177.20/45.30	YES
177.20/45.31	
177.20/45.31	Problem:
177.20/45.31	 a(x1) -> x1
177.20/45.31	 a(a(x1)) -> b(c(x1))
177.20/45.31	 a(b(b(x1))) -> b(b(a(a(x1))))
177.20/45.31	
177.20/45.31	Proof:
177.20/45.31	 DP Processor:
177.20/45.31	  DPs:
177.20/45.31	   a#(b(b(x1))) -> a#(x1)
177.20/45.31	   a#(b(b(x1))) -> a#(a(x1))
177.20/45.31	  TRS:
177.20/45.31	   a(x1) -> x1
177.20/45.31	   a(a(x1)) -> b(c(x1))
177.20/45.31	   a(b(b(x1))) -> b(b(a(a(x1))))
177.20/45.31	  Arctic Interpretation Processor:
177.20/45.31	   dimension: 2
177.20/45.31	   usable rules:
177.20/45.31	    a(x1) -> x1
177.20/45.31	    a(a(x1)) -> b(c(x1))
177.20/45.31	    a(b(b(x1))) -> b(b(a(a(x1))))
177.20/45.31	   interpretation:
177.20/45.31	    [a#](x0) = [0 0]x0 + [3],
177.20/45.31	    
177.20/45.31	              [-& 0 ]     [2]
177.20/45.31	    [b](x0) = [2  -&]x0 + [0],
177.20/45.31	    
177.20/45.31	              [-& -&]     [0]
177.20/45.31	    [c](x0) = [0  1 ]x0 + [3],
177.20/45.31	    
177.20/45.31	              [0  2 ]     [-&]
177.20/45.31	    [a](x0) = [-& 0 ]x0 + [2 ]
177.20/45.31	   orientation:
177.20/45.31	    a#(b(b(x1))) = [2 2]x1 + [4] >= [0 0]x1 + [3] = a#(x1)
177.20/45.31	    
177.20/45.31	    a#(b(b(x1))) = [2 2]x1 + [4] >= [0 2]x1 + [3] = a#(a(x1))
177.20/45.31	    
177.20/45.31	            [0  2 ]     [-&]           
177.20/45.31	    a(x1) = [-& 0 ]x1 + [2 ] >= x1 = x1
177.20/45.31	    
177.20/45.31	               [0  2 ]     [4]    [0  1 ]     [3]           
177.20/45.31	    a(a(x1)) = [-& 0 ]x1 + [2] >= [-& -&]x1 + [2] = b(c(x1))
177.20/45.31	    
177.20/45.31	                  [2  4 ]     [6]    [2  4 ]     [6]                 
177.20/45.31	    a(b(b(x1))) = [-& 2 ]x1 + [4] >= [-& 2 ]x1 + [4] = b(b(a(a(x1))))
177.20/45.31	   problem:
177.20/45.31	    DPs:
177.20/45.31	     a#(b(b(x1))) -> a#(a(x1))
177.20/45.31	    TRS:
177.20/45.31	     a(x1) -> x1
177.20/45.31	     a(a(x1)) -> b(c(x1))
177.20/45.31	     a(b(b(x1))) -> b(b(a(a(x1))))
177.20/45.31	   Restore Modifier:
177.20/45.31	    DPs:
177.20/45.31	     a#(b(b(x1))) -> a#(a(x1))
177.20/45.31	    TRS:
177.20/45.31	     a(x1) -> x1
177.20/45.31	     a(a(x1)) -> b(c(x1))
177.20/45.31	     a(b(b(x1))) -> b(b(a(a(x1))))
177.20/45.31	    Arctic Interpretation Processor:
177.20/45.31	     dimension: 2
177.20/45.31	     usable rules:
177.20/45.31	      a(x1) -> x1
177.20/45.31	      a(a(x1)) -> b(c(x1))
177.20/45.31	      a(b(b(x1))) -> b(b(a(a(x1))))
177.20/45.31	     interpretation:
177.20/45.31	      [a#](x0) = [3  -&]x0 + [0],
177.20/45.31	      
177.20/45.31	                [-& 1 ]     [0]
177.20/45.31	      [b](x0) = [0  -&]x0 + [2],
177.20/45.31	      
177.20/45.31	                [1  -&]     [0]
177.20/45.31	      [c](x0) = [-& -&]x0 + [0],
177.20/45.31	      
177.20/45.31	                [0  -&]     [1]
177.20/45.31	      [a](x0) = [1  0 ]x0 + [0]
177.20/45.31	     orientation:
177.20/45.31	      a#(b(b(x1))) = [4  -&]x1 + [6] >= [3  -&]x1 + [4] = a#(a(x1))
177.20/45.31	      
177.20/45.31	              [0  -&]     [1]           
177.20/45.31	      a(x1) = [1  0 ]x1 + [0] >= x1 = x1
177.20/45.31	      
177.20/45.31	                 [0  -&]     [1]    [-& -&]     [1]           
177.20/45.31	      a(a(x1)) = [1  0 ]x1 + [2] >= [1  -&]x1 + [2] = b(c(x1))
177.20/45.31	      
177.20/45.31	                    [1  -&]     [3]    [1  -&]     [3]                 
177.20/45.31	      a(b(b(x1))) = [2  1 ]x1 + [4] >= [2  1 ]x1 + [3] = b(b(a(a(x1))))
177.20/45.31	     problem:
177.20/45.31	      DPs:
177.20/45.31	       
177.20/45.31	      TRS:
177.20/45.31	       a(x1) -> x1
177.20/45.31	       a(a(x1)) -> b(c(x1))
177.20/45.31	       a(b(b(x1))) -> b(b(a(a(x1))))
177.20/45.31	     Qed
177.38/45.31	EOF