diff --git a/src/forest.cpp b/src/forest.cpp
index 334d848c1..b25622318 100644
--- a/src/forest.cpp
+++ b/src/forest.cpp
@@ -68,21 +68,46 @@ Constructs a forest with *n* nodes, that is initialised so that the
 :param n: the number of nodes, defaults to ``0``.
 :type n: int
 )pbdoc");
-    thing.def(py::init([](std::vector<size_t> const& parents,
-                          std::vector<size_t> const& labels) {
-                return make<Forest>(parents, labels);
-              }),
-              py::arg("parents"),
-              py::arg("labels"),
-              R"pbdoc(
-:sig=(self: Forest, parents:List[int], labels:List[int]) -> None:
+    thing.def(
+        py::init(
+            [](std::vector<std::variant<Forest::node_type, Undefined>> const&
+                   parents,
+               std::vector<std::variant<Forest::node_type, Undefined>> const&
+                   labels) {
+              using node_type = Forest::node_type;
+              std::vector<node_type> parents_as_ints;
+              std::vector<node_type> labels_as_ints;
+              for (auto const& val : parents) {
+                if (std::holds_alternative<node_type>(val)) {
+                  parents_as_ints.push_back(std::get<0>(val));
+                } else {
+                  parents_as_ints.push_back(
+                      static_cast<node_type>(std::get<1>(val)));
+                }
+              }
+              // TODO there's something like this in transf.cpp too, we should
+              // avoid code dupl
+              for (auto const& val : labels) {
+                if (std::holds_alternative<node_type>(val)) {
+                  labels_as_ints.push_back(std::get<0>(val));
+                } else {
+                  labels_as_ints.push_back(
+                      static_cast<node_type>(std::get<1>(val)));
+                }
+              }
+              return make<Forest>(parents_as_ints, labels_as_ints);
+            }),
+        py::arg("parents"),
+        py::arg("labels"),
+        R"pbdoc(
+:sig=(self: Forest, parents:List[int | Undefined], labels:List[int | Undefined]) -> None:
 
 Construct a :any:`Forest` from list of *parents* and *labels*.
 
 :param parent: the list of parents of nodes.
-:type parent: List[int]
+:type parent: List[int | Undefined]
 :param labels: the list of edge labels.
-:type labels: List[int]
+:type labels: List[int | Undefined]
 
