172.83/44.16	YES
172.83/44.17	
172.83/44.17	Problem:
172.83/44.17	 a(a(x1)) -> x1
172.83/44.17	 a(b(x1)) -> x1
172.83/44.17	 a(b(b(x1))) -> b(b(a(b(a(x1)))))
172.83/44.17	
172.83/44.17	Proof:
172.83/44.17	 String Reversal Processor:
172.83/44.17	  a(a(x1)) -> x1
172.83/44.17	  b(a(x1)) -> x1
172.83/44.17	  b(b(a(x1))) -> a(b(a(b(b(x1)))))
172.83/44.17	  DP Processor:
172.83/44.17	   DPs:
172.83/44.17	    b#(b(a(x1))) -> b#(x1)
172.83/44.17	    b#(b(a(x1))) -> b#(b(x1))
172.83/44.17	    b#(b(a(x1))) -> a#(b(b(x1)))
172.83/44.17	    b#(b(a(x1))) -> b#(a(b(b(x1))))
172.83/44.17	    b#(b(a(x1))) -> a#(b(a(b(b(x1)))))
172.83/44.17	   TRS:
172.83/44.17	    a(a(x1)) -> x1
172.83/44.17	    b(a(x1)) -> x1
172.83/44.17	    b(b(a(x1))) -> a(b(a(b(b(x1)))))
172.83/44.17	   TDG Processor:
172.83/44.17	    DPs:
172.83/44.17	     b#(b(a(x1))) -> b#(x1)
172.83/44.17	     b#(b(a(x1))) -> b#(b(x1))
172.83/44.17	     b#(b(a(x1))) -> a#(b(b(x1)))
172.83/44.17	     b#(b(a(x1))) -> b#(a(b(b(x1))))
172.83/44.17	     b#(b(a(x1))) -> a#(b(a(b(b(x1)))))
172.83/44.17	    TRS:
172.83/44.17	     a(a(x1)) -> x1
172.83/44.17	     b(a(x1)) -> x1
172.83/44.17	     b(b(a(x1))) -> a(b(a(b(b(x1)))))
172.83/44.17	    graph:
172.83/44.17	     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> a#(b(a(b(b(x1)))))
172.83/44.17	     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(a(b(b(x1))))
172.83/44.17	     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> a#(b(b(x1)))
172.83/44.17	     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(x1))
172.83/44.17	     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(x1)
172.83/44.17	     b#(b(a(x1))) -> b#(a(b(b(x1)))) ->
172.83/44.17	     b#(b(a(x1))) -> a#(b(a(b(b(x1)))))
172.83/44.17	     b#(b(a(x1))) -> b#(a(b(b(x1)))) ->
172.83/44.17	     b#(b(a(x1))) -> b#(a(b(b(x1))))
172.83/44.17	     b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) -> a#(b(b(x1)))
172.83/44.17	     b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(x1))
172.83/44.17	     b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(x1)
172.83/44.17	     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> a#(b(a(b(b(x1)))))
172.83/44.17	     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(a(b(b(x1))))
172.83/44.17	     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> a#(b(b(x1)))
172.83/44.17	     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(b(x1))
172.83/44.17	     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(x1)
172.83/44.17	    SCC Processor:
172.83/44.17	     #sccs: 1
172.83/44.17	     #rules: 3
172.83/44.17	     #arcs: 15/25
172.83/44.17	     DPs:
172.83/44.17	      b#(b(a(x1))) -> b#(b(x1))
172.83/44.17	      b#(b(a(x1))) -> b#(x1)
172.83/44.17	      b#(b(a(x1))) -> b#(a(b(b(x1))))
172.83/44.17	     TRS:
172.83/44.17	      a(a(x1)) -> x1
172.83/44.17	      b(a(x1)) -> x1
172.83/44.17	      b(b(a(x1))) -> a(b(a(b(b(x1)))))
172.83/44.17	     Arctic Interpretation Processor:
