7.70/2.26	YES
7.70/2.27	
7.70/2.27	Problem:
7.70/2.27	 strict:
7.70/2.27	  a(b(x1)) -> b(a(x1))
7.70/2.27	  d(c(x1)) -> d(a(x1))
7.70/2.27	 weak:
7.70/2.27	  a(x1) -> b(c(x1))
7.70/2.27	  b(c(x1)) -> a(c(x1))
7.70/2.27	
7.70/2.27	Proof:
7.70/2.27	 Matrix Interpretation Processor: dim=2
7.70/2.27	  
7.70/2.27	  interpretation:
7.70/2.27	             [2 1]     [1]
7.70/2.27	   [d](x0) = [2 2]x0 + [0],
7.70/2.27	   
7.70/2.27	             [1 0]     [0]
7.70/2.27	   [c](x0) = [0 0]x0 + [1],
7.70/2.27	   
7.70/2.27	             [1 0]  
7.70/2.27	   [a](x0) = [0 0]x0,
7.70/2.27	   
7.70/2.27	             [1 0]  
7.70/2.27	   [b](x0) = [0 0]x0
7.70/2.27	  orientation:
7.70/2.27	              [1 0]      [1 0]             
7.70/2.27	   a(b(x1)) = [0 0]x1 >= [0 0]x1 = b(a(x1))
7.70/2.27	   
7.70/2.27	              [2 0]     [2]    [2 0]     [1]           
7.70/2.27	   d(c(x1)) = [2 0]x1 + [2] >= [2 0]x1 + [0] = d(a(x1))
7.70/2.27	   
7.70/2.27	           [1 0]      [1 0]             
7.70/2.27	   a(x1) = [0 0]x1 >= [0 0]x1 = b(c(x1))
7.70/2.27	   
7.70/2.27	              [1 0]      [1 0]             
7.70/2.27	   b(c(x1)) = [0 0]x1 >= [0 0]x1 = a(c(x1))
7.70/2.27	  problem:
7.70/2.27	   strict:
7.70/2.27	    a(b(x1)) -> b(a(x1))
7.70/2.27	   weak:
7.70/2.27	    a(x1) -> b(c(x1))
7.70/2.27	    b(c(x1)) -> a(c(x1))
7.70/2.27	  Matrix Interpretation Processor: dim=2
7.70/2.27	   
7.70/2.27	   interpretation:
7.70/2.27	              [1 2]  
7.70/2.27	    [c](x0) = [0 0]x0,
7.70/2.27	    
7.70/2.27	              [1 2]     [0]
7.70/2.27	    [a](x0) = [0 2]x0 + [1],
7.70/2.27	    
7.70/2.27	                   [0]
7.70/2.27	    [b](x0) = x0 + [1]
7.70/2.27	   orientation:
7.70/2.27	               [1 2]     [2]    [1 2]     [0]           
7.70/2.27	    a(b(x1)) = [0 2]x1 + [3] >= [0 2]x1 + [2] = b(a(x1))
7.70/2.27	    
7.70/2.27	            [1 2]     [0]    [1 2]     [0]           
7.70/2.27	    a(x1) = [0 2]x1 + [1] >= [0 0]x1 + [1] = b(c(x1))
7.70/2.27	    
7.70/2.27	               [1 2]     [0]    [1 2]     [0]           
7.70/2.27	    b(c(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = a(c(x1))
7.70/2.27	   problem:
7.70/2.27	    strict:
7.70/2.27	     
7.70/2.27	    weak:
7.70/2.27	     a(x1) -> b(c(x1))
7.70/2.27	     b(c(x1)) -> a(c(x1))
7.70/2.27	   Qed
7.70/2.27	EOF