168.05/42.97	YES
168.05/42.98	
168.05/42.98	Problem:
168.05/42.98	 a(b(a(x1))) -> b(b(b(a(x1))))
168.05/42.98	 b(b(b(a(x1)))) -> a(a(a(b(x1))))
168.05/42.98	
168.05/42.98	Proof:
168.05/42.98	 String Reversal Processor:
168.05/42.98	  a(b(a(x1))) -> a(b(b(b(x1))))
168.05/42.98	  a(b(b(b(x1)))) -> b(a(a(a(x1))))
168.05/42.98	  DP Processor:
168.05/42.98	   DPs:
168.05/42.98	    a#(b(a(x1))) -> a#(b(b(b(x1))))
168.05/42.98	    a#(b(b(b(x1)))) -> a#(x1)
168.05/42.98	    a#(b(b(b(x1)))) -> a#(a(x1))
168.05/42.98	    a#(b(b(b(x1)))) -> a#(a(a(x1)))
168.05/42.98	   TRS:
168.05/42.98	    a(b(a(x1))) -> a(b(b(b(x1))))
168.05/42.98	    a(b(b(b(x1)))) -> b(a(a(a(x1))))
168.05/42.98	   EDG Processor:
168.05/42.98	    DPs:
168.05/42.98	     a#(b(a(x1))) -> a#(b(b(b(x1))))
168.05/42.98	     a#(b(b(b(x1)))) -> a#(x1)
168.05/42.98	     a#(b(b(b(x1)))) -> a#(a(x1))
168.05/42.98	     a#(b(b(b(x1)))) -> a#(a(a(x1)))
168.05/42.98	    TRS:
168.05/42.98	     a(b(a(x1))) -> a(b(b(b(x1))))
168.05/42.98	     a(b(b(b(x1)))) -> b(a(a(a(x1))))
168.05/42.98	    graph:
168.05/42.98	     a#(b(b(b(x1)))) -> a#(a(a(x1))) ->
168.05/42.98	     a#(b(a(x1))) -> a#(b(b(b(x1))))
168.05/42.98	     a#(b(b(b(x1)))) -> a#(a(a(x1))) -> a#(b(b(b(x1)))) -> a#(x1)
168.05/42.98	     a#(b(b(b(x1)))) -> a#(a(a(x1))) -> a#(b(b(b(x1)))) -> a#(a(x1))
168.05/42.98	     a#(b(b(b(x1)))) -> a#(a(a(x1))) -> a#(b(b(b(x1)))) -> a#(a(a(x1)))
168.05/42.98	     a#(b(b(b(x1)))) -> a#(a(x1)) -> a#(b(a(x1))) -> a#(b(b(b(x1))))
168.05/42.98	     a#(b(b(b(x1)))) -> a#(a(x1)) -> a#(b(b(b(x1)))) -> a#(x1)
168.05/42.98	     a#(b(b(b(x1)))) -> a#(a(x1)) -> a#(b(b(b(x1)))) -> a#(a(x1))
168.05/42.98	     a#(b(b(b(x1)))) -> a#(a(x1)) -> a#(b(b(b(x1)))) -> a#(a(a(x1)))
168.05/42.98	     a#(b(b(b(x1)))) -> a#(x1) -> a#(b(a(x1))) -> a#(b(b(b(x1))))
168.05/42.98	     a#(b(b(b(x1)))) -> a#(x1) -> a#(b(b(b(x1)))) -> a#(x1)
168.05/42.98	     a#(b(b(b(x1)))) -> a#(x1) -> a#(b(b(b(x1)))) -> a#(a(x1))
168.05/42.98	     a#(b(b(b(x1)))) -> a#(x1) -> a#(b(b(b(x1)))) -> a#(a(a(x1)))
168.05/42.98	     a#(b(a(x1))) -> a#(b(b(b(x1)))) -> a#(b(b(b(x1)))) -> a#(x1)
168.05/42.98	     a#(b(a(x1))) -> a#(b(b(b(x1)))) -> a#(b(b(b(x1)))) -> a#(a(x1))
168.05/42.98	     a#(b(a(x1))) -> a#(b(b(b(x1)))) -> a#(b(b(b(x1)))) -> a#(a(a(x1)))
168.05/42.98	    Matrix Interpretation Processor: dim=4
168.05/42.98	     
168.05/42.98	     interpretation:
168.05/42.98	      [a#](x0) = [0 0 1 0]x0,
168.05/42.98	      
