4.55/1.47	YES
4.55/1.47	
4.55/1.47	Problem:
4.55/1.47	 a(a(b(x1))) -> b(a(b(x1)))
4.55/1.47	 b(a(x1)) -> a(b(b(x1)))
4.55/1.47	 b(c(a(x1))) -> c(c(a(a(b(x1)))))
4.55/1.47	
4.55/1.47	Proof:
4.55/1.47	 Matrix Interpretation Processor: dim=3
4.55/1.47	  
4.55/1.47	  interpretation:
4.55/1.47	             [1 0 0]  
4.55/1.47	   [c](x0) = [0 0 1]x0
4.55/1.47	             [0 0 0]  ,
4.55/1.47	   
4.55/1.47	             [1 0 0]     [0]
4.55/1.47	   [a](x0) = [0 1 0]x0 + [0]
4.55/1.47	             [0 1 0]     [1],
4.55/1.47	   
4.55/1.47	             [1 1 0]  
4.55/1.47	   [b](x0) = [0 0 0]x0
4.55/1.47	             [0 0 1]  
4.55/1.47	  orientation:
4.55/1.47	                 [1 1 0]     [0]    [1 1 0]     [0]              
4.55/1.47	   a(a(b(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(a(b(x1)))
4.55/1.47	                 [0 0 0]     [1]    [0 0 0]     [1]              
4.55/1.47	   
4.55/1.47	              [1 1 0]     [0]    [1 1 0]     [0]              
4.55/1.47	   b(a(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(b(b(x1)))
4.55/1.47	              [0 1 0]     [1]    [0 0 0]     [1]              
4.55/1.47	   
4.55/1.47	                 [1 1 0]     [1]    [1 1 0]                      
4.55/1.47	   b(c(a(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = c(c(a(a(b(x1)))))
4.55/1.47	                 [0 0 0]     [0]    [0 0 0]                      
4.55/1.47	  problem:
4.55/1.47	   a(a(b(x1))) -> b(a(b(x1)))
4.55/1.47	   b(a(x1)) -> a(b(b(x1)))
4.55/1.47	  KBO Processor:
4.55/1.47	   weight function:
4.55/1.47	    w0 = 1
4.55/1.47	    w(a) = 1
4.55/1.47	    w(b) = 0
4.55/1.47	   precedence:
4.55/1.47	    b > a
4.55/1.47	   problem:
4.55/1.47	    
4.55/1.47	   Qed
4.55/1.47	EOF