YES(?,O(n^2))
10.48/6.73	YES(?,O(n^2))
10.48/6.73	
10.48/6.73	Problem:
10.48/6.73	 f(x,g(x)) -> x
10.48/6.73	 f(x,h(y)) -> f(h(x),y)
10.48/6.73	
10.48/6.73	Proof:
10.48/6.73	 Complexity Transformation Processor:
10.48/6.73	  strict:
10.48/6.73	   f(x,g(x)) -> x
10.48/6.73	   f(x,h(y)) -> f(h(x),y)
10.48/6.73	  weak:
10.48/6.73	   
10.48/6.73	  Matrix Interpretation Processor: dim=1
10.48/6.73	   
10.48/6.73	   max_matrix:
10.48/6.73	    1
10.48/6.73	   interpretation:
10.48/6.73	    [h](x0) = x0 + 72,
10.48/6.73	    
10.48/6.73	    [f](x0, x1) = x0 + x1 + 232,
10.48/6.73	    
10.48/6.73	    [g](x0) = x0
10.48/6.73	   orientation:
10.48/6.73	    f(x,g(x)) = 2x + 232 >= x = x
10.48/6.73	    
10.48/6.73	    f(x,h(y)) = x + y + 304 >= x + y + 304 = f(h(x),y)
10.48/6.73	   problem:
10.48/6.73	    strict:
10.48/6.73	     f(x,h(y)) -> f(h(x),y)
10.48/6.73	    weak:
10.48/6.73	     f(x,g(x)) -> x
10.48/6.73	   Matrix Interpretation Processor: dim=2
10.48/6.73	    
10.48/6.73	    max_matrix:
10.48/6.73	     [1 1]
10.48/6.73	     [0 1]
10.48/6.73	    interpretation:
10.48/6.73	                    [0]
10.48/6.73	     [h](x0) = x0 + [1],
10.48/6.73	     
10.48/6.73	                        [1 1]     [0]
10.48/6.73	     [f](x0, x1) = x0 + [0 1]x1 + [1],
10.48/6.73	     
10.48/6.73	                    [2]
10.48/6.73	     [g](x0) = x0 + [2]
10.48/6.73	    orientation:
10.48/6.73	                     [1 1]    [1]        [1 1]    [0]            
10.48/6.73	     f(x,h(y)) = x + [0 1]y + [2] >= x + [0 1]y + [2] = f(h(x),y)
10.48/6.73	     
10.48/6.73	                 [2 1]    [4]         
10.48/6.73	     f(x,g(x)) = [0 2]x + [3] >= x = x
10.48/6.73	    problem:
10.48/6.73	     strict:
10.48/6.73	      
10.48/6.73	     weak:
10.48/6.73	      f(x,h(y)) -> f(h(x),y)
10.48/6.73	      f(x,g(x)) -> x
10.48/6.73	    Qed
10.48/6.74	EOF