174.82/44.63	YES
174.82/44.64	
174.82/44.64	Problem:
174.82/44.64	 a(a(x1)) -> x1
174.82/44.64	 a(a(b(x1))) -> b(a(b(a(a(x1)))))
174.82/44.64	 b(b(x1)) -> x1
174.82/44.64	
174.82/44.64	Proof:
174.82/44.64	 DP Processor:
174.82/44.64	  DPs:
174.82/44.64	   a#(a(b(x1))) -> a#(x1)
174.82/44.64	   a#(a(b(x1))) -> a#(a(x1))
174.82/44.64	   a#(a(b(x1))) -> b#(a(a(x1)))
174.82/44.64	   a#(a(b(x1))) -> a#(b(a(a(x1))))
174.82/44.64	   a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
174.82/44.64	  TRS:
174.82/44.64	   a(a(x1)) -> x1
174.82/44.64	   a(a(b(x1))) -> b(a(b(a(a(x1)))))
174.82/44.64	   b(b(x1)) -> x1
174.82/44.64	  TDG Processor:
174.82/44.64	   DPs:
174.82/44.64	    a#(a(b(x1))) -> a#(x1)
174.82/44.64	    a#(a(b(x1))) -> a#(a(x1))
174.82/44.64	    a#(a(b(x1))) -> b#(a(a(x1)))
174.82/44.64	    a#(a(b(x1))) -> a#(b(a(a(x1))))
174.82/44.64	    a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
174.82/44.64	   TRS:
174.82/44.64	    a(a(x1)) -> x1
174.82/44.64	    a(a(b(x1))) -> b(a(b(a(a(x1)))))
174.82/44.64	    b(b(x1)) -> x1
174.82/44.64	   graph:
174.82/44.64	    a#(a(b(x1))) -> a#(b(a(a(x1)))) ->
174.82/44.64	    a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
174.82/44.64	    a#(a(b(x1))) -> a#(b(a(a(x1)))) ->
174.82/44.64	    a#(a(b(x1))) -> a#(b(a(a(x1))))
174.82/44.64	    a#(a(b(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(x1))) -> b#(a(a(x1)))
174.82/44.64	    a#(a(b(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(x1))) -> a#(a(x1))
174.82/44.64	    a#(a(b(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(x1))) -> a#(x1)
174.82/44.64	    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
174.82/44.64	    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(b(a(a(x1))))
174.82/44.64	    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1)))
174.82/44.64	    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1))
174.82/44.64	    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
174.82/44.64	    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
174.82/44.64	    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(b(a(a(x1))))
174.82/44.64	    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1)))
174.82/44.64	    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1))
174.82/44.64	    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
174.82/44.64	   SCC Processor:
174.82/44.64	    #sccs: 1
174.82/44.64	    #rules: 3
174.82/44.64	    #arcs: 15/25
174.82/44.64	    DPs:
174.82/44.64	     a#(a(b(x1))) -> a#(b(a(a(x1))))
174.82/44.64	     a#(a(b(x1))) -> a#(x1)
174.82/44.64	     a#(a(b(x1))) -> a#(a(x1))
174.82/44.64	    TRS:
174.82/44.64	     a(a(x1)) -> x1
174.82/44.64	     a(a(b(x1))) -> b(a(b(a(a(x1)))))
174.82/44.64	     b(b(x1)) -> x1
174.82/44.64	    Arctic Interpretation Processor:
174.82/44.64	     dimension: 2
174.82/44.64	     usable rules:
174.82/44.64	      a(a(x1)) -> x1
174.82/44.64	      a(a(b(x1))) -> b(a(b(a(a(x1)))))
174.82/44.64	      b(b(x1)) -> x1
174.82/44.64	     interpretation:
174.82/44.64	      [a#](x0) = [-& 0 ]x0 + [0],
174.82/44.64	      
174.82/44.64	                [1  0 ]     [3]
174.82/44.64	      [b](x0) = [0  -&]x0 + [2],
174.82/44.64	      
174.82/44.64	                [-& 0 ]     [1]
174.82/44.64	      [a](x0) = [0  -&]x0 + [1]
174.82/44.64	     orientation:
174.82/44.64	      a#(a(b(x1))) = [1 0]x1 + [3] >= [0  -&]x1 + [2] = a#(b(a(a(x1))))
174.82/44.64	      
174.82/44.64	      a#(a(b(x1))) = [1 0]x1 + [3] >= [-& 0 ]x1 + [0] = a#(x1)
174.82/44.64	      
174.82/44.64	      a#(a(b(x1))) = [1 0]x1 + [3] >= [0  -&]x1 + [1] = a#(a(x1))
174.82/44.64	      
174.82/44.64	                      [1]           
174.82/44.64	      a(a(x1)) = x1 + [1] >= x1 = x1
174.82/44.64	      
174.82/44.64	                    [1  0 ]     [3]    [1  0 ]     [3]                    
174.82/44.64	      a(a(b(x1))) = [0  -&]x1 + [2] >= [0  -&]x1 + [2] = b(a(b(a(a(x1)))))
174.82/44.64	      
174.82/44.64	                 [2 1]     [4]           
174.82/44.64	      b(b(x1)) = [1 0]x1 + [3] >= x1 = x1
174.82/44.64	     problem:
174.82/44.64	      DPs:
174.82/44.64	       a#(a(b(x1))) -> a#(x1)
174.82/44.64	      TRS:
174.82/44.64	       a(a(x1)) -> x1
174.82/44.64	       a(a(b(x1))) -> b(a(b(a(a(x1)))))
174.82/44.64	       b(b(x1)) -> x1
174.82/44.64	     Restore Modifier:
174.82/44.64	      DPs:
174.82/44.64	       a#(a(b(x1))) -> a#(x1)
174.82/44.64	      TRS:
174.82/44.64	       a(a(x1)) -> x1
174.82/44.64	       a(a(b(x1))) -> b(a(b(a(a(x1)))))
174.82/44.64	       b(b(x1)) -> x1
174.82/44.64	      EDG Processor:
174.82/44.64	       DPs:
174.82/44.64	        a#(a(b(x1))) -> a#(x1)
174.82/44.64	       TRS:
174.82/44.64	        a(a(x1)) -> x1
174.82/44.64	        a(a(b(x1))) -> b(a(b(a(a(x1)))))
174.82/44.64	        b(b(x1)) -> x1
174.82/44.64	       graph:
174.82/44.64	        a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
174.82/44.64	       Usable Rule Processor:
174.82/44.64	        DPs:
174.82/44.64	         a#(a(b(x1))) -> a#(x1)
174.82/44.64	        TRS:
174.82/44.64	         
174.82/44.64	        Arctic Interpretation Processor:
174.82/44.64	         dimension: 2
174.82/44.64	         usable rules:
174.82/44.64	          
174.82/44.64	         interpretation:
174.82/44.64	          [a#](x0) = [0  -&]x0,
174.82/44.64	          
174.82/44.64	                    [0 2]     [1 ]
174.82/44.64	          [b](x0) = [0 3]x0 + [-&],
174.82/44.64	          
174.82/44.64	                    [0  3 ]     [0]
174.82/44.64	          [a](x0) = [3  -&]x0 + [0]
174.82/44.64	         orientation:
174.82/44.64	          a#(a(b(x1))) = [3 6]x1 + [1] >= [0  -&]x1 = a#(x1)
174.82/44.64	         problem:
174.82/44.64	          DPs:
174.82/44.64	           
174.82/44.64	          TRS:
174.82/44.64	           
174.82/44.64	         Qed
174.82/44.64	EOF