14.76/4.09	YES
14.76/4.10	
14.76/4.10	Problem:
14.76/4.10	 strict:
14.76/4.10	  f(g(x)) -> g(f(f(x)))
14.76/4.10	  f(h(x)) -> h(g(x))
14.76/4.10	  f'(s(x),y,y) -> f'(y,x,s(x))
14.76/4.10	 weak:
14.76/4.10	  rand(x) -> x
14.76/4.10	  rand(x) -> rand(s(x))
14.76/4.10	
14.76/4.10	Proof:
14.76/4.10	 Matrix Interpretation Processor: dim=2
14.76/4.10	  
14.76/4.10	  interpretation:
14.76/4.10	                [2 0]     [1]
14.76/4.10	   [rand](x0) = [0 1]x0 + [0],
14.76/4.10	   
14.76/4.10	                      [3 0]     [1 0]     [2 0]     [0]
14.76/4.10	   [f'](x0, x1, x2) = [1 0]x0 + [0 0]x1 + [1 0]x2 + [2],
14.76/4.10	   
14.76/4.10	             [1 0]  
14.76/4.10	   [s](x0) = [0 0]x0,
14.76/4.10	   
14.76/4.10	             [2 2]  
14.76/4.10	   [h](x0) = [0 0]x0,
14.76/4.10	   
14.76/4.10	             [1 0]  
14.76/4.10	   [f](x0) = [0 0]x0,
14.76/4.10	   
14.76/4.10	             [1 0]  
14.76/4.10	   [g](x0) = [0 0]x0
14.76/4.10	  orientation:
14.76/4.10	             [1 0]     [1 0]              
14.76/4.10	   f(g(x)) = [0 0]x >= [0 0]x = g(f(f(x)))
14.76/4.10	   
14.76/4.10	             [2 2]     [2 0]           
14.76/4.10	   f(h(x)) = [0 0]x >= [0 0]x = h(g(x))
14.76/4.10	   
14.76/4.10	                  [3 0]    [3 0]    [0]    [3 0]    [3 0]    [0]               
14.76/4.10	   f'(s(x),y,y) = [1 0]x + [1 0]y + [2] >= [1 0]x + [1 0]y + [2] = f'(y,x,s(x))
14.76/4.10	   
14.76/4.10	             [2 0]    [1]         
14.76/4.10	   rand(x) = [0 1]x + [0] >= x = x
14.76/4.10	   
14.76/4.10	             [2 0]    [1]    [2 0]    [1]             
14.76/4.10	   rand(x) = [0 1]x + [0] >= [0 0]x + [0] = rand(s(x))
14.76/4.10	  problem:
14.76/4.10	   strict:
14.76/4.10	    f(g(x)) -> g(f(f(x)))
14.76/4.10	    f(h(x)) -> h(g(x))
14.76/4.10	    f'(s(x),y,y) -> f'(y,x,s(x))
14.76/4.10	   weak:
14.76/4.10	    rand(x) -> rand(s(x))
14.76/4.10	  Matrix Interpretation Processor: dim=2
14.76/4.10	   
14.76/4.10	   interpretation:
14.76/4.10	                 [2 0]  
14.76/4.10	    [rand](x0) = [0 0]x0,
14.76/4.10	    
14.76/4.10	                       [2 1]     [1 1]     [2 0]  
14.76/4.10	    [f'](x0, x1, x2) = [0 2]x0 + [0 1]x1 + [1 1]x2,
14.76/4.10	    
14.76/4.10	              [1 0]     [0]
14.76/4.10	    [s](x0) = [1 1]x0 + [1],
14.76/4.10	    
14.76/4.10	              [2 2]     [2]
14.76/4.10	    [h](x0) = [0 0]x0 + [0],
14.76/4.10	    
14.76/4.10	              [1 0]  
14.76/4.10	    [f](x0) = [0 0]x0,
14.76/4.10	    
14.76/4.10	              [1 1]  
14.76/4.10	    [g](x0) = [0 0]x0
14.76/4.10	   orientation:
14.76/4.10	              [1 1]     [1 0]              
14.76/4.10	    f(g(x)) = [0 0]x >= [0 0]x = g(f(f(x)))
14.76/4.10	    
14.76/4.10	              [2 2]    [2]    [2 2]    [2]          
14.76/4.10	    f(h(x)) = [0 0]x + [0] >= [0 0]x + [0] = h(g(x))
