30.07/8.07	YES
30.33/8.07	
30.33/8.07	Problem:
30.33/8.07	 strict:
30.33/8.07	  a(b(b(x1))) -> c(b(a(x1)))
30.33/8.07	  a(a(c(x1))) -> b(c(a(x1)))
30.33/8.07	  a(a(b(x1))) -> a(c(b(x1)))
30.33/8.07	 weak:
30.33/8.07	  b(a(a(x1))) -> c(a(a(x1)))
30.33/8.07	  c(b(b(x1))) -> b(a(a(x1)))
30.33/8.07	  c(b(a(x1))) -> b(c(c(x1)))
30.33/8.07	
30.33/8.07	Proof:
30.33/8.07	 String Reversal Processor:
30.33/8.07	  strict:
30.33/8.07	   b(b(a(x1))) -> a(b(c(x1)))
30.33/8.07	   c(a(a(x1))) -> a(c(b(x1)))
30.33/8.07	   b(a(a(x1))) -> b(c(a(x1)))
30.33/8.07	  weak:
30.33/8.07	   a(a(b(x1))) -> a(a(c(x1)))
30.33/8.07	   b(b(c(x1))) -> a(a(b(x1)))
30.33/8.07	   a(b(c(x1))) -> c(c(b(x1)))
30.33/8.07	  Arctic Interpretation Processor:
30.33/8.07	   dimension: 2
30.33/8.07	   interpretation:
30.33/8.07	              [0  0 ]  
30.33/8.07	    [c](x0) = [-& -&]x0,
30.33/8.07	    
30.33/8.07	              [0  4 ]  
30.33/8.07	    [a](x0) = [-& -&]x0,
30.33/8.07	    
30.33/8.07	              [0 4]  
30.33/8.07	    [b](x0) = [0 0]x0
30.33/8.07	   orientation:
30.33/8.07	                  [4 8]      [4  4 ]                
30.33/8.07	    b(b(a(x1))) = [0 4]x1 >= [-& -&]x1 = a(b(c(x1)))
30.33/8.07	    
30.33/8.07	                  [0  4 ]      [0  4 ]                
30.33/8.07	    c(a(a(x1))) = [-& -&]x1 >= [-& -&]x1 = a(c(b(x1)))
30.33/8.07	    
30.33/8.07	                  [0 4]      [0 4]                
30.33/8.07	    b(a(a(x1))) = [0 4]x1 >= [0 4]x1 = b(c(a(x1)))
30.33/8.07	    
30.33/8.07	                  [4  4 ]      [0  0 ]                
30.33/8.07	    a(a(b(x1))) = [-& -&]x1 >= [-& -&]x1 = a(a(c(x1)))
30.33/8.07	    
30.33/8.07	                  [4 4]      [4  4 ]                
30.33/8.07	    b(b(c(x1))) = [0 0]x1 >= [-& -&]x1 = a(a(b(x1)))
30.33/8.07	    
30.33/8.07	                  [4  4 ]      [0  4 ]                
30.33/8.07	    a(b(c(x1))) = [-& -&]x1 >= [-& -&]x1 = c(c(b(x1)))
30.33/8.07	   problem:
30.33/8.07	    strict:
30.33/8.07	     b(b(a(x1))) -> a(b(c(x1)))
30.33/8.07	     c(a(a(x1))) -> a(c(b(x1)))
30.33/8.07	     b(a(a(x1))) -> b(c(a(x1)))
30.33/8.07	    weak:
30.33/8.07	     b(b(c(x1))) -> a(a(b(x1)))
30.33/8.07	     a(b(c(x1))) -> c(c(b(x1)))
30.33/8.07	   RT Transformation Processor:
30.33/8.07	    b(b(a(x1))) -> a(b(c(x1)))
30.33/8.07	    c(a(a(x1))) -> a(c(b(x1)))
30.33/8.07	    b(a(a(x1))) -> b(c(a(x1)))
30.33/8.07	    b(b(c(x1))) -> a(a(b(x1)))
30.33/8.07	    a(b(c(x1))) -> c(c(b(x1)))
30.33/8.07	    Matrix Interpretation Processor: dim=1
30.33/8.07	     
30.33/8.07	     interpretation:
30.33/8.07	      [c](x0) = 2x0 + 3,
30.33/8.07	      
30.33/8.07	      [a](x0) = 2x0 + 4,
30.33/8.07	      
30.33/8.07	      [b](x0) = 2x0
30.33/8.07	     orientation:
30.33/8.07	      b(b(a(x1))) = 8x1 + 16 >= 8x1 + 16 = a(b(c(x1)))
30.33/8.07	      
30.33/8.07	      c(a(a(x1))) = 8x1 + 27 >= 8x1 + 10 = a(c(b(x1)))
30.33/8.07	      
30.33/8.07	      b(a(a(x1))) = 8x1 + 24 >= 8x1 + 22 = b(c(a(x1)))
30.33/8.07	      
30.33/8.07	      b(b(c(x1))) = 8x1 + 12 >= 8x1 + 12 = a(a(b(x1)))
30.33/8.07	      
30.33/8.07	      a(b(c(x1))) = 8x1 + 16 >= 8x1 + 9 = c(c(b(x1)))
30.33/8.07	     problem:
30.33/8.07	      b(b(a(x1))) -> a(b(c(x1)))
30.33/8.07	      b(b(c(x1))) -> a(a(b(x1)))
30.33/8.07	     Matrix Interpretation Processor: dim=3
30.33/8.07	      
30.33/8.07	      interpretation:
30.33/8.07	                 [1 1 0]  
30.33/8.07	       [c](x0) = [0 0 0]x0
30.33/8.07	                 [0 0 0]  ,
30.33/8.07	       
30.33/8.07	                 [1 0 0]  
30.33/8.07	       [a](x0) = [0 1 0]x0
30.33/8.07	                 [0 0 0]  ,
30.33/8.07	       
30.33/8.07	                 [1 1 0]     [0]
30.33/8.07	       [b](x0) = [0 0 0]x0 + [1]
30.33/8.07	                 [0 0 0]     [1]
30.33/8.07	      orientation:
30.33/8.07	                     [1 1 0]     [1]    [1 1 0]     [0]              
30.33/8.07	       b(b(a(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(c(x1)))
30.33/8.07	                     [0 0 0]     [1]    [0 0 0]     [0]              
30.33/8.07	       
30.33/8.07	                     [1 1 0]     [1]    [1 1 0]     [0]              
30.33/8.07	       b(b(c(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(b(x1)))
30.33/8.07	                     [0 0 0]     [1]    [0 0 0]     [0]              
30.33/8.07	      problem:
30.33/8.07	       
30.33/8.07	      Qed
30.33/8.08	EOF