Deduct by the rules for two schemes?

Questions
,
1

Consider the following code:

Input[1]: rules = {a -> b, b -> c, c -> x, b -> d, d -> y};a//.rules;
output[2]:x

In the above program, “b” respectively implies two variables “c” and “d”, and the two branches respectively go to the two terminal results “x” and “y”. But the program runs only one branch a->b->c->x,losing a->b->d->y. Is there any approach to run all elements of the set of rules, so that the output would be “x” and “y”?

2

Here is my not very elegant approach (I am curious to see other/better solutions):

a //. Permutations[rules] // Union
(*  Out:  {x,y}  *)
3

This solution is based on the contribution
how to get all leaves from a graph :

g = Graph[rules, VertexLabels -> Automatic];
vertices = VertexList[g];
leaves = Select[vertices, VertexOutDegree[g, #] === 0 &]

Using Graph offers the possibility to display the result:

HighlightGraph[g, Subgraph[g, leaves]]
4

So wonderful! Many thanks!

5

Excellent! Many thanks!