184.47/47.20	YES
184.47/47.21	
184.47/47.21	Problem:
184.47/47.21	 a(b(a(x1))) -> b(b(b(b(x1))))
184.47/47.21	 a(b(b(x1))) -> b(b(a(a(x1))))
184.47/47.21	
184.47/47.21	Proof:
184.47/47.21	 DP Processor:
184.47/47.21	  DPs:
184.47/47.21	   a#(b(b(x1))) -> a#(x1)
184.47/47.21	   a#(b(b(x1))) -> a#(a(x1))
184.47/47.21	  TRS:
184.47/47.21	   a(b(a(x1))) -> b(b(b(b(x1))))
184.47/47.21	   a(b(b(x1))) -> b(b(a(a(x1))))
184.47/47.21	  Arctic Interpretation Processor:
184.47/47.21	   dimension: 2
184.47/47.21	   usable rules:
184.47/47.21	    a(b(a(x1))) -> b(b(b(b(x1))))
184.47/47.21	    a(b(b(x1))) -> b(b(a(a(x1))))
184.47/47.21	   interpretation:
184.47/47.21	    [a#](x0) = [0 1]x0 + [0],
184.47/47.21	    
184.47/47.21	              [-& 1 ]     [2 ]
184.47/47.21	    [b](x0) = [0  -&]x0 + [-&],
184.47/47.21	    
184.47/47.21	              [0  2 ]     [3 ]
184.47/47.21	    [a](x0) = [-& 0 ]x0 + [-&]
184.47/47.21	   orientation:
184.47/47.21	    a#(b(b(x1))) = [1 2]x1 + [3] >= [0 1]x1 + [0] = a#(x1)
184.47/47.21	    
184.47/47.21	    a#(b(b(x1))) = [1 2]x1 + [3] >= [0 2]x1 + [3] = a#(a(x1))
184.47/47.21	    
184.47/47.21	                  [2 4]     [5]    [2  -&]     [3]                 
184.47/47.21	    a(b(a(x1))) = [0 2]x1 + [3] >= [-& 2 ]x1 + [3] = b(b(b(b(x1))))
184.47/47.21	    
184.47/47.21	                  [1  3 ]     [4]    [1  3 ]     [4]                 
184.47/47.21	    a(b(b(x1))) = [-& 1 ]x1 + [2] >= [-& 1 ]x1 + [2] = b(b(a(a(x1))))
184.47/47.21	   problem:
184.47/47.21	    DPs:
184.47/47.21	     a#(b(b(x1))) -> a#(a(x1))
184.47/47.21	    TRS:
184.47/47.21	     a(b(a(x1))) -> b(b(b(b(x1))))
184.47/47.21	     a(b(b(x1))) -> b(b(a(a(x1))))
184.47/47.21	   Restore Modifier:
184.47/47.21	    DPs:
184.47/47.21	     a#(b(b(x1))) -> a#(a(x1))
184.47/47.21	    TRS:
184.47/47.21	     a(b(a(x1))) -> b(b(b(b(x1))))
184.47/47.21	     a(b(b(x1))) -> b(b(a(a(x1))))
184.47/47.21	    Arctic Interpretation Processor:
184.47/47.21	     dimension: 2
184.47/47.21	     usable rules:
184.47/47.21	      a(b(a(x1))) -> b(b(b(b(x1))))
184.47/47.21	      a(b(b(x1))) -> b(b(a(a(x1))))
184.47/47.21	     interpretation:
184.47/47.21	      [a#](x0) = [2 0]x0 + [1],
184.47/47.21	      
184.47/47.21	                [-& 2 ]     [0 ]
184.47/47.21	      [b](x0) = [0  -&]x0 + [-&],
184.47/47.21	      
184.47/47.21	                [0  -&]     [-&]
184.47/47.21	      [a](x0) = [2  0 ]x0 + [0 ]
184.47/47.21	     orientation:
184.47/47.21	      a#(b(b(x1))) = [4 2]x1 + [2] >= [2 0]x1 + [1] = a#(a(x1))
184.47/47.21	      
184.47/47.21	                    [4 2]     [2]    [4  -&]     [2]                 
184.47/47.21	      a(b(a(x1))) = [6 4]x1 + [4] >= [-& 4 ]x1 + [2] = b(b(b(b(x1))))
184.47/47.21	      
184.47/47.21	                    [2  -&]     [0]    [2  -&]     [0]                 
184.47/47.21	      a(b(b(x1))) = [4  2 ]x1 + [2] >= [4  2 ]x1 + [2] = b(b(a(a(x1))))
184.47/47.21	     problem:
184.47/47.21	      DPs:
184.47/47.21	       
184.47/47.21	      TRS:
184.47/47.21	       a(b(a(x1))) -> b(b(b(b(x1))))
184.47/47.21	       a(b(b(x1))) -> b(b(a(a(x1))))
184.47/47.21	     Qed
184.47/47.21	EOF