170.07/43.50	YES
170.07/43.50	
170.07/43.50	Problem:
170.07/43.50	 a(x1) -> x1
170.07/43.50	 a(x1) -> b(c(b(x1)))
170.07/43.50	 a(b(b(x1))) -> b(b(a(a(x1))))
170.07/43.50	
170.07/43.50	Proof:
170.07/43.50	 DP Processor:
170.07/43.50	  DPs:
170.07/43.50	   a#(b(b(x1))) -> a#(x1)
170.07/43.50	   a#(b(b(x1))) -> a#(a(x1))
170.07/43.50	  TRS:
170.07/43.50	   a(x1) -> x1
170.07/43.50	   a(x1) -> b(c(b(x1)))
170.07/43.50	   a(b(b(x1))) -> b(b(a(a(x1))))
170.07/43.50	  Arctic Interpretation Processor:
170.07/43.50	   dimension: 2
170.07/43.50	   usable rules:
170.07/43.50	    a(x1) -> x1
170.07/43.50	    a(x1) -> b(c(b(x1)))
170.07/43.50	    a(b(b(x1))) -> b(b(a(a(x1))))
170.07/43.50	   interpretation:
170.07/43.50	    [a#](x0) = [0 0]x0 + [0],
170.07/43.50	    
170.07/43.50	              [0 ]
170.07/43.50	    [c](x0) = [-&],
170.07/43.50	    
170.07/43.50	              [0 1]     [0]
170.07/43.50	    [b](x0) = [0 0]x0 + [2],
170.07/43.50	    
170.07/43.50	              [0 0]     [0]
170.07/43.50	    [a](x0) = [0 0]x0 + [2]
170.07/43.50	   orientation:
170.07/43.50	    a#(b(b(x1))) = [1 1]x1 + [3] >= [0 0]x1 + [0] = a#(x1)
170.07/43.50	    
170.07/43.50	    a#(b(b(x1))) = [1 1]x1 + [3] >= [0 0]x1 + [2] = a#(a(x1))
170.07/43.50	    
170.07/43.50	            [0 0]     [0]           
170.07/43.50	    a(x1) = [0 0]x1 + [2] >= x1 = x1
170.07/43.50	    
170.07/43.50	            [0 0]     [0]    [0]              
170.07/43.50	    a(x1) = [0 0]x1 + [2] >= [2] = b(c(b(x1)))
170.07/43.50	    
170.07/43.50	                  [1 1]     [3]    [1 1]     [3]                 
170.07/43.50	    a(b(b(x1))) = [1 1]x1 + [3] >= [1 1]x1 + [3] = b(b(a(a(x1))))
170.07/43.50	   problem:
170.07/43.50	    DPs:
170.07/43.50	     
170.07/43.50	    TRS:
170.07/43.50	     a(x1) -> x1
170.07/43.50	     a(x1) -> b(c(b(x1)))
170.07/43.50	     a(b(b(x1))) -> b(b(a(a(x1))))
170.07/43.50	   Qed
170.07/43.51	EOF