YES(?,O(n^2))
10.52/6.37	YES(?,O(n^2))
10.52/6.38	
10.52/6.38	Problem:
10.52/6.38	 implies(not(x),y) -> or(x,y)
10.52/6.38	 implies(not(x),or(y,z)) -> implies(y,or(x,z))
10.52/6.38	 implies(x,or(y,z)) -> or(y,implies(x,z))
10.52/6.38	
10.52/6.38	Proof:
10.52/6.38	 Complexity Transformation Processor:
10.52/6.38	  strict:
10.52/6.38	   implies(not(x),y) -> or(x,y)
10.52/6.38	   implies(not(x),or(y,z)) -> implies(y,or(x,z))
10.52/6.38	   implies(x,or(y,z)) -> or(y,implies(x,z))
10.52/6.38	  weak:
10.52/6.38	   
10.52/6.38	  Matrix Interpretation Processor: dim=1
10.52/6.38	   
10.52/6.38	   max_matrix:
10.52/6.38	    1
10.52/6.38	   interpretation:
10.52/6.38	    [or](x0, x1) = x0 + x1 + 64,
10.52/6.38	    
10.52/6.38	    [implies](x0, x1) = x0 + x1,
10.52/6.38	    
10.52/6.38	    [not](x0) = x0 + 128
10.52/6.38	   orientation:
10.52/6.38	    implies(not(x),y) = x + y + 128 >= x + y + 64 = or(x,y)
10.52/6.38	    
10.52/6.38	    implies(not(x),or(y,z)) = x + y + z + 192 >= x + y + z + 64 = implies(y,or(x,z))
10.52/6.38	    
10.52/6.38	    implies(x,or(y,z)) = x + y + z + 64 >= x + y + z + 64 = or(y,implies(x,z))
10.52/6.38	   problem:
10.52/6.38	    strict:
10.52/6.38	     implies(x,or(y,z)) -> or(y,implies(x,z))
10.52/6.38	    weak:
10.52/6.38	     implies(not(x),y) -> or(x,y)
10.52/6.38	     implies(not(x),or(y,z)) -> implies(y,or(x,z))
10.52/6.38	   Matrix Interpretation Processor: dim=5
10.52/6.38	    
10.52/6.38	    max_matrix:
10.52/6.38	     [1 1 1 1 0]
10.52/6.38	     [0 1 1 0 0]
10.52/6.38	     [0 0 0 0 0]
10.52/6.38	     [0 0 0 0 1]
10.52/6.38	     [0 0 0 0 0]
10.52/6.38	    interpretation:
10.52/6.38	                    [1 0 0 0 0]     [1 0 0 0 0]     [1]
10.52/6.38	                    [0 1 1 0 0]     [0 1 0 0 0]     [1]
10.52/6.38	     [or](x0, x1) = [0 0 0 0 0]x0 + [0 0 0 0 0]x1 + [0]
10.52/6.38	                    [0 0 0 0 0]     [0 0 0 0 1]     [0]
10.52/6.38	                    [0 0 0 0 0]     [0 0 0 0 0]     [0],
10.52/6.38	     
10.52/6.38	                         [1 0 0 0 0]     [1 1 0 0 0]     [1]
10.52/6.38	                         [0 1 1 0 0]     [0 1 0 0 0]     [0]
10.52/6.38	     [implies](x0, x1) = [0 0 0 0 0]x0 + [0 0 0 0 0]x1 + [0]
10.52/6.38	                         [0 0 0 0 0]     [0 0 0 0 1]     [1]
10.52/6.38	                         [0 0 0 0 0]     [0 0 0 0 0]     [1],
10.52/6.38	     
10.52/6.38	                 [1 1 1 1 0]     [0]
10.52/6.38	                 [0 1 1 0 0]     [1]
10.52/6.38	     [not](x0) = [0 0 0 0 0]x0 + [1]
10.52/6.38	                 [0 0 0 0 1]     [0]
10.52/6.38	                 [0 0 0 0 0]     [0]
