diff --git a/colored_pentagon_reduction/example.py b/colored_pentagon_reduction/example.py
index 7d8e783..0ec18de 100644
--- a/colored_pentagon_reduction/example.py
+++ b/colored_pentagon_reduction/example.py
@@ -41,8 +41,8 @@ def operation_sequence_id(ops: list[Operation]) -> str:
     joined = "\n".join(op_to_transform_id(op) for op in ops)
     return hashlib.sha256(joined.encode()).hexdigest()
 
-def canonize_colored_graph(g: Graph, coloring: VertexColoring) -> ColoredGraphId:
-    """Mutate g and coloring to canonical labels and return a canonical ColoredGraphId"""
+def canonize_colored_graph(g: Graph, coloring: VertexColoring) -> tuple[Graph, VertexColoring, ColoredGraphId]:
+    """Return a new canonical graph, new canonical coloring, and a ColoredGraphId without mutating inputs"""
     canonical, cert = cast(
         tuple[Graph, dict[Any, int]],
         g.canonical_label(certificate=True),
@@ -55,34 +55,31 @@ def canonize_colored_graph(g: Graph, coloring: VertexColoring) -> ColoredGraphId
     for orig_v, canon_idx in cert.items():
         color_seq[canon_idx] = coloring[orig_v]
 
-    coloring.clear()
-    for canon_idx, color in enumerate(color_seq):
-        coloring[canon_idx] = color
+    canonical_coloring = {canon_idx: color for canon_idx, color in enumerate(color_seq)}
     coloring_id = base64.urlsafe_b64encode(bytes(color_seq)).decode()
-    g.relabel(cert)
-    return ColoredGraphId(graph_id=graph_id, coloring_id=coloring_id)
+    return canonical, canonical_coloring, ColoredGraphId(graph_id=graph_id, coloring_id=coloring_id)
 
 def save_colored_graph(g: Graph, coloring: VertexColoring) -> tuple[Graph, VertexColoring, ColoredGraphId]:
     """
-    Relabel g and coloring into canonical form, save to disk, and return both.
+    Canonize g and coloring, save to disk, and return the canonical forms with id.
     If already saved, load and return the cached graph.
     """
-    cid = canonize_colored_graph(g, coloring)
+    g_canon, canonical_coloring, cid = canonize_colored_graph(g, coloring)
     out_dir = DIR / "data" / "graphs" / cid['graph_id'] / cid['coloring_id']
     if (out_dir / "graph.sobj").exists():
         g_canon = cast(Graph, load(str(out_dir / 'graph')))
-        return g_canon, coloring, cid
-    g.is_planar(set_embedding=True, set_pos=True)
+        return g_canon, canonical_coloring, cid
+    g_canon.is_planar(set_embedding=True, set_pos=True)
     vertex_colors: defaultdict[str, list[Any]] = defaultdict(list)
-    for v, c in coloring.items():
+    for v, c in canonical_coloring.items():
         vertex_colors[PALETTE[c]].append(v)
     out_dir.mkdir(parents=True, exist_ok=True)
-    g.plot(
+    g_canon.plot(
         vertex_colors=dict(vertex_colors),
         title=f"graph: {cid['graph_id']} coloring: {cid['coloring_id']}",
     ).save(out_dir / 'graph.png')
-    save(g, str(out_dir / 'graph'))
-    return g, coloring, cid
+    save(g_canon, str(out_dir / 'graph'))
+    return g_canon, canonical_coloring, cid
 
 def _neighbors_form_cycle(g: Graph, v: Any) -> bool:
     """Return True if the neighbors of v induce a cycle in g."""