4.79/1.82	YES
4.79/1.83	
4.79/1.83	Problem:
4.79/1.83	 a(a(x1)) -> b(x1)
4.79/1.83	 b(a(x1)) -> a(b(x1))
4.79/1.83	 b(b(c(x1))) -> c(a(x1))
4.79/1.83	 b(b(x1)) -> a(a(a(x1)))
4.79/1.83	 c(a(x1)) -> b(a(c(x1)))
4.79/1.83	
4.79/1.83	Proof:
4.79/1.83	 Matrix Interpretation Processor: dim=1
4.79/1.83	  
4.79/1.83	  interpretation:
4.79/1.83	   [c](x0) = 3x0,
4.79/1.83	   
4.79/1.83	   [b](x0) = x0 + 8,
4.79/1.83	   
4.79/1.83	   [a](x0) = x0 + 4
4.79/1.83	  orientation:
4.79/1.83	   a(a(x1)) = x1 + 8 >= x1 + 8 = b(x1)
4.79/1.83	   
4.79/1.83	   b(a(x1)) = x1 + 12 >= x1 + 12 = a(b(x1))
4.79/1.83	   
4.79/1.83	   b(b(c(x1))) = 3x1 + 16 >= 3x1 + 12 = c(a(x1))
4.79/1.83	   
4.79/1.83	   b(b(x1)) = x1 + 16 >= x1 + 12 = a(a(a(x1)))
4.79/1.83	   
4.79/1.83	   c(a(x1)) = 3x1 + 12 >= 3x1 + 12 = b(a(c(x1)))
4.79/1.83	  problem:
4.79/1.83	   a(a(x1)) -> b(x1)
4.79/1.83	   b(a(x1)) -> a(b(x1))
4.79/1.83	   c(a(x1)) -> b(a(c(x1)))
4.79/1.83	  Matrix Interpretation Processor: dim=3
4.79/1.83	   
4.79/1.83	   interpretation:
4.79/1.83	              [1 0 0]     [1]
4.79/1.83	    [c](x0) = [0 0 0]x0 + [0]
4.79/1.83	              [1 0 0]     [1],
4.79/1.83	    
4.79/1.83	              [1 0 0]  
4.79/1.83	    [b](x0) = [0 0 0]x0
4.79/1.83	              [0 0 0]  ,
4.79/1.83	    
4.79/1.83	              [1 1 0]     [1]
4.79/1.83	    [a](x0) = [0 0 0]x0 + [0]
4.79/1.83	              [0 0 0]     [0]
4.79/1.83	   orientation:
4.79/1.83	               [1 1 0]     [2]    [1 0 0]          
4.79/1.83	    a(a(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(x1)
4.79/1.83	               [0 0 0]     [0]    [0 0 0]          
4.79/1.83	    
4.79/1.83	               [1 1 0]     [1]    [1 0 0]     [1]           
4.79/1.83	    b(a(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(b(x1))
4.79/1.83	               [0 0 0]     [0]    [0 0 0]     [0]           
4.79/1.83	    
4.79/1.83	               [1 1 0]     [2]    [1 0 0]     [2]              
4.79/1.83	    c(a(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(a(c(x1)))
4.79/1.83	               [1 1 0]     [2]    [0 0 0]     [0]              
4.79/1.83	   problem:
4.79/1.83	    b(a(x1)) -> a(b(x1))
4.79/1.83	    c(a(x1)) -> b(a(c(x1)))
4.79/1.83	   String Reversal Processor:
4.79/1.83	    a(b(x1)) -> b(a(x1))
4.79/1.83	    a(c(x1)) -> c(a(b(x1)))
4.79/1.83	    Bounds Processor:
4.79/1.83	     bound: 1
4.79/1.83	     enrichment: match
4.79/1.83	     automaton:
4.79/1.83	      final states: {4,1}
4.79/1.83	      transitions:
4.79/1.83	       b1(8) -> 9*
4.79/1.83	       a1(7) -> 8*
4.79/1.83	       f30() -> 2*
4.79/1.83	       b0(2) -> 5*
4.79/1.83	       b0(3) -> 1*
4.79/1.83	       a0(5) -> 6*
4.79/1.83	       a0(2) -> 3*
4.79/1.83	       c0(6) -> 4*
4.79/1.83	       1 -> 8,3
4.79/1.83	       2 -> 7*
4.79/1.83	       4 -> 8,3
4.79/1.83	       9 -> 6*
4.79/1.83	     problem:
4.79/1.83	      
4.79/1.83	     Qed
4.79/1.83	EOF