 :raises LibsemigroupsError:
   if  *parent* and *labels* have different sizes;
@@ -138,7 +163,8 @@ the same state as if it had just be constructed as ``Forest(n)``.
 )pbdoc");
     thing.def(
         "label",
-        [](Forest const& self, size_t i) -> std::variant<size_t, Undefined> {
+        [](Forest const&     self,
+           Forest::node_type i) -> std::variant<Forest::node_type, Undefined> {
           if (self.label(i) != UNDEFINED) {
             return {self.label(i)};
           }
@@ -168,8 +194,9 @@ Returns the label of the edge from a node to its parent.
 )pbdoc");
     thing.def(
         "labels",
-        [](Forest const& self) -> std::vector<std::variant<size_t, Undefined>> {
-          std::vector<std::variant<size_t, Undefined>> result;
+        [](Forest const& self)
+            -> std::vector<std::variant<Forest::node_type, Undefined>> {
+          std::vector<std::variant<Forest::node_type, Undefined>> result;
           for (auto node : self.labels()) {
             if (node != UNDEFINED) {
               result.emplace_back(node);
@@ -213,7 +240,8 @@ in the forest.
     thing.def(py::self == py::self, py::arg("that"));
     thing.def(
         "parent",
-        [](Forest const& self, size_t i) -> std::variant<size_t, Undefined> {
+        [](Forest const&     self,
+           Forest::node_type i) -> std::variant<Forest::node_type, Undefined> {
           if (self.parent(i) != UNDEFINED) {
             return {self.parent(i)};
           }
@@ -242,8 +270,9 @@ Returns the parent of a node.
 )pbdoc");
     thing.def(
         "parents",
-        [](Forest const& self) -> std::vector<std::variant<size_t, Undefined>> {
-          std::vector<std::variant<size_t, Undefined>> result;
+        [](Forest const& self)
+            -> std::vector<std::variant<Forest::node_type, Undefined>> {
+          std::vector<std::variant<Forest::node_type, Undefined>> result;
           for (auto node : self.parents()) {
             if (node != UNDEFINED) {
               result.emplace_back(node);
diff --git a/src/todd-coxeter.cpp b/src/todd-coxeter.cpp
index 3a3746ed3..7c80e20d8 100644
--- a/src/todd-coxeter.cpp
+++ b/src/todd-coxeter.cpp
@@ -62,7 +62,7 @@ execution of (any version of) the Todd-Coxeter algorithm.
    >>> presentation.add_rule(p, "aa", "")
    >>> presentation.add_rule(p, "a", "b")
    >>> tc.init(congruence_kind.onesided, p).strategy(options.strategy.felsch)
-   <ToddCoxeter over <monoid presentation with 2 letters, 2 rules, and length 4> with 1/1 active/nodes>
+   <1-sided ToddCoxeter over <monoid presentation with 2 letters, 2 rules, and length 4> with 0 gen. pairs + 1 node>
    >>> tc.number_of_classes()
    2
    >>> tc.contains("aaaa", "aa")
@@ -84,11 +84,11 @@ execution of (any version of) the Todd-Coxeter algorithm.
    >>> presentation.add_rule(p, "bcbdbcbdbcbdbcbdbcbdbcbdbcbdbcbd", "a");
    >>> tc = ToddCoxeter(congruence_kind.twosided, p)
    >>> tc.strategy(options.strategy.hlt).lookahead_extent(options.lookahead_extent.partial).save(False)
-   <ToddCoxeter over <semigroup presentation with 4 letters, 12 rules, and length 79> with 1/2 active/nodes>
+   <2-sided ToddCoxeter over <semigroup presentation with 4 letters, 12 rules, and length 79> with 0 gen. pairs + 1 node>
    >>> tc.number_of_classes()
    10752
    >>> tc
-   <ToddCoxeter over <semigroup presentation with 4 letters, 12 rules, and length 79> with 10753/2097153 active/nodes>
+   <2-sided ToddCoxeter over <semigroup presentation with 4 letters, 12 rules, and length 79> with 0 gen. pairs + 10,753 nodes>
    >>> tc.word_graph()
    <WordGraph with 10,753 nodes, 43,012 edges, & out-degree 4>
    >>> it = todd_coxeter.normal_forms(tc)
diff --git a/tests/test_word_graph.py b/tests/test_word_graph.py
index 5e39b3798..524b8c153 100644
--- a/tests/test_word_graph.py
+++ b/tests/test_word_graph.py
@@ -239,7 +239,7 @@ def test_spanning_tree(word_graph_fixture):
     wg1, _ = word_graph_fixture
 
     assert word_graph.spanning_tree(wg1, 0) == Forest(
-        [int(UNDEFINED), 0, 1, 2, 3], [int(UNDEFINED), 0, 0, 0, 0]
+        [UNDEFINED, 0, 1, 2, 3], [UNDEFINED, 0, 0, 0, 0]
     )
 
     f = Forest(0)
@@ -305,10 +305,7 @@ def test_joiner(word_graph_fixture):
 def test_str(word_graph_fixture):
     wg1, wg2 = word_graph_fixture
     assert str(wg1) == "WordGraph(5, [[1], [2], [3], [4], [0]])"
-    assert (
-        str(wg2)
-        == "WordGraph(10, [[1], [2], [3], [4], [0], [6], [7], [8], [9], [5]])"
-    )
+    assert str(wg2) == "WordGraph(10, [[1], [2], [3], [4], [0], [6], [7], [8], [9], [5]])"
 
 
 def test_copy(word_graph_fixture):