7.86/2.46	YES
7.86/2.46	
7.86/2.46	Problem:
7.86/2.46	 strict:
7.86/2.46	  s(a(x)) -> s(b(x))
7.86/2.46	  b(b(x)) -> a(x)
7.86/2.46	 weak:
7.86/2.46	  f(s(x),y) -> f(x,s(y))
7.86/2.46	  s(a(x)) -> a(s(x))
7.86/2.46	  s(b(x)) -> b(s(x))
7.86/2.46	  a(s(x)) -> s(a(x))
7.86/2.46	  b(s(x)) -> s(b(x))
7.86/2.46	
7.86/2.46	Proof:
7.86/2.46	 Matrix Interpretation Processor: dim=2
7.86/2.46	  
7.86/2.46	  interpretation:
7.86/2.46	                 [2 0]     [1 1]     [0]
7.86/2.46	   [f](x0, x1) = [0 0]x0 + [3 0]x1 + [2],
7.86/2.46	   
7.86/2.46	             [1 0]     [1]
7.86/2.46	   [b](x0) = [0 0]x0 + [0],
7.86/2.46	   
7.86/2.46	             [1 0]  
7.86/2.46	   [s](x0) = [0 0]x0,
7.86/2.46	   
7.86/2.46	             [1 0]     [1]
7.86/2.46	   [a](x0) = [0 0]x0 + [0]
7.86/2.46	  orientation:
7.86/2.46	             [1 0]    [1]    [1 0]    [1]          
7.86/2.46	   s(a(x)) = [0 0]x + [0] >= [0 0]x + [0] = s(b(x))
7.86/2.46	   
7.86/2.46	             [1 0]    [2]    [1 0]    [1]       
7.86/2.46	   b(b(x)) = [0 0]x + [0] >= [0 0]x + [0] = a(x)
7.86/2.46	   
7.86/2.46	               [2 0]    [1 1]    [0]    [2 0]    [1 0]    [0]            
7.86/2.46	   f(s(x),y) = [0 0]x + [3 0]y + [2] >= [0 0]x + [3 0]y + [2] = f(x,s(y))
7.86/2.46	   
7.86/2.46	             [1 0]    [1]    [1 0]    [1]          
7.86/2.46	   s(a(x)) = [0 0]x + [0] >= [0 0]x + [0] = a(s(x))
7.86/2.46	   
7.86/2.46	             [1 0]    [1]    [1 0]    [1]          
7.86/2.46	   s(b(x)) = [0 0]x + [0] >= [0 0]x + [0] = b(s(x))
7.86/2.46	   
7.86/2.46	             [1 0]    [1]    [1 0]    [1]          
7.86/2.46	   a(s(x)) = [0 0]x + [0] >= [0 0]x + [0] = s(a(x))
7.86/2.46	   
7.86/2.46	             [1 0]    [1]    [1 0]    [1]          
7.86/2.46	   b(s(x)) = [0 0]x + [0] >= [0 0]x + [0] = s(b(x))
7.86/2.46	  problem:
7.86/2.46	   strict:
7.86/2.46	    s(a(x)) -> s(b(x))
7.86/2.46	   weak:
7.86/2.46	    f(s(x),y) -> f(x,s(y))
7.86/2.46	    s(a(x)) -> a(s(x))
7.86/2.46	    s(b(x)) -> b(s(x))
7.86/2.46	    a(s(x)) -> s(a(x))
7.86/2.46	    b(s(x)) -> s(b(x))
7.86/2.46	  Matrix Interpretation Processor: dim=2
7.86/2.46	   
7.86/2.46	   interpretation:
7.86/2.46	                  [2 2]     [2 1]     [1]
7.86/2.46	    [f](x0, x1) = [0 0]x0 + [0 0]x1 + [2],
7.86/2.46	    
7.86/2.46	                
7.86/2.46	    [b](x0) = x0,
7.86/2.46	    
7.86/2.46	                   [0]
7.86/2.46	    [s](x0) = x0 + [1],
7.86/2.46	    
7.86/2.46	                   [0]
7.86/2.46	    [a](x0) = x0 + [2]
7.86/2.46	   orientation:
7.86/2.46	                  [0]        [0]          
7.86/2.46	    s(a(x)) = x + [3] >= x + [1] = s(b(x))
7.86/2.46	    
7.86/2.46	                [2 2]    [2 1]    [3]    [2 2]    [2 1]    [2]            
7.86/2.46	    f(s(x),y) = [0 0]x + [0 0]y + [2] >= [0 0]x + [0 0]y + [2] = f(x,s(y))
7.86/2.46	    
7.86/2.46	                  [0]        [0]          
7.86/2.46	    s(a(x)) = x + [3] >= x + [3] = a(s(x))
7.86/2.46	    
7.86/2.46	                  [0]        [0]          
7.86/2.46	    s(b(x)) = x + [1] >= x + [1] = b(s(x))
7.86/2.46	    
7.86/2.46	                  [0]        [0]          
7.86/2.46	    a(s(x)) = x + [3] >= x + [3] = s(a(x))
7.86/2.46	    
7.86/2.46	                  [0]        [0]          
7.86/2.46	    b(s(x)) = x + [1] >= x + [1] = s(b(x))
7.86/2.46	   problem:
7.86/2.46	    strict:
7.86/2.46	     s(a(x)) -> s(b(x))
7.86/2.46	    weak:
7.86/2.46	     s(a(x)) -> a(s(x))
7.86/2.46	     s(b(x)) -> b(s(x))
7.86/2.46	     a(s(x)) -> s(a(x))
7.86/2.46	     b(s(x)) -> s(b(x))
7.86/2.46	   String Reversal Processor:
7.86/2.46	    strict:
7.86/2.46	     a(s(x)) -> b(s(x))
7.86/2.46	    weak:
7.86/2.46	     a(s(x)) -> s(a(x))
7.86/2.46	     b(s(x)) -> s(b(x))
7.86/2.46	     s(a(x)) -> a(s(x))
7.86/2.46	     s(b(x)) -> b(s(x))
7.86/2.46	    Arctic Interpretation Processor:
7.86/2.46	     dimension: 1
7.86/2.46	     interpretation:
7.86/2.46	      [b](x0) = 4x0,
7.86/2.46	      
7.86/2.46	      [s](x0) = 12x0,
7.86/2.46	      
7.86/2.46	      [a](x0) = 12x0
7.86/2.46	     orientation:
7.86/2.46	      a(s(x)) = 24x >= 16x = b(s(x))
7.86/2.46	      
7.86/2.46	      a(s(x)) = 24x >= 24x = s(a(x))
7.86/2.46	      
7.86/2.46	      b(s(x)) = 16x >= 16x = s(b(x))
7.86/2.46	      
7.86/2.46	      s(a(x)) = 24x >= 24x = a(s(x))
7.86/2.46	      
7.86/2.46	      s(b(x)) = 16x >= 16x = b(s(x))
8.49/2.46	     problem:
8.49/2.46	      strict:
8.49/2.46	       
8.49/2.46	      weak:
8.49/2.46	       a(s(x)) -> s(a(x))
8.49/2.46	       b(s(x)) -> s(b(x))
8.49/2.46	       s(a(x)) -> a(s(x))
8.49/2.46	       s(b(x)) -> b(s(x))
8.49/2.46	     Qed
8.49/2.47	EOF