G'defined as follows. If x i s a group element of G (= equivalence class of words) let w be any word representing x.
X. x =xk 9,and l k x . x x-' l k l xF1= e, or xk x,x;' x i ' = e, or xk x, = xI xk . X. -Ix;l I l k 1 1 1 x . x . x x-1 xi1 $ 1 11 k l x . x . x x-1 x1:1 xk-l 11 R / = 9-1 xi = = x/x ix i - I x, tx-I xk-I = xI. xk x-1 xk-1 = e. i l There are four other very similar distinct methods to make this relator vanish. In additon, just setting xi -- x, makes everything drop out and making five of the six possible pairs commute also makes the relator vanish. Along similar lines there are three ways to make a relator of type (R2) vanish and two ways for a relator of type (R3).
Advances in Cryptology: Proceedings of CRYPTO 84 by S C Serpell, C B Brookson, B L Clark (auth.), George Robert Blakley, David Chaum (eds.)