YES(?,O(n^2))
39.88/23.43	YES(?,O(n^2))
39.88/23.44	
39.88/23.44	Problem:
39.88/23.44	 f(x,y) -> g(x,y)
39.88/23.44	 g(h(x),y) -> h(f(x,y))
39.88/23.44	 g(h(x),y) -> h(g(x,y))
39.88/23.44	
39.88/23.44	Proof:
39.88/23.44	 Complexity Transformation Processor:
39.88/23.44	  strict:
39.88/23.44	   f(x,y) -> g(x,y)
39.88/23.44	   g(h(x),y) -> h(f(x,y))
39.88/23.44	   g(h(x),y) -> h(g(x,y))
39.88/23.44	  weak:
39.88/23.44	   
39.88/23.44	  Matrix Interpretation Processor: dim=1
39.88/23.44	   
39.88/23.44	   max_matrix:
39.88/23.44	    1
39.88/23.44	   interpretation:
39.88/23.44	    [h](x0) = x0 + 42,
39.88/23.44	    
39.88/23.44	    [g](x0, x1) = x0 + x1 + 87,
39.88/23.44	    
39.88/23.44	    [f](x0, x1) = x0 + x1 + 212
39.88/23.44	   orientation:
39.88/23.44	    f(x,y) = x + y + 212 >= x + y + 87 = g(x,y)
39.88/23.44	    
39.88/23.44	    g(h(x),y) = x + y + 129 >= x + y + 254 = h(f(x,y))
39.88/23.44	    
39.88/23.44	    g(h(x),y) = x + y + 129 >= x + y + 129 = h(g(x,y))
39.88/23.44	   problem:
39.88/23.44	    strict:
39.88/23.44	     g(h(x),y) -> h(f(x,y))
39.88/23.44	     g(h(x),y) -> h(g(x,y))
39.88/23.44	    weak:
39.88/23.44	     f(x,y) -> g(x,y)
39.88/23.44	   Matrix Interpretation Processor: dim=2
39.88/23.44	    
39.88/23.44	    max_matrix:
39.88/23.44	     [1 1]
39.88/23.44	     [0 1]
39.88/23.44	    interpretation:
39.88/23.44	                    [1]
39.88/23.44	     [h](x0) = x0 + [1],
39.88/23.44	     
39.88/23.44	                   [1 1]     [1 0]  
39.88/23.44	     [g](x0, x1) = [0 1]x0 + [0 0]x1,
39.88/23.44	     
39.88/23.44	                   [1 1]     [1 0]     [1]
39.88/23.44	     [f](x0, x1) = [0 1]x0 + [0 0]x1 + [0]
39.88/23.44	    orientation:
39.88/23.44	                 [1 1]    [1 0]    [2]    [1 1]    [1 0]    [2]            
39.88/23.44	     g(h(x),y) = [0 1]x + [0 0]y + [1] >= [0 1]x + [0 0]y + [1] = h(f(x,y))
39.88/23.44	     
39.88/23.44	                 [1 1]    [1 0]    [2]    [1 1]    [1 0]    [1]            
39.88/23.44	     g(h(x),y) = [0 1]x + [0 0]y + [1] >= [0 1]x + [0 0]y + [1] = h(g(x,y))
39.88/23.44	     
39.88/23.44	              [1 1]    [1 0]    [1]    [1 1]    [1 0]          
39.88/23.44	     f(x,y) = [0 1]x + [0 0]y + [0] >= [0 1]x + [0 0]y = g(x,y)
39.88/23.44	    problem:
39.88/23.44	     strict:
39.88/23.44	      g(h(x),y) -> h(f(x,y))
39.88/23.44	     weak:
39.88/23.44	      g(h(x),y) -> h(g(x,y))
39.88/23.44	      f(x,y) -> g(x,y)
39.88/23.44	    Matrix Interpretation Processor: dim=2
39.88/23.44	     
39.88/23.44	     max_matrix:
39.88/23.44	      [1 1]
39.88/23.44	      [0 1]
39.88/23.44	     interpretation:
39.88/23.44	                     [0]
39.88/23.44	      [h](x0) = x0 + [1],
39.88/23.44	      
39.88/23.44	                    [1 1]          [0]
39.88/23.44	      [g](x0, x1) = [0 1]x0 + x1 + [2],
39.88/23.44	      
39.88/23.44	                    [1 1]          [0]
39.88/23.44	      [f](x0, x1) = [0 1]x0 + x1 + [2]
39.88/23.44	     orientation:
39.88/23.44	                  [1 1]        [1]    [1 1]        [0]            
39.88/23.44	      g(h(x),y) = [0 1]x + y + [3] >= [0 1]x + y + [3] = h(f(x,y))
39.88/23.44	      
39.88/23.44	                  [1 1]        [1]    [1 1]        [0]            
39.88/23.44	      g(h(x),y) = [0 1]x + y + [3] >= [0 1]x + y + [3] = h(g(x,y))
39.88/23.44	      
39.88/23.44	               [1 1]        [0]    [1 1]        [0]         
39.88/23.44	      f(x,y) = [0 1]x + y + [2] >= [0 1]x + y + [2] = g(x,y)
39.88/23.44	     problem:
39.88/23.44	      strict:
39.88/23.44	       
39.88/23.44	      weak:
39.88/23.44	       g(h(x),y) -> h(f(x,y))
39.88/23.44	       g(h(x),y) -> h(g(x,y))
39.88/23.44	       f(x,y) -> g(x,y)
39.88/23.44	     Qed
39.88/23.44	EOF