11.45/3.60	YES
12.81/3.61	
12.81/3.61	Problem:
12.81/3.61	 f(x1) -> n(c(n(a(x1))))
12.81/3.61	 c(f(x1)) -> f(n(a(c(x1))))
12.81/3.61	 n(a(x1)) -> c(x1)
12.81/3.61	 c(c(x1)) -> c(x1)
12.81/3.61	 n(s(x1)) -> f(s(s(x1)))
12.81/3.61	 n(f(x1)) -> f(n(x1))
12.81/3.61	
12.81/3.61	Proof:
12.81/3.61	 String Reversal Processor:
12.81/3.61	  f(x1) -> a(n(c(n(x1))))
12.81/3.61	  f(c(x1)) -> c(a(n(f(x1))))
12.81/3.61	  a(n(x1)) -> c(x1)
12.81/3.61	  c(c(x1)) -> c(x1)
12.81/3.61	  s(n(x1)) -> s(s(f(x1)))
12.81/3.61	  f(n(x1)) -> n(f(x1))
12.81/3.61	  Matrix Interpretation Processor: dim=3
12.81/3.61	   
12.81/3.61	   interpretation:
12.81/3.61	              [1 1 0]  
12.81/3.61	    [s](x0) = [0 0 0]x0
12.81/3.61	              [1 1 0]  ,
12.81/3.61	    
12.81/3.61	              [1 0 0]  
12.81/3.61	    [c](x0) = [0 0 0]x0
12.81/3.61	              [0 0 0]  ,
12.81/3.61	    
12.81/3.61	              [1 0 0]     [0]
12.81/3.61	    [n](x0) = [0 1 0]x0 + [1]
12.81/3.61	              [0 0 0]     [0],
12.81/3.61	    
12.81/3.61	              [1 0 0]     [0]
12.81/3.61	    [a](x0) = [0 0 0]x0 + [0]
12.81/3.61	              [0 0 0]     [1],
12.81/3.61	    
12.81/3.61	              [1 0 0]     [0]
12.81/3.61	    [f](x0) = [0 1 0]x0 + [0]
12.81/3.61	              [0 0 0]     [1]
12.81/3.61	   orientation:
12.81/3.61	            [1 0 0]     [0]    [1 0 0]     [0]                 
12.81/3.61	    f(x1) = [0 1 0]x1 + [0] >= [0 0 0]x1 + [0] = a(n(c(n(x1))))
12.81/3.61	            [0 0 0]     [1]    [0 0 0]     [1]                 
12.81/3.61	    
12.81/3.61	               [1 0 0]     [0]    [1 0 0]                   
12.81/3.61	    f(c(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 = c(a(n(f(x1))))
12.81/3.61	               [0 0 0]     [1]    [0 0 0]                   
12.81/3.61	    
12.81/3.61	               [1 0 0]     [0]    [1 0 0]          
12.81/3.61	    a(n(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 = c(x1)
12.81/3.61	               [0 0 0]     [1]    [0 0 0]          
12.81/3.61	    
12.81/3.61	               [1 0 0]      [1 0 0]          
12.81/3.61	    c(c(x1)) = [0 0 0]x1 >= [0 0 0]x1 = c(x1)
12.81/3.61	               [0 0 0]      [0 0 0]          
12.81/3.61	    
12.81/3.61	               [1 1 0]     [1]    [1 1 0]                
12.81/3.61	    s(n(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 = s(s(f(x1)))
12.81/3.61	               [1 1 0]     [1]    [1 1 0]                
12.81/3.61	    
12.81/3.61	               [1 0 0]     [0]    [1 0 0]     [0]           
12.81/3.61	    f(n(x1)) = [0 1 0]x1 + [1] >= [0 1 0]x1 + [1] = n(f(x1))
12.81/3.61	               [0 0 0]     [1]    [0 0 0]     [0]           
12.81/3.61	   problem:
12.81/3.61	    f(x1) -> a(n(c(n(x1))))
12.81/3.61	    f(c(x1)) -> c(a(n(f(x1))))
12.81/3.61	    a(n(x1)) -> c(x1)
12.81/3.61	    c(c(x1)) -> c(x1)
12.81/3.61	    f(n(x1)) -> n(f(x1))
12.81/3.61	   Matrix Interpretation Processor: dim=1
12.81/3.61	    
12.81/3.61	    interpretation:
12.81/3.61	     [c](x0) = x0,
12.81/3.61	     
12.81/3.61	     [n](x0) = x0,
12.81/3.61	     
12.81/3.61	     [a](x0) = x0,
12.81/3.61	     
12.81/3.61	     [f](x0) = x0 + 13
12.81/3.61	    orientation:
12.81/3.61	     f(x1) = x1 + 13 >= x1 = a(n(c(n(x1))))
12.81/3.61	     
12.81/3.61	     f(c(x1)) = x1 + 13 >= x1 + 13 = c(a(n(f(x1))))
12.81/3.61	     
12.81/3.61	     a(n(x1)) = x1 >= x1 = c(x1)
12.81/3.61	     
12.81/3.61	     c(c(x1)) = x1 >= x1 = c(x1)
12.81/3.61	     
12.81/3.61	     f(n(x1)) = x1 + 13 >= x1 + 13 = n(f(x1))
12.81/3.61	    problem:
12.81/3.61	     f(c(x1)) -> c(a(n(f(x1))))
12.81/3.61	     a(n(x1)) -> c(x1)
12.81/3.61	     c(c(x1)) -> c(x1)
12.81/3.61	     f(n(x1)) -> n(f(x1))
