@johncarlosbaez
you end up getting weird things like
a+ab+b=(a+b)^2+ab=
a+2ab+ba+b=a+3ab+2ba+b=
a+4ab+3ab+b=a+2ab+3ab+b (as 4=2) = ... =a+ba+b
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@johncarlosbaez
but i think you only need to square binomial things (eg ab+aba=(ab+aba)^2=2ab+2aba) in order to generate the relations we're interested in.
