User blog comment:Ikosarakt1/FB100Z's variant of BEAF/@comment-10429372-20140807181903

I got the following legion comparisons: Let ‘t’ be shorthand for {w,w/2}

2 & t = {t,t} = t^t 3 & t = {t,t,t} = psi(W^W^W+W^W) w & t = psi(W^W^W+ W^W^w) t & t = psi(W^W^W+ W^W^psi(W^W)) 3 & t & t = psi(W^W^W+W^W^psi(W^W+W)) t -> t & t = psi(W^W^W*2)

note that this is just {w,w2/2}

{w,w,2/2} = psi(W^(W^W+1)) {w,w2,2/2} = psi(W^(W^W+1)2) {w,w,3/2} = psi(W^(W^W+2)) {w,w,w/2} = psi(W^(W^W+w)) {w,w,1,2/2} = psi(W^(W^W+W)) {w,w(1)2/2} = psi(W^(W^W+W^w))

{w,w/3} = psi(W^(W^W2)) {w,w/w} = psi(W^(W^Ww)) {w,w/1,2} = psi(W^W^(W+1)) {w,w/2,2} = psi(W^(W^(W+1)+W^W)) {w,w/1,3} = psi(W^(W^(W+1)2)) {w,w/1,1,2} = psi(W^(W^(W+2))) {w,w/1(1)2} = psi(W^(W^(W+w))) {w,w/1/2} = psi(W^(W^(W2)))