12.87/3.65	YES
12.87/3.65	
12.87/3.65	Problem:
12.87/3.65	 c(b(a(a(x1)))) -> a(a(b(c(x1))))
12.87/3.65	 b(a(a(a(x1)))) -> a(a(a(b(x1))))
12.87/3.65	 a(b(c(x1))) -> c(b(a(x1)))
12.87/3.65	 c(c(b(b(x1)))) -> b(b(c(c(x1))))
12.87/3.65	
12.87/3.65	Proof:
12.87/3.65	 Matrix Interpretation Processor: dim=3
12.87/3.65	  
12.87/3.65	  interpretation:
12.87/3.65	                  [0]
12.87/3.65	   [c](x0) = x0 + [0]
12.87/3.65	                  [1],
12.87/3.65	   
12.87/3.65	             [1 1 0]  
12.87/3.65	   [b](x0) = [0 1 0]x0
12.87/3.65	             [0 0 1]  ,
12.87/3.65	   
12.87/3.65	             [1 0 1]     [0]
12.87/3.65	   [a](x0) = [0 1 0]x0 + [1]
12.87/3.65	             [0 0 1]     [0]
12.87/3.65	  orientation:
12.87/3.65	                    [1 1 2]     [2]    [1 1 2]     [2]                 
12.87/3.65	   c(b(a(a(x1)))) = [0 1 0]x1 + [2] >= [0 1 0]x1 + [2] = a(a(b(c(x1))))
12.87/3.65	                    [0 0 1]     [1]    [0 0 1]     [1]                 
12.87/3.65	   
12.87/3.65	                    [1 1 3]     [3]    [1 1 3]     [0]                 
12.87/3.65	   b(a(a(a(x1)))) = [0 1 0]x1 + [3] >= [0 1 0]x1 + [3] = a(a(a(b(x1))))
12.87/3.65	                    [0 0 1]     [0]    [0 0 1]     [0]                 
12.87/3.65	   
12.87/3.65	                 [1 1 1]     [1]    [1 1 1]     [1]              
12.87/3.65	   a(b(c(x1))) = [0 1 0]x1 + [1] >= [0 1 0]x1 + [1] = c(b(a(x1)))
12.87/3.65	                 [0 0 1]     [1]    [0 0 1]     [1]              
12.87/3.65	   
12.87/3.65	                    [1 2 0]     [0]    [1 2 0]     [0]                 
12.87/3.65	   c(c(b(b(x1)))) = [0 1 0]x1 + [0] >= [0 1 0]x1 + [0] = b(b(c(c(x1))))
12.87/3.65	                    [0 0 1]     [2]    [0 0 1]     [2]                 
12.87/3.65	  problem:
12.87/3.65	   c(b(a(a(x1)))) -> a(a(b(c(x1))))
12.87/3.65	   a(b(c(x1))) -> c(b(a(x1)))
12.87/3.65	   c(c(b(b(x1)))) -> b(b(c(c(x1))))
12.87/3.65	  Matrix Interpretation Processor: dim=3
12.87/3.65	   
12.87/3.65	   interpretation:
12.87/3.65	              [1 0 0]  
12.87/3.65	    [c](x0) = [0 0 1]x0
12.87/3.65	              [0 1 0]  ,
12.87/3.65	    
12.87/3.65	              [1 1 0]     [0]
12.87/3.65	    [b](x0) = [0 0 1]x0 + [0]
12.87/3.65	              [1 1 0]     [1],
12.87/3.65	    
12.87/3.65	              [1 0 1]     [0]
12.87/3.65	    [a](x0) = [1 0 1]x0 + [0]
12.87/3.65	              [0 0 0]     [1]
12.87/3.65	   orientation:
12.87/3.65	                     [2 0 2]     [2]    [2 0 2]     [2]                 
12.87/3.65	    c(b(a(a(x1)))) = [2 0 2]x1 + [3] >= [2 0 2]x1 + [2] = a(a(b(c(x1))))
12.87/3.65	                     [0 0 0]     [1]    [0 0 0]     [1]                 
12.87/3.65	    
12.87/3.65	                  [2 0 2]     [1]    [2 0 2]     [0]              
12.87/3.65	    a(b(c(x1))) = [2 0 2]x1 + [1] >= [2 0 2]x1 + [1] = c(b(a(x1)))
12.87/3.65	                  [0 0 0]     [1]    [0 0 0]     [1]              
12.87/3.65	    
12.87/3.65	                     [1 1 1]     [0]    [1 1 1]     [0]                 
12.87/3.65	    c(c(b(b(x1)))) = [1 1 0]x1 + [1] >= [1 1 0]x1 + [1] = b(b(c(c(x1))))
12.87/3.65	                     [1 1 1]     [1]    [1 1 1]     [1]                 
12.87/3.65	   problem:
12.87/3.65	    c(b(a(a(x1)))) -> a(a(b(c(x1))))
12.87/3.65	    c(c(b(b(x1)))) -> b(b(c(c(x1))))
12.87/3.65	   KBO Processor:
12.87/3.65	    weight function:
12.87/3.65	     w0 = 1
12.87/3.65	     w(c) = w(b) = w(a) = 1
12.87/3.65	    precedence:
12.87/3.65	     c > b ~ a
12.87/3.65	    problem:
12.87/3.65	     
12.87/3.65	    Qed
13.01/3.66	EOF