function b = is_aperiodic(S)
% is the monoid S aperiodic?

b = 1;
[n,n] = size(S);
for i=1:n
  x = i;
  if (S(x,x)~=x)  %element not idempotent
    for k=1:n
      x1 = S(x,i);
      if (x1==i) % periodic
        b = 0;
        break
      elseif (x1==x)
        break
      end
      x = x1;
    end
  end
  if ~b
    break
  end
end
return