Before connecting any pairs of letters in figure 1 with a path, the state of the problem was CAca . The uppercase letters designate letters on the left side of the diagram, while lowercase letters indicate the opposite. Any adjacent pair whose elements differ in case is called an adjoining pair . After connecting the top a and c in the diagram with a two relator path, the new state is CBCa . As well as stating that a path was formed from a to c , it makes sense to say that in the state A and c were replaced by the derivative state BC .
Derivative states play a large role in the computer algorithm.
Notice that the path from a to c moves only along the top of the relators. This occurs by virtue of the top-down nature of the algorithm. So such a path from one letter to another is called a top path . Moreover all of the presentations considered in earnest were said to be efficient . These are the left and right graphs .