10.52/6.38	    orientation:
10.52/6.38	                          [1 0 0 0 0]    [1 1 1 0 0]    [1 1 0 0 0]    [3]    [1 0 0 0 0]    [1 0 0 0 0]    [1 1 0 0 0]    [2]                     
10.52/6.38	                          [0 1 1 0 0]    [0 1 1 0 0]    [0 1 0 0 0]    [1]    [0 1 1 0 0]    [0 1 1 0 0]    [0 1 0 0 0]    [1]                     
10.52/6.38	     implies(x,or(y,z)) = [0 0 0 0 0]x + [0 0 0 0 0]y + [0 0 0 0 0]z + [0] >= [0 0 0 0 0]x + [0 0 0 0 0]y + [0 0 0 0 0]z + [0] = or(y,implies(x,z))
10.52/6.38	                          [0 0 0 0 0]    [0 0 0 0 0]    [0 0 0 0 0]    [1]    [0 0 0 0 0]    [0 0 0 0 0]    [0 0 0 0 0]    [1]                     
10.52/6.38	                          [0 0 0 0 0]    [0 0 0 0 0]    [0 0 0 0 0]    [1]    [0 0 0 0 0]    [0 0 0 0 0]    [0 0 0 0 0]    [0]                     
10.52/6.38	     
10.52/6.38	                         [1 1 1 1 0]    [1 1 0 0 0]    [1]    [1 0 0 0 0]    [1 0 0 0 0]    [1]          
10.52/6.38	                         [0 1 1 0 0]    [0 1 0 0 0]    [2]    [0 1 1 0 0]    [0 1 0 0 0]    [1]          
10.52/6.38	     implies(not(x),y) = [0 0 0 0 0]x + [0 0 0 0 0]y + [0] >= [0 0 0 0 0]x + [0 0 0 0 0]y + [0] = or(x,y)
10.52/6.38	                         [0 0 0 0 0]    [0 0 0 0 1]    [1]    [0 0 0 0 0]    [0 0 0 0 1]    [0]          
10.52/6.38	                         [0 0 0 0 0]    [0 0 0 0 0]    [1]    [0 0 0 0 0]    [0 0 0 0 0]    [0]          
10.52/6.38	     
10.52/6.38	                               [1 1 1 1 0]    [1 1 1 0 0]    [1 1 0 0 0]    [3]    [1 1 1 0 0]    [1 0 0 0 0]    [1 1 0 0 0]    [3]                     
10.52/6.38	                               [0 1 1 0 0]    [0 1 1 0 0]    [0 1 0 0 0]    [3]    [0 1 1 0 0]    [0 1 1 0 0]    [0 1 0 0 0]    [1]                     
10.52/6.38	     implies(not(x),or(y,z)) = [0 0 0 0 0]x + [0 0 0 0 0]y + [0 0 0 0 0]z + [0] >= [0 0 0 0 0]x + [0 0 0 0 0]y + [0 0 0 0 0]z + [0] = implies(y,or(x,z))
10.52/6.38	                               [0 0 0 0 0]    [0 0 0 0 0]    [0 0 0 0 0]    [1]    [0 0 0 0 0]    [0 0 0 0 0]    [0 0 0 0 0]    [1]                     
10.52/6.38	                               [0 0 0 0 0]    [0 0 0 0 0]    [0 0 0 0 0]    [1]    [0 0 0 0 0]    [0 0 0 0 0]    [0 0 0 0 0]    [1]                     
10.52/6.38	    problem:
10.52/6.38	     strict:
10.52/6.38	      
10.52/6.38	     weak:
10.52/6.38	      implies(x,or(y,z)) -> or(y,implies(x,z))
10.52/6.38	      implies(not(x),y) -> or(x,y)
10.52/6.38	      implies(not(x),or(y,z)) -> implies(y,or(x,z))
10.52/6.38	    Qed
10.52/6.39	EOF