41.89/11.46	YES
41.89/11.46	
41.89/11.46	Problem:
41.89/11.46	 b(b(x1)) -> b(a(b(x1)))
41.89/11.46	 b(b(a(b(x1)))) -> b(a(b(a(a(b(b(x1)))))))
41.89/11.46	 b(a(b(x1))) -> b(a(a(b(x1))))
41.89/11.46	 b(a(a(b(a(b(x1)))))) -> b(b(x1))
41.89/11.46	
41.89/11.46	Proof:
41.89/11.46	 Matrix Interpretation Processor: dim=3
41.89/11.46	  
41.89/11.46	  interpretation:
41.89/11.46	             [1 0 0]  
41.89/11.46	   [a](x0) = [0 0 1]x0
41.89/11.46	             [0 0 0]  ,
41.89/11.46	   
41.89/11.46	             [1 1 0]     [0]
41.89/11.46	   [b](x0) = [0 0 0]x0 + [1]
41.89/11.46	             [0 0 0]     [1]
41.89/11.46	  orientation:
41.89/11.46	              [1 1 0]     [1]    [1 1 0]     [1]              
41.89/11.46	   b(b(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(b(x1)))
41.89/11.46	              [0 0 0]     [1]    [0 0 0]     [1]              
41.89/11.46	   
41.89/11.46	                    [1 1 0]     [2]    [1 1 0]     [2]                          
41.89/11.46	   b(b(a(b(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(b(a(a(b(b(x1)))))))
41.89/11.46	                    [0 0 0]     [1]    [0 0 0]     [1]                          
41.89/11.46	   
41.89/11.46	                 [1 1 0]     [1]    [1 1 0]     [0]                 
41.89/11.46	   b(a(b(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a(a(b(x1))))
41.89/11.46	                 [0 0 0]     [1]    [0 0 0]     [1]                 
41.89/11.46	   
41.89/11.46	                          [1 1 0]     [1]    [1 1 0]     [1]           
41.89/11.46	   b(a(a(b(a(b(x1)))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b(x1))
41.89/11.46	                          [0 0 0]     [1]    [0 0 0]     [1]           
41.89/11.46	  problem:
41.89/11.46	   b(b(x1)) -> b(a(b(x1)))
41.89/11.46	   b(b(a(b(x1)))) -> b(a(b(a(a(b(b(x1)))))))
41.89/11.46	   b(a(a(b(a(b(x1)))))) -> b(b(x1))
41.89/11.46	  String Reversal Processor:
41.89/11.46	   b(b(x1)) -> b(a(b(x1)))
41.89/11.46	   b(a(b(b(x1)))) -> b(b(a(a(b(a(b(x1)))))))
41.89/11.46	   b(a(b(a(a(b(x1)))))) -> b(b(x1))
41.89/11.46	   Matrix Interpretation Processor: dim=3
41.89/11.46	    
41.89/11.46	    interpretation:
41.89/11.46	               [1 0 0]     [0]
41.89/11.46	     [a](x0) = [0 0 0]x0 + [1]
41.89/11.46	               [0 1 0]     [0],
41.89/11.46	     
41.89/11.46	               [1 0 1]     [0]
41.89/11.46	     [b](x0) = [1 0 1]x0 + [0]
41.89/11.46	               [1 0 1]     [2]
41.89/11.46	    orientation:
41.89/11.46	                [2 0 2]     [2]    [2 0 2]     [0]              
41.89/11.46	     b(b(x1)) = [2 0 2]x1 + [2] >= [2 0 2]x1 + [0] = b(a(b(x1)))
41.89/11.46	                [2 0 2]     [4]    [2 0 2]     [2]              
41.89/11.46	     
41.89/11.46	                      [4 0 4]     [4]    [4 0 4]     [4]                          
41.89/11.46	     b(a(b(b(x1)))) = [4 0 4]x1 + [4] >= [4 0 4]x1 + [4] = b(b(a(a(b(a(b(x1)))))))
41.89/11.46	                      [4 0 4]     [6]    [4 0 4]     [6]                          
41.89/11.46	     
41.89/11.46	                            [2 0 2]     [2]    [2 0 2]     [2]           
41.89/11.46	     b(a(b(a(a(b(x1)))))) = [2 0 2]x1 + [2] >= [2 0 2]x1 + [2] = b(b(x1))
41.89/11.46	                            [2 0 2]     [4]    [2 0 2]     [4]           
41.89/11.46	    problem:
41.89/11.46	     b(a(b(b(x1)))) -> b(b(a(a(b(a(b(x1)))))))
41.89/11.46	     b(a(b(a(a(b(x1)))))) -> b(b(x1))
41.89/11.46	    Bounds Processor:
41.89/11.46	     bound: 2
41.89/11.46	     enrichment: match
41.89/11.46	     automaton:
41.89/11.46	      final states: {3}
41.89/11.46	      transitions:
41.89/11.46	       b1(20) -> 21*
41.89/11.46	       b1(17) -> 18*
41.89/11.46	       b1(12) -> 13*
41.89/11.46	       b1(14) -> 15*
41.89/11.46	       b1(18) -> 19*
41.89/11.46	       a1(35) -> 36*
41.89/11.46	       a1(15) -> 16*
41.89/11.46	       a1(26) -> 27*
41.89/11.46	       a1(16) -> 17*
41.89/11.46	       a1(33) -> 34*
41.89/11.46	       a1(13) -> 14*
41.89/11.46	       b2(75) -> 76*
41.89/11.46	       b2(47) -> 48*
41.89/11.46	       b2(89) -> 90*
41.89/11.46	       b2(69) -> 70*
41.89/11.46	       b2(49) -> 50*
41.89/11.46	       b2(91) -> 92*
41.89/11.46	       b2(61) -> 62*
41.89/11.46	       b2(46) -> 47*
41.89/11.46	       b2(41) -> 42*
41.89/11.46	       b2(73) -> 74*
41.89/11.46	       b2(63) -> 64*
41.89/11.46	       b2(43) -> 44*
41.89/11.46	       b0(3) -> 3*
41.89/11.46	       a2(45) -> 46*
41.89/11.46	       a2(42) -> 43*
41.89/11.46	       a2(44) -> 45*
41.89/11.46	       a0(3) -> 3*
41.89/11.46	       3 -> 12*
41.89/11.46	       12 -> 63*
41.89/11.46	       13 -> 76,64,42,44,73,47,15,20
41.89/11.46	       14 -> 75*
41.89/11.46	       17 -> 61*
41.89/11.46	       18 -> 49,26
41.89/11.46	       19 -> 76,64,42,44,73,47,13,15,35,20,3
41.89/11.46	       20 -> 41*
41.89/11.46	       21 -> 13,15,20,33,3
41.89/11.46	       27 -> 14*
41.89/11.46	       34 -> 14*
41.89/11.46	       36 -> 14*
41.89/11.46	       42 -> 73*
41.89/11.46	       48 -> 76,47,69,44,15
41.89/11.46	       50 -> 42*
41.89/11.46	       62 -> 42*
41.89/11.46	       64 -> 42*
41.89/11.46	       70 -> 89,15
41.89/11.46	       74 -> 76,44,47,91,15
41.89/11.46	       76 -> 47*
41.89/11.46	       90 -> 76,15,44,47
41.89/11.46	       92 -> 47*
41.89/11.46	     problem:
41.89/11.46	      
41.89/11.46	     Qed
41.89/11.47	EOF