7.94/2.40	YES
7.94/2.41	
7.94/2.41	Problem:
7.94/2.41	 strict:
7.94/2.41	  f(x,c(y)) -> f(x,s(f(y,y)))
7.94/2.41	  f(s(x),y) -> f(x,s(c(y)))
7.94/2.41	 weak:
7.94/2.41	  rand(x) -> x
7.94/2.41	  rand(x) -> rand(s(x))
7.94/2.41	
7.94/2.41	Proof:
7.94/2.41	 Matrix Interpretation Processor: dim=2
7.94/2.41	  
7.94/2.41	  interpretation:
7.94/2.41	                [1 0]  
7.94/2.41	   [rand](x0) = [0 2]x0,
7.94/2.41	   
7.94/2.41	             [1 0]  
7.94/2.41	   [s](x0) = [0 0]x0,
7.94/2.41	   
7.94/2.41	                 [1 0]     [1 2]  
7.94/2.41	   [f](x0, x1) = [0 0]x0 + [1 2]x1,
7.94/2.41	   
7.94/2.41	             [1 2]     [0]
7.94/2.41	   [c](x0) = [1 0]x0 + [1]
7.94/2.41	  orientation:
7.94/2.41	               [1 0]    [3 2]    [2]    [1 0]    [2 2]                  
7.94/2.41	   f(x,c(y)) = [0 0]x + [3 2]y + [2] >= [0 0]x + [2 2]y = f(x,s(f(y,y)))
7.94/2.41	   
7.94/2.41	               [1 0]    [1 2]     [1 0]    [1 2]                
7.94/2.41	   f(s(x),y) = [0 0]x + [1 2]y >= [0 0]x + [1 2]y = f(x,s(c(y)))
7.94/2.41	   
7.94/2.41	             [1 0]          
7.94/2.41	   rand(x) = [0 2]x >= x = x
7.94/2.41	   
7.94/2.41	             [1 0]     [1 0]              
7.94/2.41	   rand(x) = [0 2]x >= [0 0]x = rand(s(x))
7.94/2.41	  problem:
7.94/2.41	   strict:
7.94/2.41	    f(s(x),y) -> f(x,s(c(y)))
7.94/2.41	   weak:
7.94/2.41	    rand(x) -> x
7.94/2.41	    rand(x) -> rand(s(x))
7.94/2.41	  Matrix Interpretation Processor: dim=2
7.94/2.41	   
7.94/2.41	   interpretation:
7.94/2.41	                 [1 0]     [1]
7.94/2.41	    [rand](x0) = [0 2]x0 + [0],
7.94/2.41	    
7.94/2.41	              [1 0]  
7.94/2.41	    [s](x0) = [0 0]x0,
7.94/2.41	    
7.94/2.41	                  [2 0]     [1 0]     [1]
7.94/2.41	    [f](x0, x1) = [0 0]x0 + [2 0]x1 + [0],
7.94/2.41	    
7.94/2.41	              [1 0]  
7.94/2.41	    [c](x0) = [0 0]x0
7.94/2.41	   orientation:
7.94/2.41	                [2 0]    [1 0]    [1]    [2 0]    [1 0]    [1]               
7.94/2.41	    f(s(x),y) = [0 0]x + [2 0]y + [0] >= [0 0]x + [2 0]y + [0] = f(x,s(c(y)))
7.94/2.41	    
7.94/2.41	              [1 0]    [1]         
7.94/2.41	    rand(x) = [0 2]x + [0] >= x = x
7.94/2.41	    
7.94/2.41	              [1 0]    [1]    [1 0]    [1]             
7.94/2.41	    rand(x) = [0 2]x + [0] >= [0 0]x + [0] = rand(s(x))
7.94/2.41	   problem:
7.94/2.41	    strict:
7.94/2.41	     f(s(x),y) -> f(x,s(c(y)))
7.94/2.41	    weak:
7.94/2.41	     rand(x) -> rand(s(x))
7.94/2.41	   Matrix Interpretation Processor: dim=2
7.94/2.41	    
7.94/2.41	    interpretation:
7.94/2.41	                  [1 0]     [2]
7.94/2.41	     [rand](x0) = [0 0]x0 + [0],
7.94/2.41	     
7.94/2.41	                    [0]
7.94/2.41	     [s](x0) = x0 + [2],
7.94/2.41	     
7.94/2.41	                   [2 1]     [2 0]     [0]
7.94/2.41	     [f](x0, x1) = [0 0]x0 + [0 0]x1 + [2],
7.94/2.41	     
7.94/2.41	               [1 0]  
7.94/2.41	     [c](x0) = [0 2]x0
7.94/2.41	    orientation:
7.94/2.41	                 [2 1]    [2 0]    [2]    [2 1]    [2 0]    [0]               
7.94/2.41	     f(s(x),y) = [0 0]x + [0 0]y + [2] >= [0 0]x + [0 0]y + [2] = f(x,s(c(y)))
7.94/2.41	     
7.94/2.41	               [1 0]    [2]    [1 0]    [2]             
7.94/2.41	     rand(x) = [0 0]x + [0] >= [0 0]x + [0] = rand(s(x))
7.94/2.41	    problem:
7.94/2.41	     strict:
7.94/2.41	      
7.94/2.41	     weak:
7.94/2.41	      rand(x) -> rand(s(x))
7.94/2.41	    Qed
7.94/2.41	EOF