YES(?,O(n^2))
10.43/6.52	YES(?,O(n^2))
10.43/6.52	
10.43/6.52	Problem:
10.43/6.52	 implies(not(x),y) -> or(x,y)
10.43/6.52	 implies(not(x),or(y,z)) -> implies(y,or(x,z))
10.43/6.52	 implies(x,or(y,z)) -> or(y,implies(x,z))
10.43/6.52	
10.43/6.52	Proof:
10.43/6.52	 Complexity Transformation Processor:
10.43/6.52	  strict:
10.43/6.52	   implies(not(x),y) -> or(x,y)
10.43/6.52	   implies(not(x),or(y,z)) -> implies(y,or(x,z))
10.43/6.52	   implies(x,or(y,z)) -> or(y,implies(x,z))
10.43/6.52	  weak:
10.43/6.52	   
10.43/6.52	  Matrix Interpretation Processor: dim=1
10.43/6.52	   
10.43/6.52	   max_matrix:
10.43/6.52	    1
10.43/6.52	   interpretation:
10.43/6.52	    [or](x0, x1) = x0 + x1 + 64,
10.43/6.52	    
10.43/6.52	    [implies](x0, x1) = x0 + x1,
10.43/6.52	    
10.43/6.52	    [not](x0) = x0 + 128
10.43/6.52	   orientation:
10.43/6.52	    implies(not(x),y) = x + y + 128 >= x + y + 64 = or(x,y)
10.43/6.52	    
10.43/6.52	    implies(not(x),or(y,z)) = x + y + z + 192 >= x + y + z + 64 = implies(y,or(x,z))
10.43/6.52	    
10.43/6.52	    implies(x,or(y,z)) = x + y + z + 64 >= x + y + z + 64 = or(y,implies(x,z))
10.43/6.52	   problem:
10.43/6.52	    strict:
10.43/6.52	     implies(x,or(y,z)) -> or(y,implies(x,z))
10.43/6.52	    weak:
10.43/6.52	     implies(not(x),y) -> or(x,y)
10.43/6.52	     implies(not(x),or(y,z)) -> implies(y,or(x,z))
10.43/6.52	   Matrix Interpretation Processor: dim=4
10.43/6.52	    
10.43/6.52	    max_matrix:
10.43/6.52	     [1 0 1 1]
10.43/6.52	     [0 0 1 0]
10.43/6.52	     [0 0 1 1]
10.43/6.52	     [0 0 0 0]
10.43/6.52	    interpretation:
10.43/6.52	                    [1 0 0 1]     [1 0 0 0]     [0]
10.43/6.52	                    [0 0 0 0]     [0 0 1 0]     [0]
10.43/6.52	     [or](x0, x1) = [0 0 0 0]x0 + [0 0 1 1]x1 + [0]
10.43/6.52	                    [0 0 0 0]     [0 0 0 0]     [1],
10.43/6.52	     
10.43/6.52	                         [1 0 0 1]     [1 0 1 1]     [0]
10.43/6.52	                         [0 0 0 0]     [0 0 1 0]     [1]
10.43/6.52	     [implies](x0, x1) = [0 0 0 0]x0 + [0 0 1 1]x1 + [1]
10.43/6.52	                         [0 0 0 0]     [0 0 0 0]     [1],
10.43/6.52	     
10.43/6.52	                 [1 0 1 1]     [1]
10.43/6.52	                 [0 0 0 0]     [0]
10.43/6.52	     [not](x0) = [0 0 0 0]x0 + [0]
10.43/6.52	                 [0 0 0 0]     [1]
10.43/6.52	    orientation:
10.43/6.52	                          [1 0 0 1]    [1 0 0 1]    [1 0 1 1]    [1]    [1 0 0 1]    [1 0 0 1]    [1 0 1 1]    [0]                     
10.43/6.52	                          [0 0 0 0]    [0 0 0 0]    [0 0 1 1]    [1]    [0 0 0 0]    [0 0 0 0]    [0 0 1 1]    [1]                     
10.43/6.52	     implies(x,or(y,z)) = [0 0 0 0]x + [0 0 0 0]y + [0 0 1 1]z + [2] >= [0 0 0 0]x + [0 0 0 0]y + [0 0 1 1]z + [2] = or(y,implies(x,z))
10.43/6.52	                          [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]    [1]                     
10.43/6.52	     
10.43/6.52	                         [1 0 1 1]    [1 0 1 1]    [2]    [1 0 0 1]    [1 0 0 0]    [0]          
10.43/6.52	                         [0 0 0 0]    [0 0 1 0]    [1]    [0 0 0 0]    [0 0 1 0]    [0]          
10.43/6.52	     implies(not(x),y) = [0 0 0 0]x + [0 0 1 1]y + [1] >= [0 0 0 0]x + [0 0 1 1]y + [0] = or(x,y)
10.43/6.52	                         [0 0 0 0]    [0 0 0 0]    [1]    [0 0 0 0]    [0 0 0 0]    [1]          
10.43/6.52	     
10.43/6.52	                               [1 0 1 1]    [1 0 0 1]    [1 0 1 1]    [3]    [1 0 0 1]    [1 0 0 1]    [1 0 1 1]    [1]                     
10.43/6.52	                               [0 0 0 0]    [0 0 0 0]    [0 0 1 1]    [1]    [0 0 0 0]    [0 0 0 0]    [0 0 1 1]    [1]                     
10.43/6.52	     implies(not(x),or(y,z)) = [0 0 0 0]x + [0 0 0 0]y + [0 0 1 1]z + [2] >= [0 0 0 0]x + [0 0 0 0]y + [0 0 1 1]z + [2] = implies(y,or(x,z))
10.43/6.52	                               [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]    [1]                     
10.43/6.52	    problem:
10.43/6.52	     strict:
10.43/6.52	      
10.43/6.52	     weak:
10.43/6.52	      implies(x,or(y,z)) -> or(y,implies(x,z))
10.43/6.52	      implies(not(x),y) -> or(x,y)
10.43/6.52	      implies(not(x),or(y,z)) -> implies(y,or(x,z))
10.43/6.52	    Qed
10.43/6.53	EOF