%given a reduced interval matrix with nonnegative entries
%the program tells whether it contains a rk 1 matrix; the positive answer
%corresponds to 1, the negative one to 0
% The program uses Theorem 10 of the paper On rank range of interval matrices


function l=rk1nnr(m,M)


  l=1;
[p,q]=size(m);
c=min(p,q);
t=c-1;

for h=2:2^t

	  %%%%%%%%%scelto h%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	  
	  X=multisubsets(p,h);
	  Y=orderedmultisubsets(q,h);
	  for a=1:size(X,1)
		  for b=1:size(Y,1)
			  d=1;
	  for i=1:h
		  d=d*m(X(a,i),Y(b,i));
		  end
		  %so I have calculated m_{X(a), Y(b)}

P=perms(Y(b,:));

  for j=1:size(P,1)
	  e=1;
	    for i=1:h
		    e=e*M(X(a,i),P(j,i));
                  end
                  %so we have calculated M_{X(a), j-th permutation of Y(b)}

if d > e
l=0;
return
end
		    

	  end %j=1:size(P,2)
		  end %for a
		  end %for b

		  
	 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
		  end %for h=2:2^t