11.49/3.50	YES
11.49/3.51	
11.49/3.51	Problem:
11.49/3.51	 strict:
11.49/3.51	  f(x) -> s(x)
11.49/3.51	  f(s(s(x))) -> s(f(f(x)))
11.49/3.51	 weak:
11.49/3.51	  rand(x) -> x
11.49/3.51	  rand(x) -> rand(s(x))
11.49/3.51	
11.49/3.51	Proof:
11.49/3.51	 Arctic Interpretation Processor:
11.49/3.51	  dimension: 1
11.49/3.51	  interpretation:
11.49/3.51	   [rand](x0) = 8x0,
11.49/3.51	   
11.49/3.51	   [s](x0) = x0,
11.49/3.51	   
11.49/3.51	   [f](x0) = x0
11.49/3.51	  orientation:
11.49/3.51	   f(x) = x >= x = s(x)
11.49/3.51	   
11.49/3.51	   f(s(s(x))) = x >= x = s(f(f(x)))
11.49/3.51	   
11.49/3.51	   rand(x) = 8x >= x = x
11.49/3.51	   
11.49/3.51	   rand(x) = 8x >= 8x = rand(s(x))
11.49/3.51	  problem:
11.49/3.51	   strict:
11.49/3.51	    f(x) -> s(x)
11.49/3.51	    f(s(s(x))) -> s(f(f(x)))
11.49/3.51	   weak:
11.49/3.51	    rand(x) -> rand(s(x))
11.49/3.51	  String Reversal Processor:
11.49/3.51	   strict:
11.49/3.51	    f(x) -> s(x)
11.49/3.51	    s(s(f(x))) -> f(f(s(x)))
11.49/3.51	   weak:
11.49/3.51	    rand(x) -> s(rand(x))
11.49/3.51	   Matrix Interpretation Processor: dim=5
11.49/3.51	    
11.49/3.51	    interpretation:
11.49/3.51	                  [1 0 0 0 0]  
11.49/3.51	                  [0 0 0 0 0]  
11.49/3.51	     [rand](x0) = [0 0 0 0 0]x0
11.49/3.51	                  [0 1 0 0 0]  
11.49/3.51	                  [0 0 0 0 0]  ,
11.49/3.51	     
11.49/3.51	               [1 0 1 0 0]  
11.49/3.51	               [0 0 1 0 1]  
11.49/3.51	     [s](x0) = [0 1 0 0 1]x0
11.49/3.51	               [0 0 0 0 0]  
11.49/3.51	               [0 1 1 0 0]  ,
11.49/3.51	     
11.49/3.51	               [1 0 1 0 0]     [0]
11.49/3.51	               [0 0 1 0 1]     [1]
11.49/3.51	     [f](x0) = [0 1 0 0 1]x0 + [0]
11.49/3.51	               [0 0 0 0 0]     [0]
11.49/3.51	               [0 1 1 0 0]     [1]
11.49/3.51	    orientation:
11.49/3.51	            [1 0 1 0 0]    [0]    [1 0 1 0 0]        
11.49/3.51	            [0 0 1 0 1]    [1]    [0 0 1 0 1]        
11.49/3.51	     f(x) = [0 1 0 0 1]x + [0] >= [0 1 0 0 1]x = s(x)
11.49/3.51	            [0 0 0 0 0]    [0]    [0 0 0 0 0]        
11.49/3.51	            [0 1 1 0 0]    [1]    [0 1 1 0 0]        
11.49/3.51	     
11.49/3.51	                  [1 2 3 0 2]    [2]    [1 2 3 0 2]    [0]             
11.49/3.51	                  [0 2 3 0 3]    [3]    [0 2 3 0 3]    [2]             
11.49/3.51	     s(s(f(x))) = [0 3 2 0 3]x + [2] >= [0 3 2 0 3]x + [2] = f(f(s(x)))
11.49/3.51	                  [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]             
11.49/3.51	                  [0 3 3 0 2]    [3]    [0 3 3 0 2]    [2]             
11.49/3.51	     
11.49/3.51	               [1 0 0 0 0]     [1 0 0 0 0]              
11.49/3.51	               [0 0 0 0 0]     [0 0 0 0 0]              
11.49/3.51	     rand(x) = [0 0 0 0 0]x >= [0 0 0 0 0]x = s(rand(x))
11.49/3.51	               [0 1 0 0 0]     [0 0 0 0 0]              
11.49/3.51	               [0 0 0 0 0]     [0 0 0 0 0]              
11.49/3.51	    problem:
11.49/3.51	     strict:
11.49/3.51	      f(x) -> s(x)
11.49/3.51	     weak:
11.49/3.51	      rand(x) -> s(rand(x))
11.49/3.51	    Arctic Interpretation Processor:
11.49/3.51	     dimension: 4
11.49/3.51	     interpretation:
11.49/3.51	                   [0 0 0 0]  
11.49/3.51	                   [0 0 0 0]  
11.49/3.51	      [rand](x0) = [0 0 0 0]x0
11.49/3.51	                   [0 0 0 0]  ,
11.49/3.51	      
11.49/3.51	                [0  -& -& 0 ]  
11.49/3.51	                [-& -& -& -&]  
11.49/3.51	      [s](x0) = [-& -& -& -&]x0
11.49/3.51	                [-& -& -& -&]  ,
11.49/3.51	      
11.49/3.51	                [3 0 0 3]  
11.49/3.51	                [0 0 0 0]  
11.49/3.51	      [f](x0) = [0 0 0 0]x0
11.49/3.51	                [0 0 0 0]  
11.49/3.51	     orientation:
11.49/3.51	             [3 0 0 3]     [0  -& -& 0 ]        
11.49/3.51	             [0 0 0 0]     [-& -& -& -&]        
11.49/3.51	      f(x) = [0 0 0 0]x >= [-& -& -& -&]x = s(x)
11.49/3.51	             [0 0 0 0]     [-& -& -& -&]        
11.49/3.51	      
11.49/3.51	                [0 0 0 0]     [0  0  0  0 ]              
11.49/3.51	                [0 0 0 0]     [-& -& -& -&]              
11.49/3.51	      rand(x) = [0 0 0 0]x >= [-& -& -& -&]x = s(rand(x))
11.49/3.51	                [0 0 0 0]     [-& -& -& -&]              
11.49/3.51	     problem:
11.49/3.51	      strict:
11.49/3.51	       
11.49/3.51	      weak:
11.49/3.51	       rand(x) -> s(rand(x))
11.49/3.51	     Qed
11.49/3.51	EOF