Wha's the meaning and significance of 'path' in BDDs or FDDs?

I read a paper, named Multilevel logic synthesis based on functional decision diagrams, which is about Functional Decision Diagrams(FDDs), that is a variant of Binary Decision Diagrams(BDDs). In this, a paragraph mentions 'path':

As an important result it is observed, that even with nearly the same number of nodes we get a reduction of the number of paths compared to BDD (see tab. 1). Since the number of paths equals the number of pi-terms of the canonical two-level RME, this means a reduction of the complexity in the function representation.

I guess 'path' means the number of roads from root to terminal in BDDs or FDDs.

For example:

The path of this example is 9(you can check this).

My question is what's the significance of this parameter or feature 'path'?

Yes, path is any single way from the root to a leaf. Roughly, the set of paths in a decision diagram can be seen as the minimum set of variables values that entirely describes the function.

For example, you can draw a decision diagram leaving ALL the variables and ALL the paths. You can see that some of them are redundant (maybe from a node both links go to the same node). In this case we are wasting memory.

The whole goal of decision diagrams is to represent a boolean function in the most compact and most efficient (operations wise) way possible. The authors are happy because they found a more compact way, don't know about efficiency.