7.00/2.08	YES
7.00/2.09	
7.00/2.09	Problem:
7.00/2.09	 a(a(x1)) -> b(b(b(x1)))
7.00/2.09	 a(x1) -> d(c(d(x1)))
7.00/2.09	 b(b(x1)) -> c(c(c(x1)))
7.00/2.09	 c(c(x1)) -> d(d(d(x1)))
7.00/2.09	 c(d(d(x1))) -> a(x1)
7.00/2.09	
7.00/2.09	Proof:
7.00/2.09	 String Reversal Processor:
7.00/2.09	  a(a(x1)) -> b(b(b(x1)))
7.00/2.09	  a(x1) -> d(c(d(x1)))
7.00/2.09	  b(b(x1)) -> c(c(c(x1)))
7.00/2.09	  c(c(x1)) -> d(d(d(x1)))
7.00/2.09	  d(d(c(x1))) -> a(x1)
7.00/2.09	  Matrix Interpretation Processor: dim=1
7.00/2.09	   
7.00/2.09	   interpretation:
7.00/2.09	    [c](x0) = x0 + 6,
7.00/2.09	    
7.00/2.09	    [d](x0) = x0 + 4,
7.00/2.09	    
7.00/2.09	    [b](x0) = x0 + 9,
7.00/2.09	    
7.00/2.09	    [a](x0) = x0 + 14
7.00/2.09	   orientation:
7.00/2.09	    a(a(x1)) = x1 + 28 >= x1 + 27 = b(b(b(x1)))
7.00/2.09	    
7.00/2.09	    a(x1) = x1 + 14 >= x1 + 14 = d(c(d(x1)))
7.00/2.09	    
7.00/2.09	    b(b(x1)) = x1 + 18 >= x1 + 18 = c(c(c(x1)))
7.00/2.09	    
7.00/2.09	    c(c(x1)) = x1 + 12 >= x1 + 12 = d(d(d(x1)))
7.00/2.09	    
7.00/2.09	    d(d(c(x1))) = x1 + 14 >= x1 + 14 = a(x1)
7.00/2.09	   problem:
7.00/2.09	    a(x1) -> d(c(d(x1)))
7.00/2.09	    b(b(x1)) -> c(c(c(x1)))
7.00/2.09	    c(c(x1)) -> d(d(d(x1)))
7.00/2.09	    d(d(c(x1))) -> a(x1)
7.00/2.09	   String Reversal Processor:
7.00/2.09	    a(x1) -> d(c(d(x1)))
7.00/2.09	    b(b(x1)) -> c(c(c(x1)))
7.00/2.09	    c(c(x1)) -> d(d(d(x1)))
7.00/2.09	    c(d(d(x1))) -> a(x1)
7.00/2.09	    Matrix Interpretation Processor: dim=1
7.00/2.09	     
7.00/2.09	     interpretation:
7.00/2.09	      [c](x0) = 2x0,
7.00/2.09	      
7.00/2.09	      [d](x0) = x0,
7.00/2.09	      
7.00/2.09	      [b](x0) = 4x0 + 6,
7.00/2.09	      
7.00/2.09	      [a](x0) = 2x0
7.00/2.09	     orientation:
7.00/2.09	      a(x1) = 2x1 >= 2x1 = d(c(d(x1)))
7.00/2.09	      
7.00/2.09	      b(b(x1)) = 16x1 + 30 >= 8x1 = c(c(c(x1)))
7.00/2.09	      
7.00/2.09	      c(c(x1)) = 4x1 >= x1 = d(d(d(x1)))
7.00/2.09	      
7.00/2.09	      c(d(d(x1))) = 2x1 >= 2x1 = a(x1)
7.00/2.09	     problem:
7.00/2.09	      a(x1) -> d(c(d(x1)))
7.00/2.09	      c(c(x1)) -> d(d(d(x1)))
7.00/2.09	      c(d(d(x1))) -> a(x1)
7.00/2.09	     Bounds Processor:
7.00/2.09	      bound: 1
7.00/2.09	      enrichment: match
7.00/2.09	      automaton:
7.00/2.09	       final states: {7,5,1}
7.00/2.09	       transitions:
7.00/2.09	        a0(2) -> 7*
7.00/2.09	        d1(10) -> 11*
7.00/2.09	        d1(8) -> 9*
7.00/2.09	        c1(9) -> 10*
7.00/2.09	        f40() -> 2*
7.00/2.09	        d0(2) -> 3*
7.00/2.09	        d0(4) -> 1*
7.00/2.09	        d0(6) -> 5*
7.00/2.09	        d0(3) -> 6*
7.00/2.09	        c0(3) -> 4*
7.00/2.09	        2 -> 8*
7.00/2.09	        7 -> 10,4
7.00/2.09	        11 -> 7*
7.00/2.09	      problem:
7.00/2.09	       
7.00/2.09	      Qed
7.00/2.09	EOF