166.64/42.50	YES
166.64/42.51	
166.64/42.51	Problem:
166.64/42.51	 a(b(b(x1))) -> b(b(a(a(x1))))
166.64/42.51	 a(b(a(x1))) -> b(b(x1))
166.64/42.51	
166.64/42.51	Proof:
166.64/42.51	 DP Processor:
166.64/42.51	  DPs:
166.64/42.51	   a#(b(b(x1))) -> a#(x1)
166.64/42.51	   a#(b(b(x1))) -> a#(a(x1))
166.64/42.51	  TRS:
166.64/42.51	   a(b(b(x1))) -> b(b(a(a(x1))))
166.64/42.51	   a(b(a(x1))) -> b(b(x1))
166.64/42.51	  Arctic Interpretation Processor:
166.64/42.51	   dimension: 2
166.64/42.51	   usable rules:
166.64/42.51	    a(b(b(x1))) -> b(b(a(a(x1))))
166.64/42.51	    a(b(a(x1))) -> b(b(x1))
166.64/42.51	   interpretation:
166.64/42.51	    [a#](x0) = [0 0]x0 + [0],
166.64/42.51	    
166.64/42.51	              [0 0]     [0]
166.64/42.51	    [a](x0) = [0 0]x0 + [0],
166.64/42.51	    
166.64/42.51	              [0 0]     [0]
166.64/42.51	    [b](x0) = [1 0]x0 + [1]
166.64/42.51	   orientation:
166.64/42.51	    a#(b(b(x1))) = [1 1]x1 + [1] >= [0 0]x1 + [0] = a#(x1)
166.64/42.51	    
166.64/42.51	    a#(b(b(x1))) = [1 1]x1 + [1] >= [0 0]x1 + [0] = a#(a(x1))
166.64/42.51	    
166.64/42.51	                  [1 1]     [1]    [1 1]     [1]                 
166.64/42.51	    a(b(b(x1))) = [1 1]x1 + [1] >= [1 1]x1 + [1] = b(b(a(a(x1))))
166.64/42.51	    
166.64/42.51	                  [1 1]     [1]    [1 0]     [1]           
166.64/42.51	    a(b(a(x1))) = [1 1]x1 + [1] >= [1 1]x1 + [1] = b(b(x1))
166.64/42.51	   problem:
166.64/42.51	    DPs:
166.64/42.51	     
166.64/42.51	    TRS:
166.64/42.51	     a(b(b(x1))) -> b(b(a(a(x1))))
166.64/42.51	     a(b(a(x1))) -> b(b(x1))
166.64/42.51	   Qed
166.64/42.51	EOF