Confluent directed acyclic graph
Yes, the "line" $u \to v \to w$ is trivially confluent, and so are the empty graph, the graph with a single node, and the "line" $u \to w$. In the case of a graph with a single node $v$ there is only one case to consider, with $v_1 = v_2 = v$. The common ancestor is then $v$ itself, and the common successor is also $v$.