11.12/3.17	YES
11.12/3.19	
11.12/3.19	Problem:
11.12/3.19	 a(x1) -> b(x1)
11.12/3.19	 a(a(x1)) -> a(b(a(x1)))
11.12/3.19	 a(b(x1)) -> b(b(b(x1)))
11.12/3.19	 a(a(a(x1))) -> a(a(b(a(a(x1)))))
11.12/3.19	 a(a(b(x1))) -> a(b(b(a(b(x1)))))
11.12/3.19	 a(b(a(x1))) -> b(a(b(b(a(x1)))))
11.12/3.19	 a(b(b(x1))) -> b(b(b(b(b(x1)))))
11.12/3.19	 b(a(x1)) -> b(b(b(x1)))
11.12/3.19	 a(b(a(x1))) -> a(b(b(a(b(x1)))))
11.12/3.19	 b(a(a(x1))) -> b(a(b(b(a(x1)))))
11.12/3.19	 b(b(a(x1))) -> b(b(b(b(b(x1)))))
11.12/3.19	
11.12/3.19	Proof:
11.12/3.19	 String Reversal Processor:
11.12/3.19	  a(x1) -> b(x1)
11.12/3.19	  a(a(x1)) -> a(b(a(x1)))
11.12/3.19	  b(a(x1)) -> b(b(b(x1)))
11.12/3.19	  a(a(a(x1))) -> a(a(b(a(a(x1)))))
11.12/3.19	  b(a(a(x1))) -> b(a(b(b(a(x1)))))
11.12/3.19	  a(b(a(x1))) -> a(b(b(a(b(x1)))))
11.12/3.19	  b(b(a(x1))) -> b(b(b(b(b(x1)))))
11.12/3.19	  a(b(x1)) -> b(b(b(x1)))
11.12/3.19	  a(b(a(x1))) -> b(a(b(b(a(x1)))))
11.12/3.19	  a(a(b(x1))) -> a(b(b(a(b(x1)))))
11.12/3.19	  a(b(b(x1))) -> b(b(b(b(b(x1)))))
11.12/3.19	  Matrix Interpretation Processor: dim=3
11.12/3.19	   
11.12/3.19	   interpretation:
11.12/3.19	              [1 0 0]  
11.12/3.19	    [b](x0) = [0 0 0]x0
11.12/3.19	              [0 0 0]  ,
11.12/3.19	    
11.12/3.19	              [1 1 0]     [0]
11.12/3.19	    [a](x0) = [0 0 1]x0 + [0]
11.12/3.19	              [1 0 1]     [1]
11.12/3.19	   orientation:
11.12/3.19	            [1 1 0]     [0]    [1 0 0]          
11.12/3.19	    a(x1) = [0 0 1]x1 + [0] >= [0 0 0]x1 = b(x1)
11.12/3.19	            [1 0 1]     [1]    [0 0 0]          
11.12/3.19	    
11.12/3.19	               [1 1 1]     [0]    [1 1 0]     [0]              
11.12/3.19	    a(a(x1)) = [1 0 1]x1 + [1] >= [0 0 0]x1 + [0] = a(b(a(x1)))
11.12/3.19	               [2 1 1]     [2]    [1 1 0]     [1]              
11.12/3.19	    
11.12/3.19	               [1 1 0]      [1 0 0]                
11.12/3.19	    b(a(x1)) = [0 0 0]x1 >= [0 0 0]x1 = b(b(b(x1)))
11.12/3.19	               [0 0 0]      [0 0 0]                
11.12/3.19	    
11.12/3.19	                  [2 1 2]     [1]    [1 1 1]     [0]                    
11.12/3.19	    a(a(a(x1))) = [2 1 1]x1 + [2] >= [1 1 1]x1 + [1] = a(a(b(a(a(x1)))))
11.12/3.19	                  [3 2 2]     [3]    [2 2 2]     [2]                    
11.12/3.19	    
11.12/3.19	                  [1 1 1]      [1 1 0]                      
11.12/3.19	    b(a(a(x1))) = [0 0 0]x1 >= [0 0 0]x1 = b(a(b(b(a(x1)))))
11.12/3.19	                  [0 0 0]      [0 0 0]                      
11.12/3.19	    
11.12/3.19	                  [1 1 0]     [0]    [1 0 0]     [0]                    
11.12/3.19	    a(b(a(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(b(b(a(b(x1)))))