172.83/44.17	      dimension: 2
172.83/44.17	      usable rules:
172.83/44.17	       a(a(x1)) -> x1
172.83/44.17	       b(a(x1)) -> x1
172.83/44.17	       b(b(a(x1))) -> a(b(a(b(b(x1)))))
172.83/44.17	      interpretation:
172.83/44.17	       [b#](x0) = [-& 0 ]x0 + [0],
172.83/44.17	       
172.83/44.17	                 [-& 0 ]     [0]
172.83/44.17	       [b](x0) = [0  -&]x0 + [0],
172.83/44.17	       
172.83/44.17	                 [1  0 ]     [2 ]
172.83/44.17	       [a](x0) = [0  -&]x0 + [-&]
172.83/44.17	      orientation:
172.83/44.17	       b#(b(a(x1))) = [1 0]x1 + [2] >= [0  -&]x1 + [0] = b#(b(x1))
172.83/44.17	       
172.83/44.17	       b#(b(a(x1))) = [1 0]x1 + [2] >= [-& 0 ]x1 + [0] = b#(x1)
172.83/44.17	       
172.83/44.17	       b#(b(a(x1))) = [1 0]x1 + [2] >= [0  -&]x1 + [0] = b#(a(b(b(x1))))
172.83/44.17	       
172.83/44.17	                  [2 1]     [3]           
172.83/44.17	       a(a(x1)) = [1 0]x1 + [2] >= x1 = x1
172.83/44.17	       
172.83/44.17	                  [0  -&]     [0]           
172.83/44.17	       b(a(x1)) = [1  0 ]x1 + [2] >= x1 = x1
172.83/44.17	       
172.83/44.17	                     [1  0 ]     [2]    [1  0 ]     [2]                    
172.83/44.17	       b(b(a(x1))) = [0  -&]x1 + [0] >= [0  -&]x1 + [0] = a(b(a(b(b(x1)))))
172.83/44.17	      problem:
172.83/44.17	       DPs:
172.83/44.17	        b#(b(a(x1))) -> b#(x1)
172.83/44.17	       TRS:
172.83/44.17	        a(a(x1)) -> x1
172.83/44.17	        b(a(x1)) -> x1
172.83/44.17	        b(b(a(x1))) -> a(b(a(b(b(x1)))))
172.83/44.17	      Restore Modifier:
172.83/44.17	       DPs:
172.83/44.17	        b#(b(a(x1))) -> b#(x1)
172.83/44.17	       TRS:
172.83/44.17	        a(a(x1)) -> x1
172.83/44.17	        b(a(x1)) -> x1
172.83/44.17	        b(b(a(x1))) -> a(b(a(b(b(x1)))))
172.83/44.17	       EDG Processor:
172.83/44.17	        DPs:
172.83/44.17	         b#(b(a(x1))) -> b#(x1)
172.83/44.17	        TRS:
172.83/44.17	         a(a(x1)) -> x1
172.83/44.17	         b(a(x1)) -> x1
172.83/44.17	         b(b(a(x1))) -> a(b(a(b(b(x1)))))
172.83/44.17	        graph:
172.83/44.17	         b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(x1)
172.83/44.17	        Usable Rule Processor:
172.83/44.17	         DPs:
172.83/44.17	          b#(b(a(x1))) -> b#(x1)
172.83/44.17	         TRS:
172.83/44.17	          
172.83/44.17	         Arctic Interpretation Processor:
172.83/44.17	          dimension: 1
172.83/44.17	          usable rules:
172.83/44.17	           
172.83/44.17	          interpretation:
172.83/44.17	           [b#](x0) = 6x0,
172.83/44.17	           
172.83/44.17	           [b](x0) = 1x0 + 12,
172.83/44.17	           
172.83/44.17	           [a](x0) = x0 + 9
172.83/44.17	          orientation:
172.83/44.17	           b#(b(a(x1))) = 7x1 + 18 >= 6x1 = b#(x1)
172.83/44.17	          problem:
172.83/44.17	           DPs:
172.83/44.17	            
172.83/44.17	           TRS:
172.83/44.17	            
172.83/44.17	          Qed
172.83/44.17	EOF