169.17/43.66	YES
169.17/43.67	
169.17/43.67	Problem:
169.17/43.67	 a(x1) -> b(x1)
169.17/43.67	 b(a(b(b(x1)))) -> b(b(b(a(a(x1)))))
169.17/43.67	
169.17/43.67	Proof:
169.17/43.67	 String Reversal Processor:
169.17/43.67	  a(x1) -> b(x1)
169.17/43.67	  b(b(a(b(x1)))) -> a(a(b(b(b(x1)))))
169.17/43.67	  DP Processor:
169.17/43.67	   DPs:
169.17/43.67	    a#(x1) -> b#(x1)
169.17/43.67	    b#(b(a(b(x1)))) -> b#(b(x1))
169.17/43.67	    b#(b(a(b(x1)))) -> b#(b(b(x1)))
169.17/43.67	    b#(b(a(b(x1)))) -> a#(b(b(b(x1))))
169.17/43.67	    b#(b(a(b(x1)))) -> a#(a(b(b(b(x1)))))
169.17/43.67	   TRS:
169.17/43.67	    a(x1) -> b(x1)
169.17/43.67	    b(b(a(b(x1)))) -> a(a(b(b(b(x1)))))
169.17/43.67	   TDG Processor:
169.17/43.67	    DPs:
169.17/43.67	     a#(x1) -> b#(x1)
169.17/43.67	     b#(b(a(b(x1)))) -> b#(b(x1))
169.17/43.67	     b#(b(a(b(x1)))) -> b#(b(b(x1)))
169.17/43.67	     b#(b(a(b(x1)))) -> a#(b(b(b(x1))))
169.17/43.67	     b#(b(a(b(x1)))) -> a#(a(b(b(b(x1)))))
169.17/43.67	    TRS:
169.17/43.67	     a(x1) -> b(x1)
169.17/43.67	     b(b(a(b(x1)))) -> a(a(b(b(b(x1)))))
169.17/43.67	    graph:
169.17/43.67	     b#(b(a(b(x1)))) -> b#(b(b(x1))) ->
169.17/43.67	     b#(b(a(b(x1)))) -> a#(a(b(b(b(x1)))))
169.17/43.67	     b#(b(a(b(x1)))) -> b#(b(b(x1))) ->
169.17/43.67	     b#(b(a(b(x1)))) -> a#(b(b(b(x1))))
169.17/43.67	     b#(b(a(b(x1)))) -> b#(b(b(x1))) ->
169.17/43.67	     b#(b(a(b(x1)))) -> b#(b(b(x1)))
169.17/43.67	     b#(b(a(b(x1)))) -> b#(b(b(x1))) -> b#(b(a(b(x1)))) -> b#(b(x1))
169.17/43.67	     b#(b(a(b(x1)))) -> b#(b(x1)) ->
169.17/43.67	     b#(b(a(b(x1)))) -> a#(a(b(b(b(x1)))))
169.17/43.67	     b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> a#(b(b(b(x1))))
169.17/43.67	     b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(b(x1)))
169.17/43.67	     b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(x1))
169.17/43.67	     b#(b(a(b(x1)))) -> a#(b(b(b(x1)))) -> a#(x1) -> b#(x1)
169.17/43.67	     b#(b(a(b(x1)))) -> a#(a(b(b(b(x1))))) -> a#(x1) -> b#(x1)
169.17/43.67	     a#(x1) -> b#(x1) -> b#(b(a(b(x1)))) -> a#(a(b(b(b(x1)))))
169.17/43.67	     a#(x1) -> b#(x1) -> b#(b(a(b(x1)))) -> a#(b(b(b(x1))))
169.17/43.67	     a#(x1) -> b#(x1) -> b#(b(a(b(x1)))) -> b#(b(b(x1)))
169.17/43.67	     a#(x1) -> b#(x1) -> b#(b(a(b(x1)))) -> b#(b(x1))
169.17/43.67	    Arctic Interpretation Processor:
169.17/43.67	     dimension: 2
169.17/43.67	     usable rules:
169.17/43.67	      a(x1) -> b(x1)
169.17/43.67	      b(b(a(b(x1)))) -> a(a(b(b(b(x1)))))
169.17/43.67	     interpretation:
169.17/43.67	      [b#](x0) = [0 2]x0 + [0],
169.17/43.67	      
169.17/43.67	      [a#](x0) = [0 2]x0 + [0],
169.17/43.67	      
169.17/43.67	                [0  -&]     [0]
169.17/43.67	      [b](x0) = [0  0 ]x0 + [1],
169.17/43.67	      
169.17/43.67	                [0 1]     [0]
169.17/43.67	      [a](x0) = [0 0]x0 + [1]
169.17/43.67	     orientation:
169.17/43.67	      a#(x1) = [0 2]x1 + [0] >= [0 2]x1 + [0] = b#(x1)
169.17/43.67	      
169.17/43.67	      b#(b(a(b(x1)))) = [3 3]x1 + [4] >= [2 2]x1 + [3] = b#(b(x1))
169.17/43.67	      
169.17/43.67	      b#(b(a(b(x1)))) = [3 3]x1 + [4] >= [2 2]x1 + [3] = b#(b(b(x1)))
169.17/43.67	      
169.17/43.67	      b#(b(a(b(x1)))) = [3 3]x1 + [4] >= [2 2]x1 + [3] = a#(b(b(b(x1))))
169.17/43.67	      
169.17/43.67	      b#(b(a(b(x1)))) = [3 3]x1 + [4] >= [2 2]x1 + [3] = a#(a(b(b(b(x1)))))
169.17/43.67	      
169.17/43.67	              [0 1]     [0]    [0  -&]     [0]        
169.17/43.67	      a(x1) = [0 0]x1 + [1] >= [0  0 ]x1 + [1] = b(x1)
169.17/43.67	      
169.17/43.67	                       [1 1]     [2]    [1 1]     [2]                    
169.17/43.67	      b(b(a(b(x1)))) = [1 1]x1 + [2] >= [1 1]x1 + [2] = a(a(b(b(b(x1)))))
169.17/43.67	     problem:
169.17/43.67	      DPs:
169.17/43.67	       a#(x1) -> b#(x1)
169.17/43.67	      TRS:
169.17/43.67	       a(x1) -> b(x1)
169.17/43.67	       b(b(a(b(x1)))) -> a(a(b(b(b(x1)))))
169.17/43.67	     Restore Modifier:
169.17/43.67	      DPs:
169.17/43.67	       a#(x1) -> b#(x1)
169.17/43.67	      TRS:
169.17/43.67	       a(x1) -> b(x1)
169.17/43.67	       b(b(a(b(x1)))) -> a(a(b(b(b(x1)))))
169.17/43.67	      EDG Processor:
169.17/43.67	       DPs:
169.17/43.67	        a#(x1) -> b#(x1)
169.17/43.67	       TRS:
169.17/43.67	        a(x1) -> b(x1)
169.17/43.67	        b(b(a(b(x1)))) -> a(a(b(b(b(x1)))))
169.17/43.67	       graph:
169.17/43.67	        
169.17/43.67	       SCC Processor:
169.17/43.67	        #sccs: 0
169.17/43.67	        #rules: 0
169.17/43.67	        #arcs: 0/1
169.17/43.67	        
169.17/43.67	EOF