User blog comment:B1mb0w/Fundamental Sequences/@comment-5529393-20151113121456/@comment-1605058-20151115095946

Substitutiong (w+1)+w in place of w+w also leads to inconsistent results. You have to figure out some kind of normal form for the expressions, so that, for example, (w+1)+w is not in normal form, but w+w is, hence fundamental sequence for both (w+1)+w and w+w (which are equal) will use the rule (γ+δ)[n]=γ+δ[n] on γ=δ=w.