178.92/45.79	YES
178.92/45.80	
178.92/45.80	Problem:
178.92/45.80	 a(x1) -> b(c(x1))
178.92/45.80	 a(a(x1)) -> x1
178.92/45.80	 a(b(b(x1))) -> b(b(a(a(x1))))
178.92/45.80	
178.92/45.80	Proof:
178.92/45.80	 DP Processor:
178.92/45.80	  DPs:
178.92/45.80	   a#(b(b(x1))) -> a#(x1)
178.92/45.80	   a#(b(b(x1))) -> a#(a(x1))
178.92/45.80	  TRS:
178.92/45.80	   a(x1) -> b(c(x1))
178.92/45.80	   a(a(x1)) -> x1
178.92/45.80	   a(b(b(x1))) -> b(b(a(a(x1))))
178.92/45.80	  Arctic Interpretation Processor:
178.92/45.80	   dimension: 2
178.92/45.80	   usable rules:
178.92/45.80	    a(x1) -> b(c(x1))
178.92/45.80	    a(a(x1)) -> x1
178.92/45.80	    a(b(b(x1))) -> b(b(a(a(x1))))
178.92/45.80	   interpretation:
178.92/45.80	    [a#](x0) = [0 2]x0 + [0],
178.92/45.80	    
178.92/45.80	              [-& 0 ]     [1]
178.92/45.80	    [b](x0) = [1  -&]x0 + [0],
178.92/45.80	    
178.92/45.80	              [-& -&]     [0]
178.92/45.80	    [c](x0) = [0  0 ]x0 + [1],
178.92/45.80	    
178.92/45.80	              [0  3 ]     [1]
178.92/45.80	    [a](x0) = [-& 0 ]x0 + [1]
178.92/45.80	   orientation:
178.92/45.80	    a#(b(b(x1))) = [1 3]x1 + [4] >= [0 2]x1 + [0] = a#(x1)
178.92/45.80	    
178.92/45.80	    a#(b(b(x1))) = [1 3]x1 + [4] >= [0 3]x1 + [3] = a#(a(x1))
178.92/45.80	    
178.92/45.80	            [0  3 ]     [1]    [0  0 ]     [1]           
178.92/45.80	    a(x1) = [-& 0 ]x1 + [1] >= [-& -&]x1 + [1] = b(c(x1))
178.92/45.80	    
178.92/45.80	               [0  3 ]     [4]           
178.92/45.80	    a(a(x1)) = [-& 0 ]x1 + [1] >= x1 = x1
178.92/45.80	    
178.92/45.80	                  [1  4 ]     [5]    [1  4 ]     [5]                 
178.92/45.80	    a(b(b(x1))) = [-& 1 ]x1 + [2] >= [-& 1 ]x1 + [2] = b(b(a(a(x1))))
178.92/45.80	   problem:
178.92/45.80	    DPs:
178.92/45.80	     a#(b(b(x1))) -> a#(a(x1))
178.92/45.80	    TRS:
178.92/45.80	     a(x1) -> b(c(x1))
178.92/45.80	     a(a(x1)) -> x1
178.92/45.80	     a(b(b(x1))) -> b(b(a(a(x1))))
178.92/45.80	   Restore Modifier:
178.92/45.80	    DPs:
178.92/45.80	     a#(b(b(x1))) -> a#(a(x1))
178.92/45.80	    TRS:
178.92/45.80	     a(x1) -> b(c(x1))
178.92/45.80	     a(a(x1)) -> x1
178.92/45.80	     a(b(b(x1))) -> b(b(a(a(x1))))
178.92/45.80	    Arctic Interpretation Processor:
178.92/45.80	     dimension: 2
178.92/45.80	     usable rules:
178.92/45.80	      a(x1) -> b(c(x1))
178.92/45.80	      a(a(x1)) -> x1
178.92/45.80	      a(b(b(x1))) -> b(b(a(a(x1))))
178.92/45.80	     interpretation:
178.92/45.80	      [a#](x0) = [-& 1 ]x0 + [0],
178.92/45.80	      
178.92/45.80	                [-& 1 ]     [1]
178.92/45.80	      [b](x0) = [0  -&]x0 + [0],
178.92/45.80	      
178.92/45.80	                [-& -&]     [0]
178.92/45.80	      [c](x0) = [-& 0 ]x0 + [1],
178.92/45.80	      
178.92/45.80	                [0  2 ]     [2]
178.92/45.80	      [a](x0) = [-& 0 ]x0 + [0]
178.92/45.80	     orientation:
178.92/45.80	      a#(b(b(x1))) = [-& 2 ]x1 + [2] >= [-& 1 ]x1 + [1] = a#(a(x1))
178.92/45.80	      
178.92/45.80	              [0  2 ]     [2]    [-& 1 ]     [2]           
178.92/45.80	      a(x1) = [-& 0 ]x1 + [0] >= [-& -&]x1 + [0] = b(c(x1))
178.92/45.80	      
178.92/45.80	                 [0  2 ]     [2]           
178.92/45.80	      a(a(x1)) = [-& 0 ]x1 + [0] >= x1 = x1
178.92/45.80	      
178.92/45.80	                    [1  3 ]     [3]    [1  3 ]     [3]                 
178.92/45.80	      a(b(b(x1))) = [-& 1 ]x1 + [1] >= [-& 1 ]x1 + [1] = b(b(a(a(x1))))
178.92/45.80	     problem:
178.92/45.80	      DPs:
178.92/45.80	       
178.92/45.80	      TRS:
178.92/45.80	       a(x1) -> b(c(x1))
178.92/45.80	       a(a(x1)) -> x1
178.92/45.80	       a(b(b(x1))) -> b(b(a(a(x1))))
178.92/45.80	     Qed
178.92/45.80	EOF