12.81/3.61	    Matrix Interpretation Processor: dim=3
12.81/3.61	     
12.81/3.61	     interpretation:
12.81/3.61	                [1 0 0]  
12.81/3.61	      [c](x0) = [0 1 1]x0
12.81/3.61	                [0 0 0]  ,
12.81/3.61	      
12.81/3.61	                [1 0 0]     [0]
12.81/3.61	      [n](x0) = [0 1 1]x0 + [0]
12.81/3.61	                [0 0 0]     [1],
12.81/3.61	      
12.81/3.61	                [1 0 0]  
12.81/3.61	      [a](x0) = [0 1 0]x0
12.81/3.61	                [0 0 0]  ,
12.81/3.61	      
12.81/3.61	                [1 1 1]  
12.81/3.61	      [f](x0) = [0 1 0]x0
12.81/3.61	                [0 0 1]  
12.81/3.61	     orientation:
12.81/3.61	                 [1 1 1]      [1 1 1]                   
12.81/3.61	      f(c(x1)) = [0 1 1]x1 >= [0 1 1]x1 = c(a(n(f(x1))))
12.81/3.61	                 [0 0 0]      [0 0 0]                   
12.81/3.61	      
12.81/3.61	                 [1 0 0]      [1 0 0]          
12.81/3.61	      a(n(x1)) = [0 1 1]x1 >= [0 1 1]x1 = c(x1)
12.81/3.61	                 [0 0 0]      [0 0 0]          
12.81/3.61	      
12.81/3.61	                 [1 0 0]      [1 0 0]          
12.81/3.61	      c(c(x1)) = [0 1 1]x1 >= [0 1 1]x1 = c(x1)
12.81/3.61	                 [0 0 0]      [0 0 0]          
12.81/3.61	      
12.81/3.61	                 [1 1 1]     [1]    [1 1 1]     [0]           
12.81/3.61	      f(n(x1)) = [0 1 1]x1 + [0] >= [0 1 1]x1 + [0] = n(f(x1))
12.81/3.61	                 [0 0 0]     [1]    [0 0 0]     [1]           
12.81/3.61	     problem:
12.81/3.61	      f(c(x1)) -> c(a(n(f(x1))))
12.81/3.61	      a(n(x1)) -> c(x1)
12.81/3.61	      c(c(x1)) -> c(x1)
12.81/3.61	     Matrix Interpretation Processor: dim=3
12.81/3.61	      
12.81/3.61	      interpretation:
12.81/3.61	                 [1 0 1]     [0]
12.81/3.61	       [c](x0) = [0 1 0]x0 + [1]
12.81/3.61	                 [0 0 0]     [1],
12.81/3.61	       
12.81/3.61	                 [1 0 1]  
12.81/3.61	       [n](x0) = [0 0 0]x0
12.81/3.61	                 [0 1 0]  ,
12.81/3.61	       
12.81/3.61	                 [1 0 0]     [0]
12.81/3.61	       [a](x0) = [0 0 1]x0 + [1]
12.81/3.61	                 [0 0 0]     [1],
12.81/3.61	       
12.81/3.61	                 [1 1 0]  
12.81/3.61	       [f](x0) = [1 1 1]x0
12.81/3.61	                 [0 0 1]  
12.81/3.61	      orientation:
12.81/3.61	                  [1 1 1]     [1]    [1 1 1]     [1]                 
12.81/3.61	       f(c(x1)) = [1 1 1]x1 + [2] >= [1 1 1]x1 + [2] = c(a(n(f(x1))))
12.81/3.61	                  [0 0 0]     [1]    [0 0 0]     [1]                 
12.81/3.61	       
12.81/3.61	                  [1 0 1]     [0]    [1 0 1]     [0]        
12.81/3.61	       a(n(x1)) = [0 1 0]x1 + [1] >= [0 1 0]x1 + [1] = c(x1)
12.81/3.61	                  [0 0 0]     [1]    [0 0 0]     [1]        
12.81/3.61	       
12.81/3.61	                  [1 0 1]     [1]    [1 0 1]     [0]        
12.81/3.61	       c(c(x1)) = [0 1 0]x1 + [2] >= [0 1 0]x1 + [1] = c(x1)
12.81/3.61	                  [0 0 0]     [1]    [0 0 0]     [1]        
12.81/3.61	      problem:
12.81/3.61	       f(c(x1)) -> c(a(n(f(x1))))
12.81/3.61	       a(n(x1)) -> c(x1)
12.81/3.61	      Bounds Processor:
12.81/3.61	       bound: 1
12.81/3.61	       enrichment: match
12.81/3.61	       automaton:
12.81/3.61	        final states: {6,1}
12.81/3.61	        transitions:
12.81/3.61	         f0(2) -> 3*
12.81/3.61	         c1(7) -> 8*
12.81/3.61	         f50() -> 2*
12.81/3.61	         c0(5) -> 1*
12.81/3.61	         c0(2) -> 6*
12.81/3.61	         a0(4) -> 5*
12.81/3.61	         n0(3) -> 4*
12.81/3.61	         1 -> 3,7
12.81/3.61	         3 -> 7*
12.81/3.61	         8 -> 5*
12.81/3.61	       problem:
12.81/3.61	        
12.81/3.61	       Qed
12.81/3.62	EOF