38.45/10.15	YES
38.45/10.16	
38.45/10.16	Problem:
38.45/10.16	 a(a(a(a(b(b(x1)))))) -> b(b(a(a(b(b(x1))))))
38.45/10.16	 b(b(a(a(x1)))) -> a(a(b(b(b(b(x1))))))
38.45/10.16	 b(b(c(c(a(a(x1)))))) -> c(c(c(c(a(a(a(a(b(b(x1))))))))))
38.45/10.16	
38.45/10.16	Proof:
38.45/10.16	 Matrix Interpretation Processor: dim=4
38.45/10.16	  
38.45/10.16	  interpretation:
38.45/10.16	             [1 0 0 0]  
38.45/10.16	             [0 0 0 0]  
38.45/10.16	   [c](x0) = [0 1 0 1]x0
38.45/10.16	             [0 1 0 0]  ,
38.45/10.16	   
38.45/10.16	             [1 0 0 0]     [0]
38.45/10.16	             [0 0 1 1]     [0]
38.45/10.16	   [a](x0) = [0 0 1 0]x0 + [0]
38.45/10.16	             [0 0 0 0]     [1],
38.45/10.16	   
38.45/10.16	             [1 0 1 0]  
38.45/10.16	             [0 1 0 0]  
38.45/10.16	   [b](x0) = [0 0 0 0]x0
38.45/10.16	             [0 0 0 1]  
38.45/10.16	  orientation:
38.45/10.16	                          [1 0 1 0]     [0]    [1 0 1 0]     [0]                       
38.45/10.16	                          [0 0 0 0]     [1]    [0 0 0 0]     [1]                       
38.45/10.16	   a(a(a(a(b(b(x1)))))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = b(b(a(a(b(b(x1))))))
38.45/10.16	                          [0 0 0 0]     [1]    [0 0 0 0]     [1]                       
38.45/10.16	   
38.45/10.16	                    [1 0 1 0]     [0]    [1 0 1 0]     [0]                       
38.45/10.16	                    [0 0 1 0]     [1]    [0 0 0 0]     [1]                       
38.45/10.16	   b(b(a(a(x1)))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = a(a(b(b(b(b(x1))))))
38.45/10.16	                    [0 0 0 0]     [1]    [0 0 0 0]     [1]                       
38.45/10.16	   
38.45/10.16	                          [1 0 1 0]     [1]    [1 0 1 0]                                     
38.45/10.16	                          [0 0 0 0]     [0]    [0 0 0 0]                                     
38.45/10.16	   b(b(c(c(a(a(x1)))))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 = c(c(c(c(a(a(a(a(b(b(x1))))))))))
38.45/10.16	                          [0 0 0 0]     [0]    [0 0 0 0]                                     
38.45/10.16	  problem:
38.45/10.16	   a(a(a(a(b(b(x1)))))) -> b(b(a(a(b(b(x1))))))
38.45/10.16	   b(b(a(a(x1)))) -> a(a(b(b(b(b(x1))))))
38.45/10.16	  KBO Processor:
38.45/10.16	   weight function:
38.45/10.16	    w0 = 1
38.45/10.16	    w(a) = 1
38.45/10.16	    w(b) = 0
38.45/10.16	   precedence:
38.45/10.16	    b > a
38.45/10.16	   problem:
38.45/10.16	    
38.45/10.16	   Qed
38.45/10.16	EOF