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+function pot = combine_pots(pot1, pot2)
+% COMBINE_POTS combine two potentials 
+% pot = combine_pots(pot1, pot2)
+
+% Reduce both potentials before trying to combine them. 
+% Cf. "Stable Local computation with Conditional Gaussian Distributions", page 9
+% Consider again two potentials with minimal tail
+
+% Guarantee minimal tails. If pot1 or pot2 are minimal, they are not changed
+pot1 = reduce_pot(pot1);
+pot2 = reduce_pot(pot2);
+
+%if the intersect set of these two potentials' head conts. combination is undifined
+if ~isempty( myintersect(pot1.cheaddom, pot2.cheaddom) )
+    return;
+end
+
+if  isempty( myintersect(pot1.domain, pot2.cheaddom) ) | isempty( myintersect(pot2.domain, pot1.cheaddom))
+    % if satisfy the condition of directed combine
+    pot = direct_combine_pots(pot1, pot2);
+else
+    % perform recursive combine
+    pot = recursive_combine_pots(pot1, pot2);
+end