4.47/1.46	YES
4.47/1.47	
4.47/1.47	Problem:
4.47/1.47	 strict:
4.47/1.47	  t(f(x),g(y),f(z)) -> t(z,g(x),g(y))
4.47/1.47	  t(g(x),g(y),f(z)) -> t(f(y),f(z),x)
4.47/1.47	 weak:
4.47/1.47	  f(g(x)) -> g(f(x))
4.47/1.47	  g(f(x)) -> f(g(x))
4.47/1.47	  f(f(x)) -> g(g(x))
4.47/1.47	  g(g(x)) -> f(f(x))
4.47/1.47	
4.47/1.47	Proof:
4.47/1.47	 Matrix Interpretation Processor: dim=2
4.47/1.47	  
4.47/1.47	  interpretation:
4.47/1.47	                     [1 0]     [1 0]     [1 0]  
4.47/1.47	   [t](x0, x1, x2) = [1 0]x0 + [1 0]x1 + [1 0]x2,
4.47/1.47	   
4.47/1.47	             [1 0]     [1]
4.47/1.47	   [g](x0) = [0 0]x0 + [0],
4.47/1.47	   
4.47/1.47	             [1 0]     [1]
4.47/1.47	   [f](x0) = [0 0]x0 + [0]
4.47/1.47	  orientation:
4.47/1.47	                       [1 0]    [1 0]    [1 0]    [3]    [1 0]    [1 0]    [1 0]    [2]                 
4.47/1.47	   t(f(x),g(y),f(z)) = [1 0]x + [1 0]y + [1 0]z + [3] >= [1 0]x + [1 0]y + [1 0]z + [2] = t(z,g(x),g(y))
4.47/1.47	   
4.47/1.47	                       [1 0]    [1 0]    [1 0]    [3]    [1 0]    [1 0]    [1 0]    [2]                 
4.47/1.47	   t(g(x),g(y),f(z)) = [1 0]x + [1 0]y + [1 0]z + [3] >= [1 0]x + [1 0]y + [1 0]z + [2] = t(f(y),f(z),x)
4.47/1.47	   
4.47/1.47	             [1 0]    [2]    [1 0]    [2]          
4.47/1.47	   f(g(x)) = [0 0]x + [0] >= [0 0]x + [0] = g(f(x))
4.47/1.47	   
4.47/1.47	             [1 0]    [2]    [1 0]    [2]          
4.47/1.47	   g(f(x)) = [0 0]x + [0] >= [0 0]x + [0] = f(g(x))
4.47/1.47	   
4.47/1.47	             [1 0]    [2]    [1 0]    [2]          
4.47/1.47	   f(f(x)) = [0 0]x + [0] >= [0 0]x + [0] = g(g(x))
4.47/1.47	   
4.47/1.47	             [1 0]    [2]    [1 0]    [2]          
4.47/1.47	   g(g(x)) = [0 0]x + [0] >= [0 0]x + [0] = f(f(x))
4.47/1.47	  problem:
4.47/1.47	   strict:
4.47/1.47	    
4.47/1.47	   weak:
4.47/1.47	    f(g(x)) -> g(f(x))
4.47/1.47	    g(f(x)) -> f(g(x))
4.47/1.47	    f(f(x)) -> g(g(x))
4.47/1.47	    g(g(x)) -> f(f(x))
4.47/1.47	  Qed
4.47/1.47	EOF