Is the triforce graph an sp-graph? Consider the examples and the statements

where a series-parallel graph (sp-graph) is defined inductively with respect to series composition and parallel composition of other sp-graphs or of $K_2$. I guess the former is not an sp-graph but I am unable to prove this, and I am also unable to prove the latter not to be an sp-graph.
Is the triforce graph a sp-graph, and how do you prove it?
 A: Consider this alternative characterization of series-parallel graphs paraphrased from Wikipedia.

Definition: A graph is an sp-graph if it may be turned into $K_2$ by a sequence of the following operations:

*

*Replacement of a pair of parallel edges with a single edge that connects their common endpoints.


*Replacement of a pair of edges incident to a vertex of degree $2$ other than the initial vertex or terminal vertex with a single edge.

Note that this characterization of sp-graphs is basically just the inductive definition considered backwards.
The $K_4$ is not an sp-graph because (1) there are no parallel edges to reduce, and (2) given any choice of initial and terminal vertices, there are no degree $2$ vertices to replace with an edge, so the algorithm given by this definition terminates.
The triforce, though, is an sp-graph. If you take any two of the degree-$4$ vertices as your initial and terminal vertex, you can apply (2) to the three degree-$2$ vertices, then apply (1) to the three resulting parallel edges to arrive at a triangle. Then you apply (2) once more and (1) once more and you have $K_2$.
