174.55/44.57	YES
174.55/44.58	
174.55/44.58	Problem:
174.55/44.58	 b(b(x1)) -> a(a(a(x1)))
174.55/44.58	 a(a(b(x1))) -> b(x1)
174.55/44.58	 a(b(a(x1))) -> a(b(b(x1)))
174.55/44.58	
174.55/44.58	Proof:
174.55/44.58	 String Reversal Processor:
174.55/44.58	  b(b(x1)) -> a(a(a(x1)))
174.55/44.58	  b(a(a(x1))) -> b(x1)
174.55/44.58	  a(b(a(x1))) -> b(b(a(x1)))
174.55/44.58	  DP Processor:
174.55/44.58	   DPs:
174.55/44.58	    b#(b(x1)) -> a#(x1)
174.55/44.58	    b#(b(x1)) -> a#(a(x1))
174.55/44.58	    b#(b(x1)) -> a#(a(a(x1)))
174.55/44.58	    b#(a(a(x1))) -> b#(x1)
174.55/44.58	    a#(b(a(x1))) -> b#(b(a(x1)))
174.55/44.58	   TRS:
174.55/44.58	    b(b(x1)) -> a(a(a(x1)))
174.55/44.58	    b(a(a(x1))) -> b(x1)
174.55/44.58	    a(b(a(x1))) -> b(b(a(x1)))
174.55/44.58	   TDG Processor:
174.55/44.58	    DPs:
174.55/44.58	     b#(b(x1)) -> a#(x1)
174.55/44.58	     b#(b(x1)) -> a#(a(x1))
174.55/44.58	     b#(b(x1)) -> a#(a(a(x1)))
174.55/44.58	     b#(a(a(x1))) -> b#(x1)
174.55/44.58	     a#(b(a(x1))) -> b#(b(a(x1)))
174.55/44.58	    TRS:
174.55/44.58	     b(b(x1)) -> a(a(a(x1)))
174.55/44.58	     b(a(a(x1))) -> b(x1)
174.55/44.58	     a(b(a(x1))) -> b(b(a(x1)))
174.55/44.58	    graph:
174.55/44.58	     a#(b(a(x1))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> b#(x1)
174.55/44.58	     a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(a(a(x1)))
174.55/44.58	     a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(a(x1))
174.55/44.58	     a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(x1)
174.55/44.58	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
174.55/44.58	     b#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(a(a(x1)))
174.55/44.58	     b#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(a(x1))
174.55/44.58	     b#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(x1)
174.55/44.58	     b#(b(x1)) -> a#(a(a(x1))) -> a#(b(a(x1))) -> b#(b(a(x1)))
174.55/44.58	     b#(b(x1)) -> a#(a(x1)) -> a#(b(a(x1))) -> b#(b(a(x1)))
174.55/44.58	     b#(b(x1)) -> a#(x1) -> a#(b(a(x1))) -> b#(b(a(x1)))
174.55/44.58	    Arctic Interpretation Processor:
174.55/44.58	     dimension: 2
174.55/44.58	     usable rules:
174.55/44.58	      b(b(x1)) -> a(a(a(x1)))
174.55/44.58	      b(a(a(x1))) -> b(x1)
174.55/44.58	      a(b(a(x1))) -> b(b(a(x1)))
174.55/44.58	     interpretation:
174.55/44.58	      [a#](x0) = [0 0]x0 + [0],
174.55/44.58	      
174.55/44.58	      [b#](x0) = [1 0]x0 + [0],
174.55/44.58	      
174.55/44.58	                [0  0 ]     [3]
174.55/44.58	      [a](x0) = [-& 0 ]x0 + [1],
174.55/44.58	      
174.55/44.58	                [0 0]     [3]
174.55/44.58	      [b](x0) = [1 0]x0 + [0]
174.55/44.58	     orientation:
174.55/44.58	      b#(b(x1)) = [1 1]x1 + [4] >= [0 0]x1 + [0] = a#(x1)
174.55/44.58	      
174.55/44.58	      b#(b(x1)) = [1 1]x1 + [4] >= [0 0]x1 + [3] = a#(a(x1))
174.55/44.58	      
174.55/44.58	      b#(b(x1)) = [1 1]x1 + [4] >= [0 0]x1 + [3] = a#(a(a(x1)))
