170.11/43.47	YES
170.31/43.47	
170.31/43.47	Problem:
170.31/43.47	 a(x1) -> x1
170.31/43.47	 a(a(x1)) -> a(b(a(b(x1))))
170.31/43.47	 b(b(b(b(x1)))) -> a(x1)
170.31/43.47	
170.31/43.47	Proof:
170.31/43.47	 String Reversal Processor:
170.31/43.47	  a(x1) -> x1
170.31/43.47	  a(a(x1)) -> b(a(b(a(x1))))
170.31/43.47	  b(b(b(b(x1)))) -> a(x1)
170.31/43.47	  DP Processor:
170.31/43.47	   DPs:
170.31/43.47	    a#(a(x1)) -> b#(a(x1))
170.31/43.47	    a#(a(x1)) -> a#(b(a(x1)))
170.31/43.47	    a#(a(x1)) -> b#(a(b(a(x1))))
170.31/43.47	    b#(b(b(b(x1)))) -> a#(x1)
170.31/43.47	   TRS:
170.31/43.47	    a(x1) -> x1
170.31/43.47	    a(a(x1)) -> b(a(b(a(x1))))
170.31/43.47	    b(b(b(b(x1)))) -> a(x1)
170.31/43.47	   TDG Processor:
170.31/43.47	    DPs:
170.31/43.47	     a#(a(x1)) -> b#(a(x1))
170.31/43.47	     a#(a(x1)) -> a#(b(a(x1)))
170.31/43.47	     a#(a(x1)) -> b#(a(b(a(x1))))
170.31/43.47	     b#(b(b(b(x1)))) -> a#(x1)
170.31/43.47	    TRS:
170.31/43.47	     a(x1) -> x1
170.31/43.47	     a(a(x1)) -> b(a(b(a(x1))))
170.31/43.47	     b(b(b(b(x1)))) -> a(x1)
170.31/43.47	    graph:
170.31/43.47	     b#(b(b(b(x1)))) -> a#(x1) -> a#(a(x1)) -> b#(a(b(a(x1))))
170.31/43.47	     b#(b(b(b(x1)))) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1)))
170.31/43.47	     b#(b(b(b(x1)))) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
170.31/43.47	     a#(a(x1)) -> b#(a(b(a(x1)))) -> b#(b(b(b(x1)))) -> a#(x1)
170.31/43.47	     a#(a(x1)) -> b#(a(x1)) -> b#(b(b(b(x1)))) -> a#(x1)
170.31/43.47	     a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(b(a(x1))))
170.31/43.47	     a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1)))
170.31/43.47	     a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1))
170.31/43.47	    Arctic Interpretation Processor:
170.31/43.47	     dimension: 2
170.31/43.47	     usable rules:
170.31/43.47	      a(x1) -> x1
170.31/43.47	      a(a(x1)) -> b(a(b(a(x1))))
170.31/43.47	      b(b(b(b(x1)))) -> a(x1)
170.31/43.47	     interpretation:
170.31/43.47	      [b#](x0) = [0 1]x0 + [0],
170.31/43.47	      
170.31/43.47	      [a#](x0) = [1 0]x0 + [0],
170.31/43.47	      
170.31/43.47	                [-& 0 ]     [0]
170.31/43.47	      [b](x0) = [0  1 ]x0 + [1],
170.31/43.47	      
170.31/43.47	                [2 1]     [3]
170.31/43.47	      [a](x0) = [1 0]x0 + [0]
170.31/43.47	     orientation:
170.31/43.47	      a#(a(x1)) = [3 2]x1 + [4] >= [2 1]x1 + [3] = b#(a(x1))
170.31/43.47	      
170.31/43.47	      a#(a(x1)) = [3 2]x1 + [4] >= [2 1]x1 + [3] = a#(b(a(x1)))
170.31/43.47	      
170.31/43.47	      a#(a(x1)) = [3 2]x1 + [4] >= [3 2]x1 + [4] = b#(a(b(a(x1))))
170.31/43.47	      
170.31/43.47	      b#(b(b(b(x1)))) = [3 4]x1 + [4] >= [1 0]x1 + [0] = a#(x1)
170.31/43.47	      
170.31/43.47	              [2 1]     [3]           
170.31/43.47	      a(x1) = [1 0]x1 + [0] >= x1 = x1
170.31/43.47	      
170.31/43.47	                 [4 3]     [5]    [2 1]     [3]                 
170.31/43.47	      a(a(x1)) = [3 2]x1 + [4] >= [3 2]x1 + [4] = b(a(b(a(x1))))
170.31/43.47	      
170.31/43.47	                       [2 3]     [3]    [2 1]     [3]        
170.31/43.47	      b(b(b(b(x1)))) = [3 4]x1 + [4] >= [1 0]x1 + [0] = a(x1)
170.31/43.47	     problem:
170.31/43.47	      DPs:
170.31/43.47	       a#(a(x1)) -> b#(a(b(a(x1))))
170.31/43.47	      TRS:
170.31/43.47	       a(x1) -> x1
170.31/43.47	       a(a(x1)) -> b(a(b(a(x1))))
170.31/43.47	       b(b(b(b(x1)))) -> a(x1)
170.31/43.47	     Restore Modifier:
170.31/43.47	      DPs:
170.31/43.47	       a#(a(x1)) -> b#(a(b(a(x1))))
170.31/43.47	      TRS:
170.31/43.47	       a(x1) -> x1
170.31/43.47	       a(a(x1)) -> b(a(b(a(x1))))
170.31/43.47	       b(b(b(b(x1)))) -> a(x1)
170.31/43.47	      EDG Processor:
170.31/43.47	       DPs:
170.31/43.47	        a#(a(x1)) -> b#(a(b(a(x1))))
170.31/43.47	       TRS:
170.31/43.47	        a(x1) -> x1
170.31/43.47	        a(a(x1)) -> b(a(b(a(x1))))
170.31/43.47	        b(b(b(b(x1)))) -> a(x1)
170.31/43.47	       graph:
170.31/43.47	        
170.31/43.47	       SCC Processor:
170.31/43.47	        #sccs: 0
170.31/43.47	        #rules: 0
170.31/43.47	        #arcs: 0/1
170.31/43.47	        
170.31/43.48	EOF