169.55/43.22	YES
169.55/43.22	
169.55/43.22	Problem:
169.55/43.22	 a(x1) -> x1
169.55/43.22	 a(a(x1)) -> b(x1)
169.55/43.22	 b(a(b(x1))) -> a(a(b(b(b(x1)))))
169.55/43.22	
169.55/43.22	Proof:
169.55/43.22	 DP Processor:
169.55/43.22	  DPs:
169.55/43.22	   a#(a(x1)) -> b#(x1)
169.55/43.22	   b#(a(b(x1))) -> b#(b(x1))
169.55/43.22	   b#(a(b(x1))) -> b#(b(b(x1)))
169.55/43.22	   b#(a(b(x1))) -> a#(b(b(b(x1))))
169.55/43.22	   b#(a(b(x1))) -> a#(a(b(b(b(x1)))))
169.55/43.22	  TRS:
169.55/43.22	   a(x1) -> x1
169.55/43.22	   a(a(x1)) -> b(x1)
169.55/43.22	   b(a(b(x1))) -> a(a(b(b(b(x1)))))
169.55/43.22	  TDG Processor:
169.55/43.22	   DPs:
169.55/43.22	    a#(a(x1)) -> b#(x1)
169.55/43.22	    b#(a(b(x1))) -> b#(b(x1))
169.55/43.22	    b#(a(b(x1))) -> b#(b(b(x1)))
169.55/43.22	    b#(a(b(x1))) -> a#(b(b(b(x1))))
169.55/43.22	    b#(a(b(x1))) -> a#(a(b(b(b(x1)))))
169.55/43.22	   TRS:
169.55/43.22	    a(x1) -> x1
169.55/43.22	    a(a(x1)) -> b(x1)
169.55/43.22	    b(a(b(x1))) -> a(a(b(b(b(x1)))))
169.55/43.22	   graph:
169.55/43.22	    b#(a(b(x1))) -> b#(b(b(x1))) -> b#(a(b(x1))) -> a#(a(b(b(b(x1)))))
169.55/43.22	    b#(a(b(x1))) -> b#(b(b(x1))) -> b#(a(b(x1))) -> a#(b(b(b(x1))))
169.55/43.22	    b#(a(b(x1))) -> b#(b(b(x1))) -> b#(a(b(x1))) -> b#(b(b(x1)))
169.55/43.22	    b#(a(b(x1))) -> b#(b(b(x1))) -> b#(a(b(x1))) -> b#(b(x1))
169.55/43.22	    b#(a(b(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> a#(a(b(b(b(x1)))))
169.55/43.22	    b#(a(b(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> a#(b(b(b(x1))))
169.55/43.22	    b#(a(b(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> b#(b(b(x1)))
169.55/43.22	    b#(a(b(x1))) -> b#(b(x1)) -> b#(a(b(x1))) -> b#(b(x1))
169.55/43.22	    b#(a(b(x1))) -> a#(b(b(b(x1)))) -> a#(a(x1)) -> b#(x1)
169.55/43.22	    b#(a(b(x1))) -> a#(a(b(b(b(x1))))) -> a#(a(x1)) -> b#(x1)
169.55/43.22	    a#(a(x1)) -> b#(x1) -> b#(a(b(x1))) -> a#(a(b(b(b(x1)))))
169.55/43.22	    a#(a(x1)) -> b#(x1) -> b#(a(b(x1))) -> a#(b(b(b(x1))))
169.55/43.22	    a#(a(x1)) -> b#(x1) -> b#(a(b(x1))) -> b#(b(b(x1)))
169.55/43.22	    a#(a(x1)) -> b#(x1) -> b#(a(b(x1))) -> b#(b(x1))
169.55/43.22	   Arctic Interpretation Processor:
169.55/43.22	    dimension: 2
169.55/43.22	    usable rules:
169.55/43.22	     a(x1) -> x1
169.55/43.22	     a(a(x1)) -> b(x1)
169.55/43.22	     b(a(b(x1))) -> a(a(b(b(b(x1)))))
169.55/43.22	    interpretation:
169.55/43.22	     [b#](x0) = [2 0]x0,
169.55/43.22	     
169.55/43.22	     [a#](x0) = [0 1]x0 + [1],
169.55/43.22	     
169.55/43.22	               [0  -&]     [-&]
169.55/43.22	     [b](x0) = [1  0 ]x0 + [0 ],
169.55/43.22	     
169.55/43.22	               [0 0]     [0 ]
169.55/43.22	     [a](x0) = [1 0]x0 + [-&]
169.55/43.22	    orientation:
169.55/43.22	     a#(a(x1)) = [2 1]x1 + [1] >= [2 0]x1 = b#(x1)
169.55/43.22	     
169.55/43.22	     b#(a(b(x1))) = [3 2]x1 + [2] >= [2 0]x1 + [0] = b#(b(x1))
169.55/43.22	     
169.55/43.22	     b#(a(b(x1))) = [3 2]x1 + [2] >= [2 0]x1 + [0] = b#(b(b(x1)))
169.55/43.22	     
169.55/43.22	     b#(a(b(x1))) = [3 2]x1 + [2] >= [2 1]x1 + [1] = a#(b(b(b(x1))))
169.55/43.22	     
169.55/43.22	     b#(a(b(x1))) = [3 2]x1 + [2] >= [2 1]x1 + [1] = a#(a(b(b(b(x1)))))
169.55/43.22	     
169.55/43.22	             [0 0]     [0 ]           
169.55/43.22	     a(x1) = [1 0]x1 + [-&] >= x1 = x1
169.55/43.22	     
169.55/43.22	                [1 0]     [0]    [0  -&]     [-&]        
169.55/43.22	     a(a(x1)) = [1 1]x1 + [1] >= [1  0 ]x1 + [0 ] = b(x1)
169.55/43.22	     
169.55/43.22	                   [1 0]     [0]    [1 0]     [0]                    
169.55/43.22	     b(a(b(x1))) = [2 1]x1 + [1] >= [2 1]x1 + [1] = a(a(b(b(b(x1)))))
169.55/43.22	    problem:
169.55/43.22	     DPs:
169.55/43.22	      a#(a(x1)) -> b#(x1)
169.55/43.22	     TRS:
169.55/43.22	      a(x1) -> x1
169.55/43.22	      a(a(x1)) -> b(x1)
169.55/43.22	      b(a(b(x1))) -> a(a(b(b(b(x1)))))
169.55/43.22	    Restore Modifier:
169.55/43.22	     DPs:
169.55/43.22	      a#(a(x1)) -> b#(x1)
169.55/43.22	     TRS:
169.55/43.22	      a(x1) -> x1
169.55/43.22	      a(a(x1)) -> b(x1)
169.55/43.22	      b(a(b(x1))) -> a(a(b(b(b(x1)))))
169.55/43.22	     EDG Processor:
169.55/43.22	      DPs:
169.55/43.22	       a#(a(x1)) -> b#(x1)
169.55/43.22	      TRS:
169.55/43.22	       a(x1) -> x1
169.55/43.22	       a(a(x1)) -> b(x1)
169.55/43.22	       b(a(b(x1))) -> a(a(b(b(b(x1)))))
169.55/43.22	      graph:
169.55/43.22	       
169.55/43.22	      SCC Processor:
169.55/43.22	       #sccs: 0
169.55/43.22	       #rules: 0
169.55/43.22	       #arcs: 0/1
169.55/43.22	       
169.55/43.23	EOF