180.71/46.23	YES
180.71/46.24	
180.71/46.24	Problem:
180.71/46.24	 a(a(b(b(x1)))) -> a(b(a(a(x1))))
180.71/46.24	 a(x1) -> b(b(b(x1)))
180.71/46.24	
180.71/46.24	Proof:
180.71/46.24	 String Reversal Processor:
180.71/46.24	  b(b(a(a(x1)))) -> a(a(b(a(x1))))
180.71/46.24	  a(x1) -> b(b(b(x1)))
180.71/46.24	  DP Processor:
180.71/46.24	   DPs:
180.71/46.24	    b#(b(a(a(x1)))) -> b#(a(x1))
180.71/46.24	    b#(b(a(a(x1)))) -> a#(b(a(x1)))
180.71/46.24	    b#(b(a(a(x1)))) -> a#(a(b(a(x1))))
180.71/46.24	    a#(x1) -> b#(x1)
180.71/46.24	    a#(x1) -> b#(b(x1))
180.71/46.24	    a#(x1) -> b#(b(b(x1)))
180.71/46.24	   TRS:
180.71/46.24	    b(b(a(a(x1)))) -> a(a(b(a(x1))))
180.71/46.24	    a(x1) -> b(b(b(x1)))
180.71/46.24	   TDG Processor:
180.71/46.24	    DPs:
180.71/46.24	     b#(b(a(a(x1)))) -> b#(a(x1))
180.71/46.24	     b#(b(a(a(x1)))) -> a#(b(a(x1)))
180.71/46.24	     b#(b(a(a(x1)))) -> a#(a(b(a(x1))))
180.71/46.24	     a#(x1) -> b#(x1)
180.71/46.24	     a#(x1) -> b#(b(x1))
180.71/46.24	     a#(x1) -> b#(b(b(x1)))
180.71/46.24	    TRS:
180.71/46.24	     b(b(a(a(x1)))) -> a(a(b(a(x1))))
180.71/46.24	     a(x1) -> b(b(b(x1)))
180.71/46.24	    graph:
180.71/46.24	     a#(x1) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> a#(a(b(a(x1))))
180.71/46.24	     a#(x1) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> a#(b(a(x1)))
180.71/46.24	     a#(x1) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> b#(a(x1))
180.71/46.24	     a#(x1) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(a(b(a(x1))))
180.71/46.24	     a#(x1) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(b(a(x1)))
180.71/46.24	     a#(x1) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(a(x1))
180.71/46.24	     a#(x1) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(a(b(a(x1))))
180.71/46.24	     a#(x1) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(b(a(x1)))
180.71/46.24	     a#(x1) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(a(x1))
180.71/46.24	     b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> a#(x1) -> b#(b(b(x1)))
180.71/46.24	     b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> a#(x1) -> b#(b(x1))
180.71/46.24	     b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> a#(x1) -> b#(x1)
180.71/46.24	     b#(b(a(a(x1)))) -> a#(b(a(x1))) -> a#(x1) -> b#(b(b(x1)))
180.71/46.24	     b#(b(a(a(x1)))) -> a#(b(a(x1))) -> a#(x1) -> b#(b(x1))
180.71/46.24	     b#(b(a(a(x1)))) -> a#(b(a(x1))) -> a#(x1) -> b#(x1)
180.71/46.24	     b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> a#(a(b(a(x1))))
180.71/46.24	     b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> a#(b(a(x1)))
180.71/46.24	     b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> b#(a(x1))
180.71/46.24	    Arctic Interpretation Processor:
180.71/46.24	     dimension: 2
180.71/46.24	     usable rules:
180.71/46.24	      b(b(a(a(x1)))) -> a(a(b(a(x1))))
180.71/46.24	      a(x1) -> b(b(b(x1)))
180.71/46.24	     interpretation:
180.71/46.24	      [a#](x0) = [1 1]x0 + [1],
180.71/46.24	      
180.71/46.24	      [b#](x0) = [-& 0 ]x0 + [0],
180.71/46.24	      
180.71/46.24	                [1  0 ]     [3]
180.71/46.24	      [a](x0) = [0  -&]x0 + [0],
180.71/46.24	      
180.71/46.24	                [-& 0 ]     [0]
180.71/46.24	      [b](x0) = [0  -&]x0 + [0]
180.71/46.24	     orientation:
180.71/46.24	      b#(b(a(a(x1)))) = [2 1]x1 + [4] >= [0  -&]x1 + [0] = b#(a(x1))
180.71/46.24	      
180.71/46.24	      b#(b(a(a(x1)))) = [2 1]x1 + [4] >= [2 1]x1 + [4] = a#(b(a(x1)))
180.71/46.24	      
180.71/46.24	      b#(b(a(a(x1)))) = [2 1]x1 + [4] >= [2 1]x1 + [4] = a#(a(b(a(x1))))
180.71/46.24	      
180.71/46.24	      a#(x1) = [1 1]x1 + [1] >= [-& 0 ]x1 + [0] = b#(x1)
180.71/46.24	      
180.71/46.24	      a#(x1) = [1 1]x1 + [1] >= [0  -&]x1 + [0] = b#(b(x1))
180.71/46.24	      
180.71/46.24	      a#(x1) = [1 1]x1 + [1] >= [-& 0 ]x1 + [0] = b#(b(b(x1)))
180.71/46.24	      
180.71/46.24	                       [2 1]     [4]    [2 1]     [4]                 
180.71/46.24	      b(b(a(a(x1)))) = [1 0]x1 + [3] >= [1 0]x1 + [3] = a(a(b(a(x1))))
180.71/46.24	      
180.71/46.24	              [1  0 ]     [3]    [-& 0 ]     [0]              
180.71/46.24	      a(x1) = [0  -&]x1 + [0] >= [0  -&]x1 + [0] = b(b(b(x1)))
180.71/46.24	     problem:
180.71/46.24	      DPs:
180.71/46.24	       b#(b(a(a(x1)))) -> a#(b(a(x1)))
180.71/46.24	       b#(b(a(a(x1)))) -> a#(a(b(a(x1))))
180.71/46.24	      TRS:
180.71/46.24	       b(b(a(a(x1)))) -> a(a(b(a(x1))))
180.71/46.24	       a(x1) -> b(b(b(x1)))
180.71/46.24	     Restore Modifier:
180.71/46.24	      DPs:
180.71/46.24	       b#(b(a(a(x1)))) -> a#(b(a(x1)))
180.71/46.24	       b#(b(a(a(x1)))) -> a#(a(b(a(x1))))
180.71/46.24	      TRS:
180.71/46.24	       b(b(a(a(x1)))) -> a(a(b(a(x1))))
180.71/46.24	       a(x1) -> b(b(b(x1)))
180.71/46.24	      EDG Processor:
180.71/46.24	       DPs:
180.71/46.24	        b#(b(a(a(x1)))) -> a#(b(a(x1)))
180.71/46.24	        b#(b(a(a(x1)))) -> a#(a(b(a(x1))))
180.71/46.24	       TRS:
180.71/46.24	        b(b(a(a(x1)))) -> a(a(b(a(x1))))
180.71/46.24	        a(x1) -> b(b(b(x1)))
180.71/46.24	       graph:
180.71/46.24	        
180.71/46.24	       SCC Processor:
180.71/46.24	        #sccs: 0
180.71/46.24	        #rules: 0
180.71/46.24	        #arcs: 0/4
180.71/46.24	        
180.71/46.25	EOF