12.68/3.54	YES
12.68/3.54	
12.68/3.54	Problem:
12.68/3.54	 strict:
12.68/3.54	  f(g(f(x))) -> f(g(g(g(f(x)))))
12.68/3.54	 weak:
12.68/3.54	  g(x) -> g(g(x))
12.68/3.54	  g(x) -> g(g(f(g(g(x)))))
12.68/3.54	  f(x) -> g(g(f(g(g(x)))))
12.68/3.54	
12.68/3.54	Proof:
12.68/3.54	 Matrix Interpretation Processor: dim=3
12.68/3.54	  
12.68/3.54	  interpretation:
12.68/3.54	             [1 0 0]  
12.68/3.54	   [g](x0) = [0 0 1]x0
12.68/3.54	             [0 0 0]  ,
12.68/3.54	   
12.68/3.54	             [1 2 0]     [0]
12.68/3.54	   [f](x0) = [0 1 2]x0 + [2]
12.68/3.54	             [2 1 0]     [2]
12.68/3.54	  orientation:
12.68/3.54	                [5 4 0]    [4]    [1 2 0]    [0]                   
12.68/3.54	   f(g(f(x))) = [2 1 0]x + [4] >= [0 0 0]x + [2] = f(g(g(g(f(x)))))
12.68/3.54	                [4 5 0]    [4]    [2 4 0]    [2]                   
12.68/3.54	   
12.68/3.54	          [1 0 0]     [1 0 0]           
12.68/3.54	   g(x) = [0 0 1]x >= [0 0 0]x = g(g(x))
12.68/3.54	          [0 0 0]     [0 0 0]           
12.68/3.54	   
12.68/3.54	          [1 0 0]     [1 0 0]                    
12.68/3.54	   g(x) = [0 0 1]x >= [0 0 0]x = g(g(f(g(g(x)))))
12.68/3.54	          [0 0 0]     [0 0 0]                    
12.68/3.54	   
12.68/3.54	          [1 2 0]    [0]    [1 0 0]                    
12.68/3.54	   f(x) = [0 1 2]x + [2] >= [0 0 0]x = g(g(f(g(g(x)))))
12.68/3.54	          [2 1 0]    [2]    [0 0 0]                    
12.68/3.54	  problem:
12.68/3.54	   strict:
12.68/3.54	    
12.68/3.54	   weak:
12.68/3.54	    g(x) -> g(g(x))
12.68/3.54	    g(x) -> g(g(f(g(g(x)))))
12.68/3.54	    f(x) -> g(g(f(g(g(x)))))
12.68/3.54	  Qed
12.68/3.55	EOF