20.26/5.71	YES
20.26/5.73	
20.26/5.73	Problem:
20.26/5.73	 r1(a(x1)) -> a(a(a(r1(x1))))
20.26/5.73	 r2(a(x1)) -> a(a(a(r2(x1))))
20.26/5.73	 a(l1(x1)) -> l1(a(a(a(x1))))
20.26/5.73	 a(a(l2(x1))) -> l2(a(a(x1)))
20.26/5.73	 r1(b(x1)) -> l1(b(x1))
20.26/5.73	 r2(b(x1)) -> l2(a(b(x1)))
20.26/5.73	 b(l1(x1)) -> b(r2(x1))
20.26/5.73	 b(l2(x1)) -> b(r1(x1))
20.26/5.73	 a(a(x1)) -> x1
20.26/5.73	
20.26/5.73	Proof:
20.26/5.73	 String Reversal Processor:
20.26/5.73	  a(r1(x1)) -> r1(a(a(a(x1))))
20.26/5.73	  a(r2(x1)) -> r2(a(a(a(x1))))
20.26/5.73	  l1(a(x1)) -> a(a(a(l1(x1))))
20.26/5.73	  l2(a(a(x1))) -> a(a(l2(x1)))
20.26/5.73	  b(r1(x1)) -> b(l1(x1))
20.26/5.73	  b(r2(x1)) -> b(a(l2(x1)))
20.26/5.73	  l1(b(x1)) -> r2(b(x1))
20.26/5.73	  l2(b(x1)) -> r1(b(x1))
20.26/5.73	  a(a(x1)) -> x1
20.26/5.73	  Matrix Interpretation Processor: dim=3
20.26/5.73	   
20.26/5.73	   interpretation:
20.26/5.73	              [1 1 0]     [0]
20.26/5.73	    [b](x0) = [1 1 0]x0 + [1]
20.26/5.73	              [0 0 0]     [0],
20.26/5.73	    
20.26/5.73	               [1 1 0]  
20.26/5.73	    [l2](x0) = [1 1 0]x0
20.26/5.73	               [0 0 0]  ,
20.26/5.73	    
20.26/5.73	                 
20.26/5.73	    [l1](x0) = x0
20.26/5.73	                 ,
20.26/5.73	    
20.26/5.73	                 
20.26/5.73	    [r2](x0) = x0
20.26/5.73	                 ,
20.26/5.73	    
20.26/5.73	                 
20.26/5.73	    [r1](x0) = x0
20.26/5.73	                 ,
20.26/5.73	    
20.26/5.73	              [1 0 0]  
20.26/5.73	    [a](x0) = [0 0 1]x0
20.26/5.73	              [0 1 0]  
20.26/5.73	   orientation:
20.26/5.73	                [1 0 0]      [1 0 0]                    
20.26/5.73	    a(r1(x1)) = [0 0 1]x1 >= [0 0 1]x1 = r1(a(a(a(x1))))
20.26/5.73	                [0 1 0]      [0 1 0]                    
20.26/5.73	    
20.26/5.73	                [1 0 0]      [1 0 0]                    
20.26/5.73	    a(r2(x1)) = [0 0 1]x1 >= [0 0 1]x1 = r2(a(a(a(x1))))
20.26/5.73	                [0 1 0]      [0 1 0]                    
20.26/5.73	    
20.26/5.73	                [1 0 0]      [1 0 0]                    
20.26/5.73	    l1(a(x1)) = [0 0 1]x1 >= [0 0 1]x1 = a(a(a(l1(x1))))
20.26/5.73	                [0 1 0]      [0 1 0]                    
20.26/5.73	    
20.26/5.73	                   [1 1 0]      [1 1 0]                 
20.26/5.73	    l2(a(a(x1))) = [1 1 0]x1 >= [1 1 0]x1 = a(a(l2(x1)))
20.26/5.73	                   [0 0 0]      [0 0 0]                 
20.26/5.73	    
20.26/5.73	                [1 1 0]     [0]    [1 1 0]     [0]            
20.26/5.73	    b(r1(x1)) = [1 1 0]x1 + [1] >= [1 1 0]x1 + [1] = b(l1(x1))
20.26/5.73	                [0 0 0]     [0]    [0 0 0]     [0]            
20.26/5.73	    
20.26/5.73	                [1 1 0]     [0]    [1 1 0]     [0]               
20.26/5.73	    b(r2(x1)) = [1 1 0]x1 + [1] >= [1 1 0]x1 + [1] = b(a(l2(x1)))
20.26/5.73	                [0 0 0]     [0]    [0 0 0]     [0]               
20.26/5.73	    
20.26/5.73	                [1 1 0]     [0]    [1 1 0]     [0]            
20.26/5.73	    l1(b(x1)) = [1 1 0]x1 + [1] >= [1 1 0]x1 + [1] = r2(b(x1))
20.26/5.73	                [0 0 0]     [0]    [0 0 0]     [0]            
