173.17/44.22	YES
173.17/44.22	
173.17/44.22	Problem:
173.17/44.22	 a(b(a(a(x1)))) -> a(a(a(a(x1))))
173.17/44.22	 b(a(b(a(x1)))) -> a(a(b(b(x1))))
173.17/44.22	 b(a(a(b(x1)))) -> b(a(b(a(x1))))
173.17/44.22	
173.17/44.22	Proof:
173.17/44.22	 Matrix Interpretation Processor: dim=1
173.17/44.22	  
173.17/44.22	  interpretation:
173.17/44.22	   [b](x0) = 4x0 + 1,
173.17/44.22	   
173.17/44.22	   [a](x0) = x0
173.17/44.22	  orientation:
173.17/44.22	   a(b(a(a(x1)))) = 4x1 + 1 >= x1 = a(a(a(a(x1))))
173.17/44.22	   
173.17/44.22	   b(a(b(a(x1)))) = 16x1 + 5 >= 16x1 + 5 = a(a(b(b(x1))))
173.17/44.22	   
173.17/44.22	   b(a(a(b(x1)))) = 16x1 + 5 >= 16x1 + 5 = b(a(b(a(x1))))
173.17/44.22	  problem:
173.17/44.22	   b(a(b(a(x1)))) -> a(a(b(b(x1))))
173.17/44.22	   b(a(a(b(x1)))) -> b(a(b(a(x1))))
173.17/44.22	  DP Processor:
173.17/44.22	   DPs:
173.17/44.22	    b#(a(b(a(x1)))) -> b#(x1)
173.17/44.22	    b#(a(b(a(x1)))) -> b#(b(x1))
173.17/44.22	    b#(a(a(b(x1)))) -> b#(a(x1))
173.17/44.22	    b#(a(a(b(x1)))) -> b#(a(b(a(x1))))
173.17/44.22	   TRS:
173.17/44.22	    b(a(b(a(x1)))) -> a(a(b(b(x1))))
173.17/44.22	    b(a(a(b(x1)))) -> b(a(b(a(x1))))
173.17/44.22	   Arctic Interpretation Processor:
173.17/44.22	    dimension: 1
173.17/44.22	    usable rules:
173.17/44.22	     b(a(b(a(x1)))) -> a(a(b(b(x1))))
173.17/44.22	     b(a(a(b(x1)))) -> b(a(b(a(x1))))
173.17/44.22	    interpretation:
173.17/44.22	     [b#](x0) = x0,
173.17/44.22	     
173.17/44.22	     [b](x0) = x0,
173.17/44.22	     
173.17/44.22	     [a](x0) = 14x0
173.17/44.22	    orientation:
173.17/44.22	     b#(a(b(a(x1)))) = 28x1 >= x1 = b#(x1)
173.17/44.23	     
173.17/44.23	     b#(a(b(a(x1)))) = 28x1 >= x1 = b#(b(x1))
173.17/44.23	     
173.17/44.23	     b#(a(a(b(x1)))) = 28x1 >= 14x1 = b#(a(x1))
173.17/44.23	     
173.17/44.23	     b#(a(a(b(x1)))) = 28x1 >= 28x1 = b#(a(b(a(x1))))
173.17/44.23	     
173.17/44.23	     b(a(b(a(x1)))) = 28x1 >= 28x1 = a(a(b(b(x1))))
173.17/44.23	     
173.17/44.23	     b(a(a(b(x1)))) = 28x1 >= 28x1 = b(a(b(a(x1))))
173.17/44.23	    problem:
173.17/44.23	     DPs:
173.17/44.23	      b#(a(a(b(x1)))) -> b#(a(b(a(x1))))
173.17/44.23	     TRS:
173.17/44.23	      b(a(b(a(x1)))) -> a(a(b(b(x1))))
173.17/44.23	      b(a(a(b(x1)))) -> b(a(b(a(x1))))
173.17/44.23	    Restore Modifier:
173.17/44.23	     DPs:
173.17/44.23	      b#(a(a(b(x1)))) -> b#(a(b(a(x1))))
173.17/44.23	     TRS:
173.17/44.23	      b(a(b(a(x1)))) -> a(a(b(b(x1))))
173.17/44.23	      b(a(a(b(x1)))) -> b(a(b(a(x1))))
173.17/44.23	     Matrix Interpretation Processor: dim=4
173.17/44.23	      
173.17/44.23	      interpretation:
173.17/44.23	       [b#](x0) = [0 1 0 0]x0,
173.17/44.23	       
173.17/44.23	                 [0 0 0 0]     [1]
173.17/44.23	                 [0 1 0 1]     [0]
173.17/44.23	       [b](x0) = [0 0 0 0]x0 + [0]
173.17/44.23	                 [0 0 0 0]     [0],
173.17/44.23	       
173.17/44.23	                 [0 0 0 0]  
173.17/44.23	                 [0 0 0 1]  
173.17/44.23	       [a](x0) = [0 0 0 0]x0
173.17/44.23	                 [1 0 0 0]  
173.17/44.23	      orientation:
173.17/44.23	       b#(a(a(b(x1)))) = [1] >= [0] = b#(a(b(a(x1))))
173.17/44.23	       
173.17/44.23	                        [1]    [0]                 
173.17/44.23	                        [1]    [1]                 
173.17/44.23	       b(a(b(a(x1)))) = [0] >= [0] = a(a(b(b(x1))))
173.17/44.23	                        [0]    [0]                 
173.17/44.23	       
173.17/44.23	                        [1]    [1]                 
173.17/44.23	                        [1]    [1]                 
173.17/44.23	       b(a(a(b(x1)))) = [0] >= [0] = b(a(b(a(x1))))
173.17/44.23	                        [0]    [0]                 
173.17/44.23	      problem:
173.17/44.23	       DPs:
173.17/44.23	        
173.17/44.23	       TRS:
173.17/44.23	        b(a(b(a(x1)))) -> a(a(b(b(x1))))
173.17/44.23	        b(a(a(b(x1)))) -> b(a(b(a(x1))))
173.17/44.23	      Qed
173.17/44.23	EOF