4.61/1.47	YES
4.61/1.48	
4.61/1.48	Problem:
4.61/1.48	 strict:
4.61/1.48	  g(x,y) -> x
4.61/1.48	  g(x,y) -> y
4.61/1.48	  f(s(x),y,y) -> f(y,x,s(x))
4.61/1.48	 weak:
4.61/1.48	  rand(x) -> x
4.61/1.48	  rand(x) -> rand(s(x))
4.61/1.48	
4.61/1.48	Proof:
4.61/1.48	 Matrix Interpretation Processor: dim=2
4.61/1.48	  
4.61/1.48	  interpretation:
4.61/1.48	                [1 1]     [1]
4.61/1.48	   [rand](x0) = [0 2]x0 + [0],
4.61/1.48	   
4.61/1.48	                     [2 0]     [1 0]     [1 2]     [0]
4.61/1.48	   [f](x0, x1, x2) = [2 0]x0 + [2 0]x1 + [0 0]x2 + [2],
4.61/1.48	   
4.61/1.48	             [1 1]  
4.61/1.48	   [s](x0) = [0 0]x0,
4.61/1.48	   
4.61/1.48	                 [1 2]     [2 0]     [1]
4.61/1.48	   [g](x0, x1) = [2 2]x0 + [0 2]x1 + [2]
4.61/1.48	  orientation:
4.61/1.48	            [1 2]    [2 0]    [1]         
4.61/1.48	   g(x,y) = [2 2]x + [0 2]y + [2] >= x = x
4.61/1.48	   
4.61/1.48	            [1 2]    [2 0]    [1]         
4.61/1.48	   g(x,y) = [2 2]x + [0 2]y + [2] >= y = y
4.61/1.48	   
4.61/1.48	                 [2 2]    [2 2]    [0]    [2 1]    [2 0]    [0]              
4.61/1.48	   f(s(x),y,y) = [2 2]x + [2 0]y + [2] >= [2 0]x + [2 0]y + [2] = f(y,x,s(x))
4.61/1.48	   
4.61/1.48	             [1 1]    [1]         
4.61/1.48	   rand(x) = [0 2]x + [0] >= x = x
4.61/1.48	   
4.61/1.48	             [1 1]    [1]    [1 1]    [1]             
4.61/1.48	   rand(x) = [0 2]x + [0] >= [0 0]x + [0] = rand(s(x))
4.61/1.48	  problem:
4.61/1.48	   strict:
4.61/1.48	    f(s(x),y,y) -> f(y,x,s(x))
4.61/1.48	   weak:
4.61/1.48	    rand(x) -> rand(s(x))
4.61/1.48	  Matrix Interpretation Processor: dim=3
4.61/1.48	   
4.61/1.48	   interpretation:
4.61/1.48	                 [1 0 0]     [0]
4.61/1.48	    [rand](x0) = [2 0 0]x0 + [0]
4.61/1.48	                 [2 0 0]     [1],
4.61/1.48	    
4.61/1.48	                      [1 3 0]     [1 3 0]     [2 0 0]     [0]
4.61/1.48	    [f](x0, x1, x2) = [2 2 0]x0 + [0 1 0]x1 + [3 1 0]x2 + [2]
4.61/1.48	                      [0 0 1]     [0 0 2]     [0 0 0]     [1],
4.61/1.48	    
4.61/1.48	              [1 0 0]     [0]
4.61/1.48	    [s](x0) = [1 1 0]x0 + [1]
4.61/1.48	              [0 0 3]     [3]
4.61/1.48	   orientation:
4.61/1.48	                  [4 3 0]    [3 3 0]    [3]    [3 3 0]    [1 3 0]    [0]              
4.61/1.48	    f(s(x),y,y) = [4 2 0]x + [3 2 0]y + [4] >= [4 2 0]x + [2 2 0]y + [3] = f(y,x,s(x))
4.61/1.48	                  [0 0 3]    [0 0 2]    [4]    [0 0 2]    [0 0 1]    [1]              
4.61/1.48	    
4.61/1.48	              [1 0 0]    [0]    [1 0 0]    [0]             
4.61/1.48	    rand(x) = [2 0 0]x + [0] >= [2 0 0]x + [0] = rand(s(x))
4.61/1.48	              [2 0 0]    [1]    [2 0 0]    [1]             
4.61/1.48	   problem:
4.61/1.48	    strict:
4.61/1.48	     
4.61/1.48	    weak:
4.61/1.48	     rand(x) -> rand(s(x))
4.61/1.48	   Qed
4.61/1.48	EOF