31.59/8.33	YES
31.59/8.33	
31.59/8.33	Problem:
31.59/8.33	 strict:
31.59/8.33	  b(b(c(x1))) -> b(a(a(x1)))
31.59/8.33	  a(c(c(x1))) -> a(a(b(x1)))
31.59/8.33	 weak:
31.59/8.33	  a(c(b(x1))) -> c(a(b(x1)))
31.59/8.33	  a(c(c(x1))) -> c(c(b(x1)))
31.59/8.33	  a(a(a(x1))) -> a(b(a(x1)))
31.59/8.33	  a(b(a(x1))) -> a(b(c(x1)))
31.59/8.33	
31.59/8.33	Proof:
31.59/8.33	 String Reversal Processor:
31.59/8.33	  strict:
31.59/8.33	   c(b(b(x1))) -> a(a(b(x1)))
31.59/8.33	   c(c(a(x1))) -> b(a(a(x1)))
31.59/8.33	  weak:
31.59/8.33	   b(c(a(x1))) -> b(a(c(x1)))
31.59/8.33	   c(c(a(x1))) -> b(c(c(x1)))
31.59/8.33	   a(a(a(x1))) -> a(b(a(x1)))
31.59/8.33	   a(b(a(x1))) -> c(b(a(x1)))
31.59/8.33	  Matrix Interpretation Processor: dim=2
31.59/8.33	   
31.59/8.33	   interpretation:
31.59/8.33	              [1 1]     [0]
31.59/8.33	    [a](x0) = [0 0]x0 + [1],
31.59/8.33	    
31.59/8.33	              [1 0]     [1]
31.59/8.33	    [b](x0) = [0 0]x0 + [0],
31.59/8.33	    
31.59/8.33	              [1 1]     [0]
31.59/8.33	    [c](x0) = [0 0]x0 + [1]
31.59/8.33	   orientation:
31.59/8.33	                  [1 0]     [2]    [1 0]     [2]              
31.59/8.33	    c(b(b(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = a(a(b(x1)))
31.59/8.33	    
31.59/8.33	                  [1 1]     [2]    [1 1]     [2]              
31.59/8.33	    c(c(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [0] = b(a(a(x1)))
31.59/8.33	    
31.59/8.33	                  [1 1]     [2]    [1 1]     [2]              
31.59/8.33	    b(c(a(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = b(a(c(x1)))
31.59/8.33	    
31.59/8.33	                  [1 1]     [2]    [1 1]     [2]              
31.59/8.33	    c(c(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [0] = b(c(c(x1)))
31.59/8.33	    
31.59/8.33	                  [1 1]     [2]    [1 1]     [1]              
31.59/8.33	    a(a(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = a(b(a(x1)))
31.59/8.33	    
31.59/8.33	                  [1 1]     [1]    [1 1]     [1]              
31.59/8.33	    a(b(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = c(b(a(x1)))
31.59/8.33	   problem:
31.59/8.33	    strict:
31.59/8.33	     c(b(b(x1))) -> a(a(b(x1)))
31.59/8.33	     c(c(a(x1))) -> b(a(a(x1)))
31.59/8.33	    weak:
31.59/8.33	     b(c(a(x1))) -> b(a(c(x1)))
31.59/8.33	     c(c(a(x1))) -> b(c(c(x1)))
31.59/8.33	     a(b(a(x1))) -> c(b(a(x1)))
31.59/8.33	   Arctic Interpretation Processor:
31.59/8.33	    dimension: 2
31.59/8.33	    interpretation:
31.59/8.33	               [0 0]  
31.59/8.33	     [a](x0) = [0 0]x0,
31.59/8.33	     
31.59/8.33	               [0  0 ]  
31.59/8.33	     [b](x0) = [-& -&]x0,
31.59/8.33	     
31.59/8.33	               [0  4 ]  
31.59/8.33	     [c](x0) = [0  -&]x0
31.59/8.33	    orientation:
31.59/8.33	                   [0 0]      [0 0]                
31.59/8.33	     c(b(b(x1))) = [0 0]x1 >= [0 0]x1 = a(a(b(x1)))
31.59/8.33	     
31.59/8.33	                   [4 4]      [0  0 ]                
31.59/8.33	     c(c(a(x1))) = [4 4]x1 >= [-& -&]x1 = b(a(a(x1)))
31.59/8.33	     
31.59/8.33	                   [4  4 ]      [0  4 ]                
31.59/8.33	     b(c(a(x1))) = [-& -&]x1 >= [-& -&]x1 = b(a(c(x1)))
31.59/8.33	     
31.59/8.33	                   [4 4]      [4  4 ]                
31.59/8.33	     c(c(a(x1))) = [4 4]x1 >= [-& -&]x1 = b(c(c(x1)))
31.59/8.33	     
31.59/8.33	                   [0 0]      [0 0]                
31.59/8.33	     a(b(a(x1))) = [0 0]x1 >= [0 0]x1 = c(b(a(x1)))
31.59/8.33	    problem:
31.59/8.33	     strict:
31.59/8.33	      c(b(b(x1))) -> a(a(b(x1)))
31.59/8.33	     weak:
31.59/8.33	      b(c(a(x1))) -> b(a(c(x1)))
31.59/8.33	      c(c(a(x1))) -> b(c(c(x1)))
31.59/8.33	      a(b(a(x1))) -> c(b(a(x1)))
31.59/8.33	    RT Transformation Processor:
31.59/8.33	     c(b(b(x1))) -> a(a(b(x1)))
31.59/8.33	     b(c(a(x1))) -> b(a(c(x1)))
31.59/8.33	     c(c(a(x1))) -> b(c(c(x1)))
31.59/8.33	     a(b(a(x1))) -> c(b(a(x1)))
31.59/8.33	     Matrix Interpretation Processor: dim=1
31.59/8.33	      
31.59/8.33	      interpretation:
31.59/8.33	       [a](x0) = 2x0 + 1,
31.59/8.33	       
31.59/8.33	       [b](x0) = 2x0 + 2,
31.59/8.33	       
31.59/8.33	       [c](x0) = 2x0
31.59/8.33	      orientation:
31.59/8.33	       c(b(b(x1))) = 8x1 + 12 >= 8x1 + 11 = a(a(b(x1)))
31.59/8.33	       
31.59/8.33	       b(c(a(x1))) = 8x1 + 6 >= 8x1 + 4 = b(a(c(x1)))
31.59/8.33	       
31.59/8.33	       c(c(a(x1))) = 8x1 + 4 >= 8x1 + 2 = b(c(c(x1)))
31.59/8.33	       
31.59/8.33	       a(b(a(x1))) = 8x1 + 9 >= 8x1 + 8 = c(b(a(x1)))
31.59/8.33	      problem:
31.59/8.33	       
31.59/8.33	      Qed
31.59/8.34	EOF