9.90/2.82	YES
9.90/2.82	
9.90/2.82	Problem:
9.90/2.82	 a(b(x1)) -> b(d(x1))
9.90/2.82	 a(c(x1)) -> d(d(d(x1)))
9.90/2.82	 b(d(x1)) -> a(c(b(x1)))
9.90/2.82	 c(f(x1)) -> d(d(c(x1)))
9.90/2.82	 d(d(x1)) -> f(x1)
9.90/2.82	 f(f(x1)) -> a(x1)
9.90/2.82	
9.90/2.82	Proof:
9.90/2.82	 Matrix Interpretation Processor: dim=1
9.90/2.82	  
9.90/2.82	  interpretation:
9.90/2.82	   [f](x0) = x0 + 2,
9.90/2.82	   
9.90/2.82	   [c](x0) = x0,
9.90/2.82	   
9.90/2.82	   [d](x0) = x0 + 1,
9.90/2.82	   
9.90/2.82	   [a](x0) = x0 + 3,
9.90/2.82	   
9.90/2.82	   [b](x0) = 3x0
9.90/2.82	  orientation:
9.90/2.82	   a(b(x1)) = 3x1 + 3 >= 3x1 + 3 = b(d(x1))
9.90/2.82	   
9.90/2.82	   a(c(x1)) = x1 + 3 >= x1 + 3 = d(d(d(x1)))
9.90/2.82	   
9.90/2.82	   b(d(x1)) = 3x1 + 3 >= 3x1 + 3 = a(c(b(x1)))
9.90/2.82	   
9.90/2.82	   c(f(x1)) = x1 + 2 >= x1 + 2 = d(d(c(x1)))
9.90/2.82	   
9.90/2.82	   d(d(x1)) = x1 + 2 >= x1 + 2 = f(x1)
9.90/2.82	   
9.90/2.82	   f(f(x1)) = x1 + 4 >= x1 + 3 = a(x1)
9.90/2.82	  problem:
9.90/2.82	   a(b(x1)) -> b(d(x1))
9.90/2.82	   a(c(x1)) -> d(d(d(x1)))
9.90/2.82	   b(d(x1)) -> a(c(b(x1)))
9.90/2.82	   c(f(x1)) -> d(d(c(x1)))
9.90/2.82	   d(d(x1)) -> f(x1)
9.90/2.82	  String Reversal Processor:
9.90/2.82	   b(a(x1)) -> d(b(x1))
9.90/2.82	   c(a(x1)) -> d(d(d(x1)))
9.90/2.82	   d(b(x1)) -> b(c(a(x1)))
9.90/2.82	   f(c(x1)) -> c(d(d(x1)))
9.90/2.82	   d(d(x1)) -> f(x1)
9.90/2.82	   Matrix Interpretation Processor: dim=2
9.90/2.82	    
9.90/2.82	    interpretation:
9.90/2.82	               [1 0]  
9.90/2.82	     [f](x0) = [0 0]x0,
9.90/2.82	     
9.90/2.82	               [1 0]  
9.90/2.82	     [c](x0) = [0 0]x0,
9.90/2.82	     
9.90/2.82	               [1 0]  
9.90/2.82	     [d](x0) = [0 0]x0,
9.90/2.82	     
9.90/2.82	               [1 0]     [0]
9.90/2.82	     [a](x0) = [2 2]x0 + [2],
9.90/2.82	     
9.90/2.82	               [1 2]  
9.90/2.82	     [b](x0) = [0 1]x0
9.90/2.82	    orientation:
9.90/2.82	                [5 4]     [4]    [1 2]             
9.90/2.82	     b(a(x1)) = [2 2]x1 + [2] >= [0 0]x1 = d(b(x1))
9.90/2.82	     
9.90/2.82	                [1 0]      [1 0]                
9.90/2.82	     c(a(x1)) = [0 0]x1 >= [0 0]x1 = d(d(d(x1)))
9.90/2.82	     
9.90/2.82	                [1 2]      [1 0]                
9.90/2.82	     d(b(x1)) = [0 0]x1 >= [0 0]x1 = b(c(a(x1)))
9.90/2.82	     
9.90/2.82	                [1 0]      [1 0]                
9.90/2.82	     f(c(x1)) = [0 0]x1 >= [0 0]x1 = c(d(d(x1)))
9.90/2.82	     
9.90/2.82	                [1 0]      [1 0]          