20.26/5.73	    
20.26/5.73	                [2 2 0]     [1]    [1 1 0]     [0]            
20.26/5.73	    l2(b(x1)) = [2 2 0]x1 + [1] >= [1 1 0]x1 + [1] = r1(b(x1))
20.26/5.73	                [0 0 0]     [0]    [0 0 0]     [0]            
20.26/5.73	    
20.26/5.73	                            
20.26/5.73	    a(a(x1)) = x1 >= x1 = x1
20.26/5.73	                            
20.26/5.73	   problem:
20.26/5.73	    a(r1(x1)) -> r1(a(a(a(x1))))
20.26/5.73	    a(r2(x1)) -> r2(a(a(a(x1))))
20.26/5.73	    l1(a(x1)) -> a(a(a(l1(x1))))
20.26/5.73	    l2(a(a(x1))) -> a(a(l2(x1)))
20.26/5.73	    b(r1(x1)) -> b(l1(x1))
20.26/5.73	    b(r2(x1)) -> b(a(l2(x1)))
20.26/5.73	    l1(b(x1)) -> r2(b(x1))
20.26/5.73	    a(a(x1)) -> x1
20.26/5.73	   Matrix Interpretation Processor: dim=1
20.26/5.73	    
20.26/5.73	    interpretation:
20.26/5.73	     [b](x0) = 8x0 + 11,
20.26/5.73	     
20.26/5.73	     [l2](x0) = x0,
20.26/5.73	     
20.26/5.73	     [l1](x0) = x0 + 1,
20.26/5.73	     
20.26/5.73	     [r2](x0) = x0 + 1,
20.26/5.73	     
20.26/5.73	     [r1](x0) = 2x0 + 2,
20.26/5.73	     
20.26/5.73	     [a](x0) = x0
20.26/5.73	    orientation:
20.26/5.73	     a(r1(x1)) = 2x1 + 2 >= 2x1 + 2 = r1(a(a(a(x1))))
20.26/5.73	     
20.26/5.73	     a(r2(x1)) = x1 + 1 >= x1 + 1 = r2(a(a(a(x1))))
20.26/5.73	     
20.26/5.73	     l1(a(x1)) = x1 + 1 >= x1 + 1 = a(a(a(l1(x1))))
20.26/5.73	     
20.26/5.73	     l2(a(a(x1))) = x1 >= x1 = a(a(l2(x1)))
20.26/5.73	     
20.26/5.73	     b(r1(x1)) = 16x1 + 27 >= 8x1 + 19 = b(l1(x1))
20.26/5.73	     
20.26/5.73	     b(r2(x1)) = 8x1 + 19 >= 8x1 + 11 = b(a(l2(x1)))
20.26/5.73	     
20.26/5.73	     l1(b(x1)) = 8x1 + 12 >= 8x1 + 12 = r2(b(x1))
20.26/5.73	     
20.26/5.73	     a(a(x1)) = x1 >= x1 = x1
20.26/5.73	    problem:
20.26/5.73	     a(r1(x1)) -> r1(a(a(a(x1))))
20.26/5.73	     a(r2(x1)) -> r2(a(a(a(x1))))
20.26/5.73	     l1(a(x1)) -> a(a(a(l1(x1))))
20.26/5.73	     l2(a(a(x1))) -> a(a(l2(x1)))
20.26/5.73	     l1(b(x1)) -> r2(b(x1))
20.26/5.73	     a(a(x1)) -> x1
20.26/5.73	    Matrix Interpretation Processor: dim=1
20.26/5.73	     
20.26/5.73	     interpretation:
20.26/5.73	      [b](x0) = x0,
20.26/5.73	      
20.26/5.73	      [l2](x0) = 8x0 + 8,
20.26/5.73	      
20.26/5.73	      [l1](x0) = 8x0 + 4,
20.26/5.73	      
20.26/5.73	      [r2](x0) = 8x0,
20.26/5.73	      
20.26/5.73	      [r1](x0) = 14x0 + 2,
20.26/5.73	      
20.26/5.73	      [a](x0) = x0
20.26/5.73	     orientation:
20.26/5.73	      a(r1(x1)) = 14x1 + 2 >= 14x1 + 2 = r1(a(a(a(x1))))
20.26/5.73	      
20.26/5.73	      a(r2(x1)) = 8x1 >= 8x1 = r2(a(a(a(x1))))
20.26/5.73	      
20.26/5.73	      l1(a(x1)) = 8x1 + 4 >= 8x1 + 4 = a(a(a(l1(x1))))
20.26/5.73	      
20.26/5.73	      l2(a(a(x1))) = 8x1 + 8 >= 8x1 + 8 = a(a(l2(x1)))
20.26/5.73	      
20.26/5.73	      l1(b(x1)) = 8x1 + 4 >= 8x1 = r2(b(x1))
20.26/5.73	      
20.26/5.73	      a(a(x1)) = x1 >= x1 = x1
20.26/5.73	     problem:
20.26/5.73	      a(r1(x1)) -> r1(a(a(a(x1))))
20.26/5.73	      a(r2(x1)) -> r2(a(a(a(x1))))
20.26/5.73	      l1(a(x1)) -> a(a(a(l1(x1))))
20.26/5.73	      l2(a(a(x1))) -> a(a(l2(x1)))
20.26/5.73	      a(a(x1)) -> x1
20.26/5.73	     Matrix Interpretation Processor: dim=2
20.26/5.73	      
