4.16/1.39	YES
4.16/1.40	
4.16/1.40	Problem:
4.16/1.40	 strict:
4.16/1.40	  f(s(x),y,y) -> f(y,x,s(x))
4.16/1.40	 weak:
4.16/1.40	  rand(x) -> x
4.16/1.40	  rand(x) -> rand(s(x))
4.16/1.40	
4.16/1.40	Proof:
4.16/1.40	 Matrix Interpretation Processor: dim=2
4.16/1.40	  
4.16/1.40	  interpretation:
4.16/1.40	                [1 1]     [1]
4.16/1.40	   [rand](x0) = [0 2]x0 + [0],
4.16/1.40	   
4.16/1.40	                     [3 3]     [2 2]     [1 1]     [0]
4.16/1.40	   [f](x0, x1, x2) = [0 2]x0 + [0 2]x1 + [0 0]x2 + [2],
4.16/1.40	   
4.16/1.40	               
4.16/1.40	   [s](x0) = x0
4.16/1.40	  orientation:
4.16/1.40	                 [3 3]    [3 3]    [0]    [3 3]    [3 3]    [0]              
4.16/1.40	   f(s(x),y,y) = [0 2]x + [0 2]y + [2] >= [0 2]x + [0 2]y + [2] = f(y,x,s(x))
4.16/1.40	   
4.16/1.40	             [1 1]    [1]         
4.16/1.40	   rand(x) = [0 2]x + [0] >= x = x
4.16/1.40	   
4.16/1.40	             [1 1]    [1]    [1 1]    [1]             
4.16/1.40	   rand(x) = [0 2]x + [0] >= [0 2]x + [0] = rand(s(x))
4.16/1.40	  problem:
4.16/1.40	   strict:
4.16/1.40	    f(s(x),y,y) -> f(y,x,s(x))
4.16/1.40	   weak:
4.16/1.40	    rand(x) -> rand(s(x))
4.16/1.40	  Matrix Interpretation Processor: dim=5
4.16/1.40	   
4.16/1.40	   interpretation:
4.16/1.40	                 [1 0 0 0 0]     [1]
4.16/1.40	                 [0 0 0 0 0]     [0]
4.16/1.40	    [rand](x0) = [0 0 0 0 0]x0 + [0]
4.16/1.40	                 [1 0 0 0 0]     [0]
4.16/1.40	                 [0 0 0 0 0]     [0],
4.16/1.40	    
4.16/1.40	                      [1 1 1 0 1]     [1 1 0 0 1]     [1 0 1 0 0]     [0]
4.16/1.40	                      [0 0 1 0 1]     [0 0 0 0 1]     [0 0 1 0 0]     [1]
4.16/1.40	    [f](x0, x1, x2) = [1 0 0 1 0]x0 + [0 0 0 0 0]x1 + [1 0 0 1 0]x2 + [1]
4.16/1.40	                      [0 0 1 0 0]     [0 0 0 0 0]     [0 0 1 0 0]     [0]
4.16/1.40	                      [1 0 1 0 0]     [1 0 0 0 0]     [0 0 1 0 0]     [0],
4.16/1.40	    
4.16/1.40	              [1 0 0 0 0]     [0]
4.16/1.40	              [1 1 0 0 0]     [0]
4.16/1.40	    [s](x0) = [1 0 0 0 1]x0 + [0]
4.16/1.40	              [0 1 0 0 0]     [0]
4.16/1.40	              [0 0 0 0 1]     [1]
4.16/1.40	   orientation:
4.16/1.40	                  [3 1 0 0 2]    [2 1 1 0 1]    [1]    [3 1 0 0 2]    [1 1 1 0 1]    [0]              
4.16/1.40	                  [1 0 0 0 2]    [0 0 1 0 1]    [2]    [1 0 0 0 2]    [0 0 1 0 1]    [1]              
4.16/1.40	    f(s(x),y,y) = [1 1 0 0 0]x + [1 0 0 1 0]y + [1] >= [1 1 0 0 0]x + [1 0 0 1 0]y + [1] = f(y,x,s(x))
4.16/1.40	                  [1 0 0 0 1]    [0 0 1 0 0]    [0]    [1 0 0 0 1]    [0 0 1 0 0]    [0]              
4.16/1.40	                  [2 0 0 0 1]    [1 0 1 0 0]    [0]    [2 0 0 0 1]    [1 0 1 0 0]    [0]              
4.16/1.40	    
4.16/1.40	              [1 0 0 0 0]    [1]    [1 0 0 0 0]    [1]             
4.16/1.40	              [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]             
4.16/1.40	    rand(x) = [0 0 0 0 0]x + [0] >= [0 0 0 0 0]x + [0] = rand(s(x))
4.16/1.40	              [1 0 0 0 0]    [0]    [1 0 0 0 0]    [0]             
4.16/1.40	              [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]             
4.16/1.40	   problem:
4.16/1.40	    strict:
4.16/1.40	     
4.16/1.40	    weak:
4.16/1.40	     rand(x) -> rand(s(x))
4.16/1.40	   Qed
4.16/1.40	EOF