11.12/3.19	                  [1 1 0]     [1]    [1 0 0]     [1]                    
11.12/3.19	    
11.12/3.19	                  [1 1 0]      [1 0 0]                      
11.12/3.19	    b(b(a(x1))) = [0 0 0]x1 >= [0 0 0]x1 = b(b(b(b(b(x1)))))
11.12/3.19	                  [0 0 0]      [0 0 0]                      
11.12/3.19	    
11.12/3.19	               [1 0 0]     [0]    [1 0 0]                
11.12/3.19	    a(b(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(b(b(x1)))
11.12/3.19	               [1 0 0]     [1]    [0 0 0]                
11.12/3.19	    
11.12/3.19	                  [1 1 0]     [0]    [1 1 0]                      
11.12/3.19	    a(b(a(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(a(b(b(a(x1)))))
11.12/3.19	                  [1 1 0]     [1]    [0 0 0]                      
11.12/3.19	    
11.12/3.19	                  [1 0 0]     [0]    [1 0 0]     [0]                    
11.12/3.19	    a(a(b(x1))) = [1 0 0]x1 + [1] >= [0 0 0]x1 + [0] = a(b(b(a(b(x1)))))
11.12/3.19	                  [2 0 0]     [2]    [1 0 0]     [1]                    
11.12/3.19	    
11.12/3.19	                  [1 0 0]     [0]    [1 0 0]                      
11.12/3.19	    a(b(b(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(b(b(b(b(x1)))))
11.12/3.19	                  [1 0 0]     [1]    [0 0 0]                      
11.12/3.19	   problem:
11.12/3.19	    a(x1) -> b(x1)
11.12/3.19	    a(a(x1)) -> a(b(a(x1)))
11.12/3.19	    b(a(x1)) -> b(b(b(x1)))
11.12/3.19	    b(a(a(x1))) -> b(a(b(b(a(x1)))))
11.12/3.19	    a(b(a(x1))) -> a(b(b(a(b(x1)))))
11.12/3.19	    b(b(a(x1))) -> b(b(b(b(b(x1)))))
11.12/3.19	    a(b(x1)) -> b(b(b(x1)))
11.12/3.19	    a(b(a(x1))) -> b(a(b(b(a(x1)))))
11.12/3.19	    a(a(b(x1))) -> a(b(b(a(b(x1)))))
11.12/3.19	    a(b(b(x1))) -> b(b(b(b(b(x1)))))
11.12/3.19	   String Reversal Processor:
11.12/3.19	    a(x1) -> b(x1)
11.12/3.19	    a(a(x1)) -> a(b(a(x1)))
11.12/3.19	    a(b(x1)) -> b(b(b(x1)))
11.12/3.19	    a(a(b(x1))) -> a(b(b(a(b(x1)))))
11.12/3.19	    a(b(a(x1))) -> b(a(b(b(a(x1)))))
11.12/3.19	    a(b(b(x1))) -> b(b(b(b(b(x1)))))
11.12/3.19	    b(a(x1)) -> b(b(b(x1)))
11.12/3.19	    a(b(a(x1))) -> a(b(b(a(b(x1)))))
11.12/3.19	    b(a(a(x1))) -> b(a(b(b(a(x1)))))
11.12/3.19	    b(b(a(x1))) -> b(b(b(b(b(x1)))))
11.12/3.19	    Matrix Interpretation Processor: dim=1
11.12/3.19	     
11.12/3.19	     interpretation:
11.12/3.19	      [b](x0) = x0,
11.12/3.19	      
11.12/3.19	      [a](x0) = 4x0 + 1
11.12/3.19	     orientation:
11.12/3.19	      a(x1) = 4x1 + 1 >= x1 = b(x1)
11.12/3.19	      
11.12/3.19	      a(a(x1)) = 16x1 + 5 >= 16x1 + 5 = a(b(a(x1)))
11.12/3.19	      
11.12/3.19	      a(b(x1)) = 4x1 + 1 >= x1 = b(b(b(x1)))
11.12/3.19	      
11.12/3.19	      a(a(b(x1))) = 16x1 + 5 >= 16x1 + 5 = a(b(b(a(b(x1)))))
