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The plan of Schlieffen resulted in a stalemate. This was so because the German high command did not sufficiently commit to that plan.
The plan called for a very token force to be left to defend Germany against a possible French attack in the south. In the meantime, a right-wing was made to come around from the north and crush the French. But the German high command made the left wing too strong and right-wing relatively weak. Thus the right one was not able to break the French and result in a stalemate.