YES(?,O(n^2))
971.71/295.29	YES(?,O(n^2))
971.81/295.30	
971.81/295.30	Problem:
971.81/295.30	 a(a(x1)) -> c(b(x1))
971.81/295.30	 b(b(x1)) -> a(c(x1))
971.81/295.30	 c(c(x1)) -> b(a(x1))
971.81/295.30	
971.81/295.30	Proof:
971.81/295.30	 Complexity Transformation Processor:
971.81/295.30	  strict:
971.81/295.30	   a(a(x1)) -> c(b(x1))
971.81/295.30	   b(b(x1)) -> a(c(x1))
971.81/295.30	   c(c(x1)) -> b(a(x1))
971.81/295.30	  weak:
971.81/295.30	   
971.81/295.30	  Matrix Interpretation Processor: dim=1
971.81/295.30	   
971.81/295.30	   max_matrix:
971.81/295.30	    1
971.81/295.30	   interpretation:
971.81/295.30	    [c](x0) = x0 + 39,
971.81/295.30	    
971.81/295.30	    [b](x0) = x0 + 11,
971.81/295.30	    
971.81/295.30	    [a](x0) = x0 + 2
971.81/295.30	   orientation:
971.81/295.30	    a(a(x1)) = x1 + 4 >= x1 + 50 = c(b(x1))
971.81/295.30	    
971.81/295.30	    b(b(x1)) = x1 + 22 >= x1 + 41 = a(c(x1))
971.81/295.30	    
971.81/295.30	    c(c(x1)) = x1 + 78 >= x1 + 13 = b(a(x1))
971.81/295.30	   problem:
971.81/295.30	    strict:
971.81/295.30	     a(a(x1)) -> c(b(x1))
971.81/295.30	     b(b(x1)) -> a(c(x1))
971.81/295.30	    weak:
971.81/295.30	     c(c(x1)) -> b(a(x1))
971.81/295.30	   Matrix Interpretation Processor: dim=1
971.81/295.30	    
971.81/295.30	    max_matrix:
971.81/295.30	     1
971.81/295.30	    interpretation:
971.81/295.30	     [c](x0) = x0 + 128,
971.81/295.30	     
971.81/295.30	     [b](x0) = x0 + 24,
971.81/295.30	     
971.81/295.30	     [a](x0) = x0 + 136
971.81/295.30	    orientation:
971.81/295.30	     a(a(x1)) = x1 + 272 >= x1 + 152 = c(b(x1))
971.81/295.30	     
971.81/295.30	     b(b(x1)) = x1 + 48 >= x1 + 264 = a(c(x1))
971.81/295.30	     
971.81/295.30	     c(c(x1)) = x1 + 256 >= x1 + 160 = b(a(x1))
971.81/295.30	    problem:
971.81/295.30	     strict:
971.81/295.30	      b(b(x1)) -> a(c(x1))
971.81/295.30	     weak:
971.81/295.30	      a(a(x1)) -> c(b(x1))
971.81/295.30	      c(c(x1)) -> b(a(x1))
971.81/295.30	    Matrix Interpretation Processor: dim=4
971.81/295.30	     
971.81/295.30	     max_matrix:
971.81/295.30	      [1 1 1 1]
971.81/295.30	      [0 0 0 1]
971.81/295.30	      [0 1 0 0]
971.81/295.30	      [0 0 1 0]
971.81/295.30	     interpretation:
971.81/295.30	                [1 0 0 1]     [0]
971.81/295.30	                [0 0 0 1]     [0]
971.81/295.30	      [c](x0) = [0 0 0 0]x0 + [0]
971.81/295.30	                [0 0 1 0]     [1],
971.81/295.30	      
971.81/295.30	                [1 1 0 0]     [0]
971.81/295.30	                [0 0 0 1]     [1]
971.81/295.30	      [b](x0) = [0 1 0 0]x0 + [0]
971.81/295.30	                [0 0 0 0]     [0],
971.81/295.30	      
971.81/295.30	                [1 0 1 0]     [0]
971.81/295.30	                [0 0 0 0]     [0]
971.81/295.30	      [a](x0) = [0 1 0 0]x0 + [1]
971.81/295.30	                [0 0 1 0]     [0]
971.81/295.30	     orientation:
971.81/295.30	                 [1 1 0 1]     [1]    [1 0 0 1]     [0]           
971.81/295.30	                 [0 0 0 0]     [1]    [0 0 0 0]     [0]           
971.81/295.30	      b(b(x1)) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 + [1] = a(c(x1))
971.81/295.30	                 [0 0 0 0]     [0]    [0 0 0 0]     [0]           
971.81/295.30	      
971.81/295.30	                 [1 1 1 0]     [1]    [1 1 0 0]     [0]           
971.81/295.30	                 [0 0 0 0]     [0]    [0 0 0 0]     [0]           
971.81/295.30	      a(a(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [0] = c(b(x1))
971.81/295.30	                 [0 1 0 0]     [1]    [0 1 0 0]     [1]           
971.81/295.30	      
971.81/295.30	                 [1 0 1 1]     [1]    [1 0 1 0]     [0]           
971.81/295.30	                 [0 0 1 0]     [1]    [0 0 1 0]     [1]           
971.81/295.30	      c(c(x1)) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = b(a(x1))
971.81/295.30	                 [0 0 0 0]     [1]    [0 0 0 0]     [0]           
971.81/295.30	     problem:
971.81/295.30	      strict:
971.81/295.30	       
971.81/295.30	      weak:
971.81/295.30	       b(b(x1)) -> a(c(x1))
971.81/295.30	       a(a(x1)) -> c(b(x1))
971.81/295.30	       c(c(x1)) -> b(a(x1))
971.81/295.30	     Qed
971.81/295.30	EOF