189.38/48.18	YES
189.38/48.19	
189.38/48.19	Problem:
189.38/48.19	 a(a(b(x1))) -> b(b(a(a(x1))))
189.38/48.19	 b(a(b(x1))) -> a(a(a(a(x1))))
189.38/48.19	
189.38/48.19	Proof:
189.38/48.19	 String Reversal Processor:
189.38/48.19	  b(a(a(x1))) -> a(a(b(b(x1))))
189.38/48.19	  b(a(b(x1))) -> a(a(a(a(x1))))
189.38/48.19	  DP Processor:
189.38/48.19	   DPs:
189.38/48.19	    b#(a(a(x1))) -> b#(x1)
189.38/48.19	    b#(a(a(x1))) -> b#(b(x1))
189.38/48.19	   TRS:
189.38/48.19	    b(a(a(x1))) -> a(a(b(b(x1))))
189.38/48.19	    b(a(b(x1))) -> a(a(a(a(x1))))
189.38/48.19	   Arctic Interpretation Processor:
189.38/48.19	    dimension: 2
189.38/48.19	    usable rules:
189.38/48.19	     b(a(a(x1))) -> a(a(b(b(x1))))
189.38/48.19	     b(a(b(x1))) -> a(a(a(a(x1))))
189.38/48.19	    interpretation:
189.38/48.19	     [b#](x0) = [1 0]x0,
189.38/48.19	     
189.38/48.19	               [-& 1 ]     [0 ]
189.38/48.19	     [a](x0) = [0  -&]x0 + [-&],
189.38/48.19	     
189.38/48.19	               [0  -&]     [-&]
189.38/48.19	     [b](x0) = [2  0 ]x0 + [0 ]
189.38/48.19	    orientation:
189.38/48.19	     b#(a(a(x1))) = [2 1]x1 + [1] >= [1 0]x1 = b#(x1)
189.38/48.19	     
189.38/48.19	     b#(a(a(x1))) = [2 1]x1 + [1] >= [2 0]x1 + [0] = b#(b(x1))
189.38/48.19	     
189.38/48.19	                   [1  -&]     [0]    [1  -&]     [0]                 
189.38/48.19	     b(a(a(x1))) = [3  1 ]x1 + [2] >= [3  1 ]x1 + [1] = a(a(b(b(x1))))
189.38/48.19	     
189.38/48.19	                   [3 1]     [1]    [2  -&]     [1]                 
189.38/48.19	     b(a(b(x1))) = [5 3]x1 + [3] >= [-& 2 ]x1 + [1] = a(a(a(a(x1))))
189.38/48.19	    problem:
189.38/48.19	     DPs:
189.38/48.19	      b#(a(a(x1))) -> b#(b(x1))
189.38/48.19	     TRS:
189.38/48.19	      b(a(a(x1))) -> a(a(b(b(x1))))
189.38/48.19	      b(a(b(x1))) -> a(a(a(a(x1))))
189.38/48.19	    Restore Modifier:
189.38/48.19	     DPs:
189.38/48.19	      b#(a(a(x1))) -> b#(b(x1))
189.38/48.19	     TRS:
189.38/48.19	      b(a(a(x1))) -> a(a(b(b(x1))))
189.38/48.19	      b(a(b(x1))) -> a(a(a(a(x1))))
189.38/48.19	     Arctic Interpretation Processor:
189.38/48.19	      dimension: 2
189.38/48.19	      usable rules:
189.38/48.19	       b(a(a(x1))) -> a(a(b(b(x1))))
189.38/48.19	       b(a(b(x1))) -> a(a(a(a(x1))))
189.38/48.19	      interpretation:
189.38/48.19	       [b#](x0) = [-& 0 ]x0 + [0],
189.38/48.19	       
189.38/48.19	                 [-& 0 ]     [0]
189.38/48.19	       [a](x0) = [1  -&]x0 + [1],
189.38/48.19	       
189.38/48.19	                 [0  3 ]     [1 ]
189.38/48.19	       [b](x0) = [-& 0 ]x0 + [-&]
189.38/48.19	      orientation:
189.38/48.19	       b#(a(a(x1))) = [-& 1 ]x1 + [1] >= [-& 0 ]x1 + [0] = b#(b(x1))
189.38/48.19	       
189.38/48.19	                     [1  4 ]     [4]    [1  4 ]     [2]                 
189.38/48.19	       b(a(a(x1))) = [-& 1 ]x1 + [1] >= [-& 1 ]x1 + [1] = a(a(b(b(x1))))
189.38/48.19	       
189.38/48.19	                     [4 7]     [5]    [2  -&]     [2]                 
189.38/48.19	       b(a(b(x1))) = [1 4]x1 + [2] >= [-& 2 ]x1 + [2] = a(a(a(a(x1))))
189.38/48.19	      problem:
189.38/48.19	       DPs:
189.38/48.19	        
189.38/48.19	       TRS:
189.38/48.19	        b(a(a(x1))) -> a(a(b(b(x1))))
189.38/48.19	        b(a(b(x1))) -> a(a(a(a(x1))))
189.38/48.19	      Qed
189.38/48.19	EOF