I recently came across the following problem which seems to fall in the context of graph rewriting problems:
Input: A graph $G=(V,E)$ with maximum degree 3, an edge $e_0 \in E$ and pairs of graphs $(A_1,B_1),\ldots,(A_k,B_k)$ where both $A_i$ and $B_i$ are subgraphs of the complete graph with vertex set $V$ and $A_i$ is isomorphic to $B_i$ for $i=1,\ldots,k$.
Question: Is there a sequence $a_1,\ldots,a_n$ such that successively replacing the subgraphs $A_{a_i}$ with $B_{a_i}$ in $G_{i-1}$ (where $G_0=G$) to obtain $G_i$ yields a graph $G_n$ with $e_0 \in E(G_n)$.
Note that one can only replace $A_{a_i}$ with $B_{a_i}$ in $G_{i-1}$ if $E(A_{a_i}) \subseteq E(G_{i-1})$.
Is anything about the complexity of this problem known (in particular is it NP-hard?).