5.64/1.79	YES
5.64/1.80	
5.64/1.80	Problem:
5.64/1.80	 f(x1) -> n(c(c(x1)))
5.64/1.80	 c(f(x1)) -> f(c(c(x1)))
5.64/1.80	 c(c(x1)) -> c(x1)
5.64/1.80	 n(s(x1)) -> f(s(s(x1)))
5.64/1.80	 n(f(x1)) -> f(n(x1))
5.64/1.80	
5.64/1.80	Proof:
5.64/1.80	 Matrix Interpretation Processor: dim=3
5.64/1.80	  
5.64/1.80	  interpretation:
5.64/1.80	             [1 0 0]     [0]
5.64/1.80	   [s](x0) = [0 0 0]x0 + [1]
5.64/1.80	             [0 1 0]     [1],
5.64/1.80	   
5.64/1.80	             [1 1 0]  
5.64/1.80	   [n](x0) = [0 0 1]x0
5.64/1.80	             [0 1 1]  ,
5.64/1.80	   
5.64/1.80	             [1 0 0]  
5.64/1.80	   [c](x0) = [0 0 0]x0
5.64/1.80	             [0 0 0]  ,
5.64/1.80	   
5.64/1.80	               
5.64/1.80	   [f](x0) = x0
5.64/1.80	               
5.64/1.80	  orientation:
5.64/1.80	                 [1 0 0]                
5.64/1.80	   f(x1) = x1 >= [0 0 0]x1 = n(c(c(x1)))
5.64/1.80	                 [0 0 0]                
5.64/1.80	   
5.64/1.80	              [1 0 0]      [1 0 0]                
5.64/1.80	   c(f(x1)) = [0 0 0]x1 >= [0 0 0]x1 = f(c(c(x1)))
5.64/1.80	              [0 0 0]      [0 0 0]                
5.64/1.80	   
5.64/1.80	              [1 0 0]      [1 0 0]          
5.64/1.80	   c(c(x1)) = [0 0 0]x1 >= [0 0 0]x1 = c(x1)
5.64/1.80	              [0 0 0]      [0 0 0]          
5.64/1.80	   
5.64/1.80	              [1 0 0]     [1]    [1 0 0]     [0]              
5.64/1.80	   n(s(x1)) = [0 1 0]x1 + [1] >= [0 0 0]x1 + [1] = f(s(s(x1)))
5.64/1.80	              [0 1 0]     [2]    [0 0 0]     [2]              
5.64/1.80	   
5.64/1.80	              [1 1 0]      [1 1 0]             
5.64/1.80	   n(f(x1)) = [0 0 1]x1 >= [0 0 1]x1 = f(n(x1))
5.64/1.80	              [0 1 1]      [0 1 1]             
5.64/1.80	  problem:
5.64/1.80	   f(x1) -> n(c(c(x1)))
5.64/1.80	   c(f(x1)) -> f(c(c(x1)))
5.64/1.80	   c(c(x1)) -> c(x1)
5.64/1.80	   n(f(x1)) -> f(n(x1))
5.64/1.80	  Matrix Interpretation Processor: dim=3
5.64/1.80	   
5.64/1.80	   interpretation:
5.64/1.80	              [1 1 0]  
5.64/1.80	    [n](x0) = [1 1 0]x0
5.64/1.80	              [0 0 1]  ,
5.64/1.80	    
5.64/1.80	              [1 0 0]  
5.64/1.80	    [c](x0) = [0 1 0]x0
5.64/1.80	              [0 0 0]  ,
5.64/1.80	    
5.64/1.80	              [1 1 1]     [0]
5.64/1.80	    [f](x0) = [1 1 0]x0 + [1]
5.64/1.80	              [0 0 0]     [0]
5.64/1.80	   orientation:
5.64/1.80	            [1 1 1]     [0]    [1 1 0]                
5.64/1.80	    f(x1) = [1 1 0]x1 + [1] >= [1 1 0]x1 = n(c(c(x1)))
5.64/1.80	            [0 0 0]     [0]    [0 0 0]                
5.64/1.80	    
5.64/1.80	               [1 1 1]     [0]    [1 1 0]     [0]              
5.64/1.80	    c(f(x1)) = [1 1 0]x1 + [1] >= [1 1 0]x1 + [1] = f(c(c(x1)))
5.64/1.80	               [0 0 0]     [0]    [0 0 0]     [0]              
5.64/1.80	    
5.64/1.80	               [1 0 0]      [1 0 0]          
5.64/1.80	    c(c(x1)) = [0 1 0]x1 >= [0 1 0]x1 = c(x1)
5.64/1.80	               [0 0 0]      [0 0 0]          
5.64/1.80	    
5.64/1.80	               [2 2 1]     [1]    [2 2 1]     [0]           
5.64/1.80	    n(f(x1)) = [2 2 1]x1 + [1] >= [2 2 0]x1 + [1] = f(n(x1))
5.64/1.80	               [0 0 0]     [0]    [0 0 0]     [0]           
5.64/1.80	   problem:
5.64/1.80	    f(x1) -> n(c(c(x1)))
5.64/1.80	    c(f(x1)) -> f(c(c(x1)))
5.64/1.80	    c(c(x1)) -> c(x1)
5.64/1.80	   KBO Processor:
5.64/1.80	    weight function:
5.64/1.80	     w0 = 1
5.64/1.80	     w(n) = w(f) = 1
5.64/1.80	     w(c) = 0
5.64/1.80	    precedence:
5.64/1.80	     c > f > n
5.64/1.80	    problem:
5.64/1.80	     
5.64/1.80	    Qed
5.64/1.80	EOF