10.27/2.99	YES
10.27/3.00	
10.27/3.00	Problem:
10.27/3.00	 t(f(x1)) -> t(c(n(x1)))
10.27/3.00	 n(f(x1)) -> f(n(x1))
10.27/3.00	 o(f(x1)) -> f(o(x1))
10.27/3.00	 n(s(x1)) -> f(s(x1))
10.27/3.00	 o(s(x1)) -> f(s(x1))
10.27/3.00	 c(f(x1)) -> f(c(x1))
10.27/3.00	 c(n(x1)) -> n(c(x1))
10.27/3.00	 c(o(x1)) -> o(c(x1))
10.27/3.00	 c(o(x1)) -> o(x1)
10.27/3.00	
10.27/3.00	Proof:
10.27/3.00	 String Reversal Processor:
10.27/3.00	  f(t(x1)) -> n(c(t(x1)))
10.27/3.00	  f(n(x1)) -> n(f(x1))
10.27/3.00	  f(o(x1)) -> o(f(x1))
10.27/3.00	  s(n(x1)) -> s(f(x1))
10.27/3.00	  s(o(x1)) -> s(f(x1))
10.27/3.00	  f(c(x1)) -> c(f(x1))
10.27/3.00	  n(c(x1)) -> c(n(x1))
10.27/3.00	  o(c(x1)) -> c(o(x1))
10.27/3.00	  o(c(x1)) -> o(x1)
10.27/3.00	  Matrix Interpretation Processor: dim=1
10.27/3.00	   
10.27/3.00	   interpretation:
10.27/3.00	    [s](x0) = x0 + 8,
10.27/3.00	    
10.27/3.00	    [o](x0) = 4x0 + 8,
10.27/3.00	    
10.27/3.00	    [c](x0) = x0,
10.27/3.00	    
10.27/3.00	    [n](x0) = 2x0 + 2,
10.27/3.00	    
10.27/3.00	    [t](x0) = 8x0,
10.27/3.00	    
10.27/3.00	    [f](x0) = 2x0 + 2
10.27/3.00	   orientation:
10.27/3.00	    f(t(x1)) = 16x1 + 2 >= 16x1 + 2 = n(c(t(x1)))
10.27/3.00	    
10.27/3.00	    f(n(x1)) = 4x1 + 6 >= 4x1 + 6 = n(f(x1))
10.27/3.00	    
10.27/3.00	    f(o(x1)) = 8x1 + 18 >= 8x1 + 16 = o(f(x1))
10.27/3.00	    
10.27/3.00	    s(n(x1)) = 2x1 + 10 >= 2x1 + 10 = s(f(x1))
10.27/3.00	    
10.27/3.00	    s(o(x1)) = 4x1 + 16 >= 2x1 + 10 = s(f(x1))
10.27/3.00	    
10.27/3.00	    f(c(x1)) = 2x1 + 2 >= 2x1 + 2 = c(f(x1))
10.27/3.00	    
10.27/3.00	    n(c(x1)) = 2x1 + 2 >= 2x1 + 2 = c(n(x1))
10.27/3.00	    
10.27/3.00	    o(c(x1)) = 4x1 + 8 >= 4x1 + 8 = c(o(x1))
10.27/3.00	    
10.27/3.00	    o(c(x1)) = 4x1 + 8 >= 4x1 + 8 = o(x1)
10.27/3.00	   problem:
10.27/3.00	    f(t(x1)) -> n(c(t(x1)))
10.27/3.00	    f(n(x1)) -> n(f(x1))
10.27/3.00	    s(n(x1)) -> s(f(x1))
10.27/3.00	    f(c(x1)) -> c(f(x1))
10.27/3.00	    n(c(x1)) -> c(n(x1))
10.27/3.00	    o(c(x1)) -> c(o(x1))
10.27/3.00	    o(c(x1)) -> o(x1)
10.27/3.00	   String Reversal Processor:
10.27/3.00	    t(f(x1)) -> t(c(n(x1)))
10.27/3.00	    n(f(x1)) -> f(n(x1))
10.27/3.00	    n(s(x1)) -> f(s(x1))
10.27/3.00	    c(f(x1)) -> f(c(x1))
10.27/3.00	    c(n(x1)) -> n(c(x1))
10.27/3.00	    c(o(x1)) -> o(c(x1))
10.27/3.00	    c(o(x1)) -> o(x1)
10.27/3.00	    Matrix Interpretation Processor: dim=3
10.27/3.00	     
10.27/3.00	     interpretation:
10.27/3.00	                [1 0 0]     [0]
10.27/3.00	      [s](x0) = [0 0 0]x0 + [0]
10.27/3.00	                [0 0 0]     [1],
10.27/3.00	      
10.27/3.00	                [1 1 0]  
10.27/3.00	      [o](x0) = [0 0 0]x0
10.27/3.00	                [0 0 0]  ,
10.27/3.00	      
10.27/3.00	                [1 1 0]  
10.27/3.00	      [c](x0) = [0 0 0]x0
10.27/3.00	                [0 0 0]  ,
10.27/3.00	      
10.27/3.00	                [1 0 1]  
10.27/3.00	      [n](x0) = [0 1 0]x0
10.27/3.00	                [0 0 1]  ,
10.27/3.00	      
10.27/3.00	                [1 0 1]     [0]
10.27/3.00	      [t](x0) = [0 0 0]x0 + [0]
10.27/3.00	                [0 0 1]     [1],
10.27/3.00	      
10.27/3.00	                [1 1 0]  
10.27/3.00	      [f](x0) = [0 0 0]x0
