8.83/2.56	YES
8.83/2.56	
8.83/2.56	Problem:
8.83/2.56	 f(f(x1)) -> b(b(b(x1)))
8.83/2.56	 a(f(x1)) -> f(a(a(x1)))
8.83/2.56	 b(b(x1)) -> c(c(a(c(x1))))
8.83/2.56	 d(b(x1)) -> d(a(b(x1)))
8.83/2.56	 c(c(x1)) -> d(d(d(x1)))
8.83/2.56	 b(d(x1)) -> d(b(x1))
8.83/2.56	 c(d(d(x1))) -> f(x1)
8.83/2.56	
8.83/2.56	Proof:
8.83/2.56	 Matrix Interpretation Processor: dim=1
8.83/2.56	  
8.83/2.56	  interpretation:
8.83/2.56	   [d](x0) = x0 + 4,
8.83/2.56	   
8.83/2.56	   [c](x0) = x0 + 6,
8.83/2.56	   
8.83/2.56	   [a](x0) = x0,
8.83/2.56	   
8.83/2.56	   [b](x0) = x0 + 9,
8.83/2.56	   
8.83/2.56	   [f](x0) = x0 + 14
8.83/2.56	  orientation:
8.83/2.56	   f(f(x1)) = x1 + 28 >= x1 + 27 = b(b(b(x1)))
8.83/2.56	   
8.83/2.56	   a(f(x1)) = x1 + 14 >= x1 + 14 = f(a(a(x1)))
8.83/2.56	   
8.83/2.56	   b(b(x1)) = x1 + 18 >= x1 + 18 = c(c(a(c(x1))))
8.83/2.56	   
8.83/2.56	   d(b(x1)) = x1 + 13 >= x1 + 13 = d(a(b(x1)))
8.83/2.56	   
8.83/2.56	   c(c(x1)) = x1 + 12 >= x1 + 12 = d(d(d(x1)))
8.83/2.56	   
8.83/2.56	   b(d(x1)) = x1 + 13 >= x1 + 13 = d(b(x1))
8.83/2.56	   
8.83/2.56	   c(d(d(x1))) = x1 + 14 >= x1 + 14 = f(x1)
8.83/2.56	  problem:
8.83/2.56	   a(f(x1)) -> f(a(a(x1)))
8.83/2.56	   b(b(x1)) -> c(c(a(c(x1))))
8.83/2.56	   d(b(x1)) -> d(a(b(x1)))
8.83/2.56	   c(c(x1)) -> d(d(d(x1)))
8.83/2.56	   b(d(x1)) -> d(b(x1))
8.83/2.56	   c(d(d(x1))) -> f(x1)
8.83/2.56	  String Reversal Processor:
8.83/2.56	   f(a(x1)) -> a(a(f(x1)))
8.83/2.56	   b(b(x1)) -> c(a(c(c(x1))))
8.83/2.56	   b(d(x1)) -> b(a(d(x1)))
8.83/2.56	   c(c(x1)) -> d(d(d(x1)))
8.83/2.56	   d(b(x1)) -> b(d(x1))
8.83/2.56	   d(d(c(x1))) -> f(x1)
8.83/2.56	   Matrix Interpretation Processor: dim=1
8.83/2.56	    
8.83/2.56	    interpretation:
8.83/2.56	     [d](x0) = x0 + 4,
8.83/2.56	     
8.83/2.56	     [c](x0) = x0 + 8,
8.83/2.56	     
8.83/2.56	     [a](x0) = x0,
8.83/2.56	     
8.83/2.56	     [b](x0) = x0 + 14,
8.83/2.56	     
8.83/2.56	     [f](x0) = x0 + 4
8.83/2.56	    orientation:
8.83/2.56	     f(a(x1)) = x1 + 4 >= x1 + 4 = a(a(f(x1)))
8.83/2.56	     
8.83/2.56	     b(b(x1)) = x1 + 28 >= x1 + 24 = c(a(c(c(x1))))
8.83/2.56	     
8.83/2.56	     b(d(x1)) = x1 + 18 >= x1 + 18 = b(a(d(x1)))
8.83/2.56	     
8.83/2.56	     c(c(x1)) = x1 + 16 >= x1 + 12 = d(d(d(x1)))
8.83/2.56	     
8.83/2.56	     d(b(x1)) = x1 + 18 >= x1 + 18 = b(d(x1))
8.83/2.56	     
8.83/2.56	     d(d(c(x1))) = x1 + 16 >= x1 + 4 = f(x1)
8.83/2.56	    problem:
8.83/2.56	     f(a(x1)) -> a(a(f(x1)))
8.83/2.56	     b(d(x1)) -> b(a(d(x1)))
8.83/2.56	     d(b(x1)) -> b(d(x1))
8.83/2.56	    Bounds Processor:
8.83/2.56	     bound: 1
8.83/2.56	     enrichment: match
8.83/2.56	     automaton:
8.83/2.56	      final states: {8,5,1}
8.83/2.56	      transitions:
8.83/2.56	       f50() -> 2*
8.83/2.56	       a0(4) -> 1*
8.83/2.56	       a0(6) -> 7*
8.83/2.56	       a0(3) -> 4*
8.83/2.56	       f0(2) -> 3*
8.83/2.56	       b0(7) -> 5*
8.83/2.56	       b0(6) -> 8*
8.83/2.56	       d0(2) -> 6*
8.83/2.56	       b1(15) -> 16*
8.83/2.56	       a1(14) -> 15*
8.83/2.56	       d1(13) -> 14*
8.83/2.56	       1 -> 3*
8.83/2.56	       2 -> 13*
8.83/2.56	       8 -> 14,6
8.83/2.56	       16 -> 8*
8.83/2.56	     problem:
8.83/2.56	      
8.83/2.56	     Qed
8.83/2.56	EOF