174.55/44.58	      
174.55/44.58	      b#(a(a(x1))) = [1 1]x1 + [4] >= [1 0]x1 + [0] = b#(x1)
174.55/44.58	      
174.55/44.58	      a#(b(a(x1))) = [1 1]x1 + [4] >= [1 1]x1 + [4] = b#(b(a(x1)))
174.55/44.58	      
174.55/44.58	                 [1 0]     [3]    [0  0 ]     [3]              
174.55/44.58	      b(b(x1)) = [1 1]x1 + [4] >= [-& 0 ]x1 + [1] = a(a(a(x1)))
174.55/44.58	      
174.55/44.58	                    [0 0]     [3]    [0 0]     [3]        
174.55/44.58	      b(a(a(x1))) = [1 1]x1 + [4] >= [1 0]x1 + [0] = b(x1)
174.55/44.58	      
174.55/44.58	                    [1 1]     [4]    [1 1]     [4]              
174.55/44.58	      a(b(a(x1))) = [1 1]x1 + [4] >= [1 1]x1 + [4] = b(b(a(x1)))
174.55/44.58	     problem:
174.55/44.58	      DPs:
174.55/44.58	       b#(a(a(x1))) -> b#(x1)
174.55/44.58	       a#(b(a(x1))) -> b#(b(a(x1)))
174.55/44.58	      TRS:
174.55/44.58	       b(b(x1)) -> a(a(a(x1)))
174.55/44.58	       b(a(a(x1))) -> b(x1)
174.55/44.58	       a(b(a(x1))) -> b(b(a(x1)))
174.55/44.58	     Restore Modifier:
174.55/44.58	      DPs:
174.55/44.58	       b#(a(a(x1))) -> b#(x1)
174.55/44.58	       a#(b(a(x1))) -> b#(b(a(x1)))
174.55/44.58	      TRS:
174.55/44.58	       b(b(x1)) -> a(a(a(x1)))
174.55/44.58	       b(a(a(x1))) -> b(x1)
174.55/44.58	       a(b(a(x1))) -> b(b(a(x1)))
174.55/44.58	      EDG Processor:
174.55/44.58	       DPs:
174.55/44.58	        b#(a(a(x1))) -> b#(x1)
174.55/44.58	        a#(b(a(x1))) -> b#(b(a(x1)))
174.55/44.58	       TRS:
174.55/44.58	        b(b(x1)) -> a(a(a(x1)))
174.55/44.58	        b(a(a(x1))) -> b(x1)
174.55/44.58	        a(b(a(x1))) -> b(b(a(x1)))
174.55/44.58	       graph:
174.55/44.58	        a#(b(a(x1))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> b#(x1)
174.55/44.58	        b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
174.55/44.58	       SCC Processor:
174.55/44.58	        #sccs: 1
174.55/44.58	        #rules: 1
174.55/44.58	        #arcs: 2/4
174.55/44.58	        DPs:
174.55/44.58	         b#(a(a(x1))) -> b#(x1)
174.55/44.58	        TRS:
174.55/44.58	         b(b(x1)) -> a(a(a(x1)))
174.55/44.58	         b(a(a(x1))) -> b(x1)
174.55/44.58	         a(b(a(x1))) -> b(b(a(x1)))
174.55/44.58	        Usable Rule Processor:
174.55/44.58	         DPs:
174.55/44.58	          b#(a(a(x1))) -> b#(x1)
174.55/44.58	         TRS:
174.55/44.58	          
174.55/44.58	         Arctic Interpretation Processor:
174.55/44.58	          dimension: 1
174.55/44.58	          usable rules:
174.55/44.58	           
174.55/44.58	          interpretation:
174.55/44.58	           [b#](x0) = 2x0,
174.55/44.58	           
174.55/44.58	           [a](x0) = 2x0
174.55/44.58	          orientation:
174.55/44.58	           b#(a(a(x1))) = 6x1 >= 2x1 = b#(x1)
174.55/44.58	          problem:
174.55/44.58	           DPs:
174.55/44.58	            
174.55/44.58	           TRS:
174.55/44.58	            
174.55/44.58	          Qed
174.55/44.58	EOF