation of a group with unsolvable word problem given in
Donald J. Collins: A simple presentation of a group with unsolvable word problem. Illinois J. Math. 30(1986), no. 2, 230-234.
is a tautology, namely $ka^{-3}ta^3 = ka^{-3}ta^3$. As the total length of the presentation (i.e. sum of the lengths of the relators) is given in the paper as 421, and as the other 26 relators have together length 402, I concluded that the correct last relator would probably have length 19, provided that nothing else is wrong. A Google search for an erratum found a proposed corrected relator $a^{-3}ta^3k = ka^{-3}ta^3$ here (see Section Decision problems). However this relator has length 16, and thus the presentation has then total length 418 rather than 421.
Question: Have I miscounted something, or is there still something more wrong with the presentation in the paper?