10.27/3.00	                [0 0 1]  
10.27/3.00	     orientation:
10.27/3.00	                 [1 1 1]     [0]    [1 1 1]     [0]              
10.27/3.00	      t(f(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = t(c(n(x1)))
10.27/3.00	                 [0 0 1]     [1]    [0 0 0]     [1]              
10.27/3.00	      
10.27/3.00	                 [1 1 1]      [1 1 1]             
10.27/3.00	      n(f(x1)) = [0 0 0]x1 >= [0 0 0]x1 = f(n(x1))
10.27/3.00	                 [0 0 1]      [0 0 1]             
10.27/3.00	      
10.27/3.00	                 [1 0 0]     [1]    [1 0 0]     [0]           
10.27/3.00	      n(s(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = f(s(x1))
10.27/3.00	                 [0 0 0]     [1]    [0 0 0]     [1]           
10.27/3.00	      
10.27/3.00	                 [1 1 0]      [1 1 0]             
10.27/3.00	      c(f(x1)) = [0 0 0]x1 >= [0 0 0]x1 = f(c(x1))
10.27/3.00	                 [0 0 0]      [0 0 0]             
10.27/3.00	      
10.27/3.00	                 [1 1 1]      [1 1 0]             
10.27/3.00	      c(n(x1)) = [0 0 0]x1 >= [0 0 0]x1 = n(c(x1))
10.27/3.00	                 [0 0 0]      [0 0 0]             
10.27/3.00	      
10.27/3.00	                 [1 1 0]      [1 1 0]             
10.27/3.00	      c(o(x1)) = [0 0 0]x1 >= [0 0 0]x1 = o(c(x1))
10.27/3.00	                 [0 0 0]      [0 0 0]             
10.27/3.00	      
10.27/3.00	                 [1 1 0]      [1 1 0]          
10.27/3.00	      c(o(x1)) = [0 0 0]x1 >= [0 0 0]x1 = o(x1)
10.27/3.00	                 [0 0 0]      [0 0 0]          
10.27/3.00	     problem:
10.27/3.00	      t(f(x1)) -> t(c(n(x1)))
10.27/3.00	      n(f(x1)) -> f(n(x1))
10.27/3.00	      c(f(x1)) -> f(c(x1))
10.27/3.00	      c(n(x1)) -> n(c(x1))
10.27/3.00	      c(o(x1)) -> o(c(x1))
10.27/3.00	      c(o(x1)) -> o(x1)
10.27/3.00	     Matrix Interpretation Processor: dim=1
10.27/3.00	      
10.27/3.00	      interpretation:
10.27/3.00	       [o](x0) = x0,
10.27/3.00	       
10.27/3.00	       [c](x0) = x0,
10.27/3.00	       
10.27/3.00	       [n](x0) = x0,
10.27/3.00	       
10.27/3.00	       [t](x0) = 4x0 + 8,
10.27/3.00	       
10.27/3.00	       [f](x0) = 4x0 + 2
10.27/3.00	      orientation:
10.27/3.00	       t(f(x1)) = 16x1 + 16 >= 4x1 + 8 = t(c(n(x1)))
10.27/3.00	       
10.27/3.00	       n(f(x1)) = 4x1 + 2 >= 4x1 + 2 = f(n(x1))
10.27/3.00	       
10.27/3.00	       c(f(x1)) = 4x1 + 2 >= 4x1 + 2 = f(c(x1))
10.27/3.00	       
10.27/3.00	       c(n(x1)) = x1 >= x1 = n(c(x1))
10.27/3.00	       
10.27/3.00	       c(o(x1)) = x1 >= x1 = o(c(x1))
10.27/3.00	       
10.27/3.00	       c(o(x1)) = x1 >= x1 = o(x1)
10.27/3.00	      problem:
10.27/3.00	       n(f(x1)) -> f(n(x1))
10.27/3.00	       c(f(x1)) -> f(c(x1))
10.27/3.00	       c(n(x1)) -> n(c(x1))
10.27/3.00	       c(o(x1)) -> o(c(x1))
10.27/3.00	       c(o(x1)) -> o(x1)
10.27/3.00	      KBO Processor:
10.27/3.00	       weight function:
10.27/3.00	        w0 = 1
10.27/3.00	        w(o) = w(n) = w(f) = 1
10.27/3.00	        w(c) = 0
10.27/3.00	       precedence:
10.27/3.00	        c > n > o ~ f
10.27/3.00	       problem:
10.27/3.00	        
10.27/3.00	       Qed
10.27/3.01	EOF