14.76/4.10	    
14.76/4.10	                   [3 1]    [3 1]    [1]    [3 1]    [2 1]    [0]               
14.76/4.10	    f'(s(x),y,y) = [2 2]x + [1 2]y + [2] >= [2 2]x + [0 2]y + [1] = f'(y,x,s(x))
14.76/4.10	    
14.76/4.10	              [2 0]     [2 0]              
14.76/4.10	    rand(x) = [0 0]x >= [0 0]x = rand(s(x))
14.76/4.10	   problem:
14.76/4.10	    strict:
14.76/4.10	     f(g(x)) -> g(f(f(x)))
14.76/4.10	     f(h(x)) -> h(g(x))
14.76/4.10	    weak:
14.76/4.10	     rand(x) -> rand(s(x))
14.76/4.10	   Matrix Interpretation Processor: dim=2
14.76/4.10	    
14.76/4.10	    interpretation:
14.76/4.10	                  [1 1]  
14.76/4.10	     [rand](x0) = [2 2]x0,
14.76/4.10	     
14.76/4.10	               [1 0]  
14.76/4.10	     [s](x0) = [0 0]x0,
14.76/4.10	     
14.76/4.10	               [1 0]     [0]
14.76/4.10	     [h](x0) = [1 0]x0 + [2],
14.76/4.10	     
14.76/4.10	               [1 1]  
14.76/4.10	     [f](x0) = [0 1]x0,
14.76/4.10	     
14.76/4.10	               [1 0]  
14.76/4.10	     [g](x0) = [0 2]x0
14.76/4.10	    orientation:
14.76/4.10	               [1 2]     [1 2]              
14.76/4.10	     f(g(x)) = [0 2]x >= [0 2]x = g(f(f(x)))
14.76/4.10	     
14.76/4.10	               [2 0]    [2]    [1 0]    [0]          
14.76/4.10	     f(h(x)) = [1 0]x + [2] >= [1 0]x + [2] = h(g(x))
14.76/4.10	     
14.76/4.10	               [1 1]     [1 0]              
14.76/4.10	     rand(x) = [2 2]x >= [2 0]x = rand(s(x))
14.76/4.10	    problem:
14.76/4.10	     strict:
14.76/4.10	      f(g(x)) -> g(f(f(x)))
14.76/4.10	     weak:
14.76/4.10	      rand(x) -> rand(s(x))
14.76/4.10	    String Reversal Processor:
14.76/4.10	     strict:
14.76/4.10	      g(f(x)) -> f(f(g(x)))
14.76/4.10	     weak:
14.76/4.10	      rand(x) -> s(rand(x))
14.76/4.10	     Matrix Interpretation Processor: dim=2
14.76/4.10	      
14.76/4.10	      interpretation:
14.76/4.10	                    [2 2]     [1]
14.76/4.10	       [rand](x0) = [3 2]x0 + [2],
14.76/4.10	       
14.76/4.10	                 [1 0]     [0]
14.76/4.10	       [s](x0) = [1 0]x0 + [1],
14.76/4.10	       
14.76/4.10	                      [0]
14.76/4.10	       [f](x0) = x0 + [1],
14.76/4.10	       
14.76/4.10	                 [1 1]  
14.76/4.10	       [g](x0) = [0 2]x0
14.76/4.10	      orientation:
14.76/4.10	                 [1 1]    [1]    [1 1]    [0]             
14.76/4.10	       g(f(x)) = [0 2]x + [2] >= [0 2]x + [2] = f(f(g(x)))
14.76/4.10	       
14.76/4.10	                 [2 2]    [1]    [2 2]    [1]             
14.76/4.10	       rand(x) = [3 2]x + [2] >= [2 2]x + [2] = s(rand(x))
14.76/4.10	      problem:
14.76/4.10	       strict:
14.76/4.10	        
14.76/4.10	       weak:
14.76/4.10	        rand(x) -> s(rand(x))
14.76/4.10	      Qed
14.76/4.10	EOF