YES(?,O(n^1))
8.01/2.77	YES(?,O(n^1))
8.01/2.77	
8.01/2.77	Problem:
8.01/2.77	 f(a()) -> g(h(a()))
8.01/2.77	 h(g(x)) -> g(h(f(x)))
8.01/2.77	 k(x,h(x),a()) -> h(x)
8.01/2.77	 k(f(x),y,x) -> f(x)
8.01/2.77	
8.01/2.77	Proof:
8.01/2.77	 Complexity Transformation Processor:
8.01/2.77	  strict:
8.01/2.77	   f(a()) -> g(h(a()))
8.01/2.77	   h(g(x)) -> g(h(f(x)))
8.01/2.77	   k(x,h(x),a()) -> h(x)
8.01/2.77	   k(f(x),y,x) -> f(x)
8.01/2.77	  weak:
8.01/2.77	   
8.01/2.77	  Matrix Interpretation Processor: dim=1
8.01/2.77	   
8.01/2.77	   max_matrix:
8.01/2.77	    1
8.01/2.77	   interpretation:
8.01/2.77	    [k](x0, x1, x2) = x0 + x1 + x2 + 191,
8.01/2.77	    
8.01/2.77	    [g](x0) = x0 + 96,
8.01/2.77	    
8.01/2.77	    [h](x0) = x0 + 65,
8.01/2.77	    
8.01/2.77	    [f](x0) = x0,
8.01/2.77	    
8.01/2.77	    [a] = 132
8.01/2.77	   orientation:
8.01/2.77	    f(a()) = 132 >= 293 = g(h(a()))
8.01/2.77	    
8.01/2.77	    h(g(x)) = x + 161 >= x + 161 = g(h(f(x)))
8.01/2.77	    
8.01/2.77	    k(x,h(x),a()) = 2x + 388 >= x + 65 = h(x)
8.01/2.77	    
8.01/2.77	    k(f(x),y,x) = 2x + y + 191 >= x = f(x)
8.01/2.77	   problem:
8.01/2.77	    strict:
8.01/2.77	     f(a()) -> g(h(a()))
8.01/2.77	     h(g(x)) -> g(h(f(x)))
8.01/2.77	    weak:
8.01/2.77	     k(x,h(x),a()) -> h(x)
8.01/2.77	     k(f(x),y,x) -> f(x)
8.01/2.77	   Matrix Interpretation Processor: dim=1
8.01/2.77	    
8.01/2.77	    max_matrix:
8.01/2.77	     1
8.01/2.77	    interpretation:
8.01/2.77	     [k](x0, x1, x2) = x0 + x1 + x2 + 65,
8.01/2.77	     
8.01/2.77	     [g](x0) = x0 + 1,
8.01/2.77	     
8.01/2.77	     [h](x0) = x0,
8.01/2.77	     
8.01/2.77	     [f](x0) = x0 + 2,
8.01/2.77	     
8.01/2.77	     [a] = 2
8.01/2.77	    orientation:
8.01/2.77	     f(a()) = 4 >= 3 = g(h(a()))
8.01/2.77	     
8.01/2.77	     h(g(x)) = x + 1 >= x + 3 = g(h(f(x)))
8.01/2.77	     
8.01/2.77	     k(x,h(x),a()) = 2x + 67 >= x = h(x)
8.01/2.77	     
8.01/2.77	     k(f(x),y,x) = 2x + y + 67 >= x + 2 = f(x)
8.01/2.77	    problem:
8.01/2.77	     strict:
8.01/2.77	      h(g(x)) -> g(h(f(x)))
8.01/2.77	     weak:
8.01/2.77	      f(a()) -> g(h(a()))
8.01/2.77	      k(x,h(x),a()) -> h(x)
8.01/2.77	      k(f(x),y,x) -> f(x)
8.01/2.77	    Matrix Interpretation Processor: dim=5
8.01/2.77	     
8.01/2.77	     max_matrix:
8.01/2.77	      [1 1 1 1 1]
8.01/2.77	      [0 0 1 0 0]
8.01/2.77	      [0 0 0 1 1]
8.01/2.77	      [0 0 0 0 1]
8.01/2.77	      [0 0 0 0 0]
8.01/2.77	     interpretation:
8.01/2.77	                        [1 0 1 1 0]     [1 1 0 0 0]     [1 0 0 0 0]     [0]
8.01/2.77	                        [0 0 1 0 0]     [0 0 0 0 0]     [0 0 0 0 0]     [1]
8.01/2.77	      [k](x0, x1, x2) = [0 0 0 0 1]x0 + [0 0 0 0 1]x1 + [0 0 0 1 1]x2 + [1]
8.01/2.77	                        [0 0 0 0 0]     [0 0 0 0 0]     [0 0 0 0 1]     [0]