168.05/42.98	                [0 0 0 0]     [0]
168.05/42.98	                [1 0 1 0]     [0]
168.05/42.98	      [b](x0) = [1 0 0 1]x0 + [1]
168.05/42.98	                [0 1 0 0]     [0],
168.05/42.98	      
168.05/42.98	                [1 0 0 0]  
168.05/42.98	                [0 0 1 0]  
168.05/42.98	      [a](x0) = [0 0 1 0]x0
168.05/42.98	                [0 0 1 0]  
168.05/42.98	     orientation:
168.05/42.98	      a#(b(a(x1))) = [1 0 1 0]x1 + [1] >= [1 0 1 0]x1 + [1] = a#(b(b(b(x1))))
168.05/42.98	      
168.05/42.98	      a#(b(b(b(x1)))) = [1 0 1 0]x1 + [1] >= [0 0 1 0]x1 = a#(x1)
168.05/42.98	      
168.05/42.98	      a#(b(b(b(x1)))) = [1 0 1 0]x1 + [1] >= [0 0 1 0]x1 = a#(a(x1))
168.05/42.98	      
168.05/42.98	      a#(b(b(b(x1)))) = [1 0 1 0]x1 + [1] >= [0 0 1 0]x1 = a#(a(a(x1)))
168.05/42.98	      
168.05/42.98	                    [0 0 0 0]     [0]    [0 0 0 0]     [0]                 
168.05/42.98	                    [1 0 1 0]     [1]    [1 0 1 0]     [1]                 
168.05/42.98	      a(b(a(x1))) = [1 0 1 0]x1 + [1] >= [1 0 1 0]x1 + [1] = a(b(b(b(x1))))
168.05/42.98	                    [1 0 1 0]     [1]    [1 0 1 0]     [1]                 
168.05/42.98	      
168.05/42.98	                       [0 0 0 0]     [0]    [0 0 0 0]     [0]                 
168.05/42.98	                       [1 0 1 0]     [1]    [1 0 1 0]     [0]                 
168.05/42.98	      a(b(b(b(x1)))) = [1 0 1 0]x1 + [1] >= [1 0 1 0]x1 + [1] = b(a(a(a(x1))))
168.05/42.98	                       [1 0 1 0]     [1]    [0 0 1 0]     [0]                 
168.05/42.98	     problem:
168.05/42.98	      DPs:
168.05/42.98	       a#(b(a(x1))) -> a#(b(b(b(x1))))
168.05/42.98	      TRS:
168.05/42.98	       a(b(a(x1))) -> a(b(b(b(x1))))
168.05/42.98	       a(b(b(b(x1)))) -> b(a(a(a(x1))))
168.05/42.98	     Restore Modifier:
168.05/42.98	      DPs:
168.05/42.98	       a#(b(a(x1))) -> a#(b(b(b(x1))))
168.05/42.98	      TRS:
168.05/42.98	       a(b(a(x1))) -> a(b(b(b(x1))))
168.05/42.98	       a(b(b(b(x1)))) -> b(a(a(a(x1))))
168.05/42.98	      EDG Processor:
168.05/42.98	       DPs:
168.05/42.98	        a#(b(a(x1))) -> a#(b(b(b(x1))))
168.05/42.98	       TRS:
168.05/42.98	        a(b(a(x1))) -> a(b(b(b(x1))))
168.05/42.98	        a(b(b(b(x1)))) -> b(a(a(a(x1))))
168.05/42.98	       graph:
168.05/42.98	        
168.05/42.98	       SCC Processor:
168.05/42.98	        #sccs: 0
168.05/42.98	        #rules: 0
168.05/42.98	        #arcs: 0/1
168.05/42.98	        
168.05/42.98	EOF