11.12/3.19	      
11.12/3.19	      a(b(a(x1))) = 16x1 + 5 >= 16x1 + 5 = b(a(b(b(a(x1)))))
11.12/3.19	      
11.12/3.19	      a(b(b(x1))) = 4x1 + 1 >= x1 = b(b(b(b(b(x1)))))
11.12/3.19	      
11.12/3.19	      b(a(x1)) = 4x1 + 1 >= x1 = b(b(b(x1)))
11.12/3.19	      
11.12/3.19	      a(b(a(x1))) = 16x1 + 5 >= 16x1 + 5 = a(b(b(a(b(x1)))))
11.12/3.19	      
11.12/3.19	      b(a(a(x1))) = 16x1 + 5 >= 16x1 + 5 = b(a(b(b(a(x1)))))
11.12/3.19	      
11.12/3.19	      b(b(a(x1))) = 4x1 + 1 >= x1 = b(b(b(b(b(x1)))))
11.12/3.19	     problem:
11.12/3.19	      a(a(x1)) -> a(b(a(x1)))
11.12/3.19	      a(a(b(x1))) -> a(b(b(a(b(x1)))))
11.12/3.19	      a(b(a(x1))) -> b(a(b(b(a(x1)))))
11.12/3.19	      a(b(a(x1))) -> a(b(b(a(b(x1)))))
11.12/3.19	      b(a(a(x1))) -> b(a(b(b(a(x1)))))
11.12/3.19	     String Reversal Processor:
11.12/3.19	      a(a(x1)) -> a(b(a(x1)))
11.12/3.19	      b(a(a(x1))) -> b(a(b(b(a(x1)))))
11.12/3.19	      a(b(a(x1))) -> a(b(b(a(b(x1)))))
11.12/3.19	      a(b(a(x1))) -> b(a(b(b(a(x1)))))
11.12/3.19	      a(a(b(x1))) -> a(b(b(a(b(x1)))))
11.12/3.19	      Bounds Processor:
11.12/3.19	       bound: 1
11.12/3.19	       enrichment: match
11.12/3.19	       automaton:
11.12/3.19	        final states: {8,5,1}
11.12/3.19	        transitions:
11.12/3.19	         f20() -> 2*
11.12/3.19	         a0(12) -> 8*
11.12/3.19	         a0(2) -> 3*
11.12/3.19	         a0(9) -> 10*
11.12/3.19	         a0(4) -> 1*
11.12/3.19	         a0(6) -> 7*
11.12/3.19	         b0(10) -> 11*
11.12/3.19	         b0(7) -> 5*
11.12/3.19	         b0(2) -> 9*
11.12/3.19	         b0(4) -> 6*
11.12/3.19	         b0(11) -> 12*
11.12/3.19	         b0(3) -> 4*
11.12/3.19	         b1(55) -> 56*
11.12/3.19	         b1(45) -> 46*
11.12/3.19	         b1(37) -> 38*
11.12/3.19	         b1(27) -> 28*
11.12/3.19	         b1(22) -> 23*
11.12/3.19	         b1(29) -> 30*
11.12/3.19	         b1(19) -> 20*
11.12/3.19	         b1(26) -> 27*
11.12/3.19	         b1(21) -> 22*
11.12/3.19	         b1(43) -> 44*
11.12/3.19	         a1(25) -> 26*
11.12/3.19	         a1(20) -> 21*
11.12/3.19	         a1(57) -> 58*
11.12/3.19	         a1(51) -> 52*
11.12/3.19	         a1(28) -> 29*
11.12/3.19	         a1(23) -> 24*
11.12/3.19	         1 -> 3*
11.12/3.19	         2 -> 25,19
11.12/3.19	         4 -> 51,43
11.12/3.19	         5 -> 20,9,4
11.12/3.19	         6 -> 57,55
11.12/3.19	         23 -> 37*
11.12/3.19	         24 -> 21,10,52,26,45,1
11.12/3.19	         30 -> 21,10,52,26,1
11.12/3.19	         38 -> 20*
11.12/3.19	         44 -> 20*
11.12/3.19	         46 -> 27*
11.12/3.19	         52 -> 26*
11.12/3.19	         56 -> 20*
11.12/3.19	         58 -> 26*
11.12/3.19	       problem:
11.12/3.19	        
11.12/3.19	       Qed
11.12/3.19	EOF