8.01/2.77	                        [0 0 0 0 0]     [0 0 0 0 0]     [0 0 0 0 0]     [0],
8.01/2.77	      
8.01/2.77	                [1 0 0 0 0]     [0]
8.01/2.77	                [0 0 0 0 0]     [1]
8.01/2.77	      [g](x0) = [0 0 0 0 1]x0 + [0]
8.01/2.77	                [0 0 0 0 1]     [1]
8.01/2.77	                [0 0 0 0 0]     [0],
8.01/2.77	      
8.01/2.77	                [1 1 1 1 0]     [1]
8.01/2.77	                [0 0 1 0 0]     [1]
8.01/2.77	      [h](x0) = [0 0 0 0 0]x0 + [1]
8.01/2.77	                [0 0 0 0 0]     [1]
8.01/2.77	                [0 0 0 0 0]     [0],
8.01/2.77	      
8.01/2.77	                [1 0 0 0 1]     [0]
8.01/2.77	                [0 0 0 0 0]     [1]
8.01/2.77	      [f](x0) = [0 0 0 0 0]x0 + [0]
8.01/2.77	                [0 0 0 0 1]     [0]
8.01/2.77	                [0 0 0 0 0]     [0],
8.01/2.77	      
8.01/2.77	            [0]
8.01/2.77	            [0]
8.01/2.77	      [a] = [0]
8.01/2.77	            [0]
8.01/2.77	            [1]
8.01/2.77	     orientation:
8.01/2.77	                [1 0 0 0 2]    [3]    [1 0 0 0 2]    [2]             
8.01/2.77	                [0 0 0 0 1]    [1]    [0 0 0 0 0]    [1]             
8.01/2.77	      h(g(x)) = [0 0 0 0 0]x + [1] >= [0 0 0 0 0]x + [0] = g(h(f(x)))
8.01/2.77	                [0 0 0 0 0]    [1]    [0 0 0 0 0]    [1]             
8.01/2.77	                [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]             
8.01/2.77	      
8.01/2.77	               [1]    [1]            
8.01/2.77	               [1]    [1]            
8.01/2.77	      f(a()) = [0] >= [0] = g(h(a()))
8.01/2.77	               [1]    [1]            
8.01/2.77	               [0]    [0]            
8.01/2.77	      
8.01/2.77	                      [2 1 3 2 0]    [2]    [1 1 1 1 0]    [1]       
8.01/2.77	                      [0 0 1 0 0]    [1]    [0 0 1 0 0]    [1]       
8.01/2.77	      k(x,h(x),a()) = [0 0 0 0 1]x + [2] >= [0 0 0 0 0]x + [1] = h(x)
8.01/2.77	                      [0 0 0 0 0]    [1]    [0 0 0 0 0]    [1]       
8.01/2.77	                      [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]       
8.01/2.77	      
8.01/2.77	                    [2 0 0 0 2]    [1 1 0 0 0]    [0]    [1 0 0 0 1]    [0]       
8.01/2.77	                    [0 0 0 0 0]    [0 0 0 0 0]    [1]    [0 0 0 0 0]    [1]       
8.01/2.77	      k(f(x),y,x) = [0 0 0 1 1]x + [0 0 0 0 1]y + [1] >= [0 0 0 0 0]x + [0] = f(x)
8.01/2.77	                    [0 0 0 0 1]    [0 0 0 0 0]    [0]    [0 0 0 0 1]    [0]       
8.01/2.77	                    [0 0 0 0 0]    [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]       
8.01/2.77	     problem:
8.01/2.77	      strict:
8.01/2.77	       
8.01/2.77	      weak:
8.01/2.77	       h(g(x)) -> g(h(f(x)))
8.01/2.77	       f(a()) -> g(h(a()))
8.01/2.77	       k(x,h(x),a()) -> h(x)
8.01/2.77	       k(f(x),y,x) -> f(x)
8.01/2.77	     Qed
8.01/2.78	EOF