YES(?,O(n^2))
8.42/5.81	YES(?,O(n^2))
8.42/5.81	
8.42/5.81	Problem:
8.42/5.81	 g(f(x),y) -> f(h(x,y))
8.42/5.81	 h(x,y) -> g(x,f(y))
8.42/5.81	
8.42/5.81	Proof:
8.42/5.81	 Complexity Transformation Processor:
8.42/5.81	  strict:
8.42/5.81	   g(f(x),y) -> f(h(x,y))
8.42/5.81	   h(x,y) -> g(x,f(y))
8.42/5.81	  weak:
8.42/5.81	   
8.42/5.81	  Matrix Interpretation Processor: dim=1
8.42/5.81	   
8.42/5.81	   max_matrix:
8.42/5.81	    1
8.42/5.81	   interpretation:
8.42/5.81	    [h](x0, x1) = x0 + x1 + 237,
8.42/5.81	    
8.42/5.81	    [g](x0, x1) = x0 + x1 + 76,
8.42/5.81	    
8.42/5.81	    [f](x0) = x0 + 64
8.42/5.81	   orientation:
8.42/5.81	    g(f(x),y) = x + y + 140 >= x + y + 301 = f(h(x,y))
8.42/5.81	    
8.42/5.81	    h(x,y) = x + y + 237 >= x + y + 140 = g(x,f(y))
8.42/5.81	   problem:
8.42/5.81	    strict:
8.42/5.81	     g(f(x),y) -> f(h(x,y))
8.42/5.81	    weak:
8.42/5.81	     h(x,y) -> g(x,f(y))
8.42/5.81	   Matrix Interpretation Processor: dim=2
8.42/5.81	    
8.42/5.81	    max_matrix:
8.42/5.81	     [1 2]
8.42/5.81	     [0 1]
8.42/5.81	    interpretation:
8.42/5.81	                   [1 2]     [1 0]  
8.42/5.81	     [h](x0, x1) = [0 1]x0 + [0 0]x1,
8.42/5.81	     
8.42/5.81	                   [1 2]     [1 0]  
8.42/5.81	     [g](x0, x1) = [0 1]x0 + [0 0]x1,
8.42/5.81	     
8.42/5.81	                    [0]
8.42/5.81	     [f](x0) = x0 + [5]
8.42/5.81	    orientation:
8.42/5.81	                 [1 2]    [1 0]    [10]    [1 2]    [1 0]    [0]            
8.42/5.81	     g(f(x),y) = [0 1]x + [0 0]y + [5 ] >= [0 1]x + [0 0]y + [5] = f(h(x,y))
8.42/5.81	     
8.42/5.81	              [1 2]    [1 0]     [1 2]    [1 0]             
8.42/5.81	     h(x,y) = [0 1]x + [0 0]y >= [0 1]x + [0 0]y = g(x,f(y))
8.42/5.81	    problem:
8.42/5.81	     strict:
8.42/5.81	      
8.42/5.81	     weak:
8.42/5.81	      g(f(x),y) -> f(h(x,y))
8.42/5.81	      h(x,y) -> g(x,f(y))
8.42/5.81	    Qed
8.42/5.82	EOF