20.26/5.73	      interpretation:
20.26/5.73	                  [2 2]     [1]
20.26/5.73	       [l2](x0) = [0 3]x0 + [0],
20.26/5.73	       
20.26/5.73	                  [1 0]     [0]
20.26/5.73	       [l1](x0) = [0 3]x0 + [3],
20.26/5.73	       
20.26/5.73	                  [1 0]     [3]
20.26/5.73	       [r2](x0) = [0 0]x0 + [3],
20.26/5.73	       
20.26/5.73	                  [2 0]  
20.26/5.73	       [r1](x0) = [0 0]x0,
20.26/5.73	       
20.26/5.73	                      [0]
20.26/5.73	       [a](x0) = x0 + [1]
20.26/5.73	      orientation:
20.26/5.73	                   [2 0]     [0]    [2 0]                    
20.26/5.73	       a(r1(x1)) = [0 0]x1 + [1] >= [0 0]x1 = r1(a(a(a(x1))))
20.26/5.73	       
20.26/5.73	                   [1 0]     [3]    [1 0]     [3]                  
20.26/5.73	       a(r2(x1)) = [0 0]x1 + [4] >= [0 0]x1 + [3] = r2(a(a(a(x1))))
20.26/5.73	       
20.26/5.73	                   [1 0]     [0]    [1 0]     [0]                  
20.26/5.73	       l1(a(x1)) = [0 3]x1 + [6] >= [0 3]x1 + [6] = a(a(a(l1(x1))))
20.26/5.73	       
20.26/5.73	                      [2 2]     [5]    [2 2]     [1]               
20.26/5.73	       l2(a(a(x1))) = [0 3]x1 + [6] >= [0 3]x1 + [2] = a(a(l2(x1)))
20.26/5.73	       
20.26/5.73	                       [0]           
20.26/5.73	       a(a(x1)) = x1 + [2] >= x1 = x1
20.26/5.73	      problem:
20.26/5.73	       a(r1(x1)) -> r1(a(a(a(x1))))
20.26/5.73	       a(r2(x1)) -> r2(a(a(a(x1))))
20.26/5.73	       l1(a(x1)) -> a(a(a(l1(x1))))
20.26/5.73	       a(a(x1)) -> x1
20.26/5.73	      Matrix Interpretation Processor: dim=2
20.26/5.73	       
20.26/5.73	       interpretation:
20.26/5.73	                   [1 1]     [0]
20.26/5.73	        [l1](x0) = [0 3]x0 + [1],
20.26/5.73	        
20.26/5.73	                   [1 0]     [3]
20.26/5.73	        [r2](x0) = [2 0]x0 + [1],
20.26/5.73	        
20.26/5.73	                   [1 0]     [0]
20.26/5.73	        [r1](x0) = [0 0]x0 + [1],
20.26/5.73	        
20.26/5.73	                       [0]
20.26/5.73	        [a](x0) = x0 + [1]
20.26/5.73	       orientation:
20.26/5.73	                    [1 0]     [0]    [1 0]     [0]                  
20.26/5.73	        a(r1(x1)) = [0 0]x1 + [2] >= [0 0]x1 + [1] = r1(a(a(a(x1))))
20.26/5.73	        
20.26/5.73	                    [1 0]     [3]    [1 0]     [3]                  
20.26/5.73	        a(r2(x1)) = [2 0]x1 + [2] >= [2 0]x1 + [1] = r2(a(a(a(x1))))
20.26/5.73	        
20.26/5.73	                    [1 1]     [1]    [1 1]     [0]                  
20.26/5.73	        l1(a(x1)) = [0 3]x1 + [4] >= [0 3]x1 + [4] = a(a(a(l1(x1))))
20.26/5.73	        
20.26/5.73	                        [0]           
20.26/5.73	        a(a(x1)) = x1 + [2] >= x1 = x1
20.26/5.73	       problem:
20.26/5.73	        a(r1(x1)) -> r1(a(a(a(x1))))
20.26/5.73	        a(r2(x1)) -> r2(a(a(a(x1))))
20.26/5.73	        a(a(x1)) -> x1
20.26/5.73	       KBO Processor:
20.26/5.73	        weight function:
20.26/5.73	         w0 = 1
20.26/5.73	         w(r2) = w(r1) = 1
20.26/5.73	         w(a) = 0
20.26/5.73	        precedence:
20.26/5.73	         a > r2 ~ r1
20.26/5.73	        problem:
20.26/5.73	         
20.26/5.73	        Qed
20.26/5.73	EOF