168.34/42.99	YES
168.34/42.99	
168.34/42.99	Problem:
168.34/42.99	 a(b(b(x1))) -> b(a(a(a(x1))))
168.34/42.99	 a(a(b(x1))) -> b(a(b(x1)))
168.34/42.99	
168.34/42.99	Proof:
168.34/42.99	 DP Processor:
168.34/42.99	  DPs:
168.34/42.99	   a#(b(b(x1))) -> a#(x1)
168.34/42.99	   a#(b(b(x1))) -> a#(a(x1))
168.34/42.99	   a#(b(b(x1))) -> a#(a(a(x1)))
168.34/42.99	  TRS:
168.34/42.99	   a(b(b(x1))) -> b(a(a(a(x1))))
168.34/42.99	   a(a(b(x1))) -> b(a(b(x1)))
168.34/42.99	  Matrix Interpretation Processor: dim=4
168.34/42.99	   
168.34/42.99	   interpretation:
168.34/42.99	    [a#](x0) = [0 1 0 0]x0,
168.34/42.99	    
168.34/42.99	              [0 1 1 0]     [0]
168.34/42.99	              [0 1 0 0]     [0]
168.34/42.99	    [a](x0) = [0 0 0 0]x0 + [1]
168.34/42.99	              [0 1 0 0]     [0],
168.34/42.99	    
168.34/42.99	              [0 1 0 0]     [1]
168.34/42.99	              [1 0 0 0]     [0]
168.34/42.99	    [b](x0) = [0 0 0 0]x0 + [0]
168.34/42.99	              [0 1 0 0]     [0]
168.34/42.99	   orientation:
168.34/42.99	    a#(b(b(x1))) = [0 1 0 0]x1 + [1] >= [0 1 0 0]x1 = a#(x1)
168.34/42.99	    
168.34/42.99	    a#(b(b(x1))) = [0 1 0 0]x1 + [1] >= [0 1 0 0]x1 = a#(a(x1))
168.34/42.99	    
168.34/42.99	    a#(b(b(x1))) = [0 1 0 0]x1 + [1] >= [0 1 0 0]x1 = a#(a(a(x1)))
168.34/42.99	    
168.34/42.99	                  [0 1 0 0]     [1]    [0 1 0 0]     [1]                 
168.34/42.99	                  [0 1 0 0]     [1]    [0 1 0 0]     [1]                 
168.34/42.99	    a(b(b(x1))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [0] = b(a(a(a(x1))))
168.34/42.99	                  [0 1 0 0]     [1]    [0 1 0 0]     [0]                 
168.34/42.99	    
168.34/42.99	                  [1 0 0 0]     [1]    [1 0 0 0]     [1]              
168.34/42.99	                  [1 0 0 0]     [0]    [1 0 0 0]     [0]              
168.34/42.99	    a(a(b(x1))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [0] = b(a(b(x1)))
168.34/42.99	                  [1 0 0 0]     [0]    [1 0 0 0]     [0]              
168.34/42.99	   problem:
168.34/42.99	    DPs:
168.34/42.99	     
168.34/42.99	    TRS:
168.34/42.99	     a(b(b(x1))) -> b(a(a(a(x1))))
168.34/42.99	     a(a(b(x1))) -> b(a(b(x1)))
168.34/42.99	   Qed
168.34/43.00	EOF