function b = is_jtriv(S)
% is the monoid S J-trivial?
% a monoid is J-trivial iff 
% for all a,b in S, SaS = SbS implies a=b

b = 1;
[n,n] = size(S);
for i=1:n
  for j=i+1:n
    Si = Sab(S,i);
    Sj = Sab(S,j);
    b = ~seteq(Si,Sj);
    % we can't have i=j, so Si should not be equal to Sj
    if ~b, 
      %keyboard
      break, 
    end
  end
  if ~b, break, end
end
return



function Si = Sab(S,a)
[n,n] = size(S);
Si = [];
for i=1:n
  for j=1:n
    Si(end+1) = S(S(i,a),j);
  end
end
return