9.90/2.82	     d(d(x1)) = [0 0]x1 >= [0 0]x1 = f(x1)
9.90/2.82	    problem:
9.90/2.82	     c(a(x1)) -> d(d(d(x1)))
9.90/2.82	     d(b(x1)) -> b(c(a(x1)))
9.90/2.82	     f(c(x1)) -> c(d(d(x1)))
9.90/2.82	     d(d(x1)) -> f(x1)
9.90/2.82	    Matrix Interpretation Processor: dim=2
9.90/2.82	     
9.90/2.82	     interpretation:
9.90/2.82	                [1 2]  
9.90/2.82	      [f](x0) = [0 1]x0,
9.90/2.82	      
9.90/2.82	                  
9.90/2.82	      [c](x0) = x0,
9.90/2.82	      
9.90/2.82	                [1 1]  
9.90/2.82	      [d](x0) = [0 1]x0,
9.90/2.82	      
9.90/2.82	                [1 3]  
9.90/2.82	      [a](x0) = [0 1]x0,
9.90/2.82	      
9.90/2.82	                [1 2]     [0]
9.90/2.82	      [b](x0) = [0 3]x0 + [2]
9.90/2.82	     orientation:
9.90/2.82	                 [1 3]      [1 3]                
9.90/2.82	      c(a(x1)) = [0 1]x1 >= [0 1]x1 = d(d(d(x1)))
9.90/2.82	      
9.90/2.82	                 [1 5]     [2]    [1 5]     [0]              
9.90/2.82	      d(b(x1)) = [0 3]x1 + [2] >= [0 3]x1 + [2] = b(c(a(x1)))
9.90/2.82	      
9.90/2.82	                 [1 2]      [1 2]                
9.90/2.82	      f(c(x1)) = [0 1]x1 >= [0 1]x1 = c(d(d(x1)))
9.90/2.82	      
9.90/2.82	                 [1 2]      [1 2]          
9.90/2.82	      d(d(x1)) = [0 1]x1 >= [0 1]x1 = f(x1)
9.90/2.82	     problem:
9.90/2.82	      c(a(x1)) -> d(d(d(x1)))
9.90/2.82	      f(c(x1)) -> c(d(d(x1)))
9.90/2.82	      d(d(x1)) -> f(x1)
9.90/2.82	     String Reversal Processor:
9.90/2.82	      a(c(x1)) -> d(d(d(x1)))
9.90/2.82	      c(f(x1)) -> d(d(c(x1)))
9.90/2.82	      d(d(x1)) -> f(x1)
9.90/2.82	      Bounds Processor:
9.90/2.82	       bound: 1
9.90/2.82	       enrichment: match
9.90/2.82	       automaton:
9.90/2.82	        final states: {8,5,1}
9.90/2.82	        transitions:
9.90/2.82	         f50() -> 2*
9.90/2.82	         d0(7) -> 5*
9.90/2.82	         d0(2) -> 3*
9.90/2.82	         d0(4) -> 1*
9.90/2.82	         d0(6) -> 7*
9.90/2.82	         d0(3) -> 4*
9.90/2.82	         c0(2) -> 6*
9.90/2.82	         f0(2) -> 8*
9.90/2.82	         f1(19) -> 20*
9.90/2.82	         f1(21) -> 22*
9.90/2.82	         f1(11) -> 12*
9.90/2.82	         f1(13) -> 14*
9.90/2.82	         2 -> 13*
9.90/2.82	         3 -> 11*
9.90/2.82	         5 -> 6,19
9.90/2.82	         6 -> 19*
9.90/2.82	         7 -> 21*
9.90/2.82	         8 -> 3,11
9.90/2.82	         12 -> 1*
9.90/2.82	         14 -> 4*
9.90/2.82	         20 -> 5*
9.90/2.82	         22 -> 7*
9.90/2.82	       problem:
9.90/2.82	        
9.90/2.82	       Qed
9.90/2.83	EOF