diff --git a/cotengra/interface.py b/cotengra/interface.py
index b026dd8..df95820 100644
--- a/cotengra/interface.py
+++ b/cotengra/interface.py
@@ -2,8 +2,9 @@
 
 import autoray as ar
 
-from .oe import get_path_fn, find_output_str
+from .oe import get_path_fn
 from .core import ContractionTree
+from .utils import find_output_str
 
 
 class Variadic:
diff --git a/cotengra/pathfinders/path_basic.py b/cotengra/pathfinders/path_basic.py
index 53794c7..b5034e5 100644
--- a/cotengra/pathfinders/path_basic.py
+++ b/cotengra/pathfinders/path_basic.py
@@ -331,7 +331,7 @@ def pop_node(self, i):
             try:
                 ix_nodes = self.edges[ix]
                 ix_nodes.pop(i, None)
-                if len(ix_nodes) == 1:
+                if len(ix_nodes) == 0:
                     del self.edges[ix]
             except KeyError:
                 # repeated index already removed
@@ -345,10 +345,19 @@ def add_node(self, legs):
         i = self.ssa
         self.ssa += 1
         self.nodes[i] = legs
-        for j, _ in legs:
-            self.edges.setdefault(j, {})[i] = None
+        for ix, _ in legs:
+            self.edges.setdefault(ix, {})[i] = None
         return i
 
+    def check(self):
+        """Check that the current graph is valid, useful for debugging."""
+        for node, legs in self.nodes.items():
+            for ix, _ in legs:
+                assert node in self.edges[ix]
+        for ix, ix_nodes in self.edges.items():
+            for node in ix_nodes:
+                assert ix in {jx for jx, _ in self.nodes[node]}
+
     def contract_nodes(self, i, j):
         """Contract the nodes ``i`` and ``j``, adding a new node to the graph
         and returning its index.
diff --git a/cotengra/utils.py b/cotengra/utils.py
index 3d876e6..6bd3475 100644
--- a/cotengra/utils.py
+++ b/cotengra/utils.py
@@ -1082,6 +1082,24 @@ def eq_to_inputs_output(eq):
     return inputs, output
 
 
+def inputs_output_to_eq(inputs, output):
+    """Convert an explicit list of inputs and output to a str einsum equation.
+
+    Parameters
+    ----------
+    inputs : list[list[str]]
+        The input terms.
+    output : list[str]
+        The output term.
+
+    Returns
+    -------
+    eq : str
+        The einsum equation.
+    """
+    return f"{','.join(map(''.join, inputs))}->{''.join(output)}"
+
+
 def make_rand_size_dict_from_inputs(inputs, d_min=2, d_max=3, seed=None):
     """Get a random size dictionary for a given set of inputs.
 
diff --git a/tests/test_compute.py b/tests/test_compute.py
index 56a872a..612655a 100644
--- a/tests/test_compute.py
+++ b/tests/test_compute.py
@@ -134,7 +134,7 @@ def test_rand_equation(
         seed=seed,
     )
     arrays = [np.random.normal(size=s) for s in shapes]
-    eq = ",".join(map("".join, inputs)) + "->" + "".join(output)
+    eq = ctg.utils.inputs_output_to_eq(inputs, output)
 
     path, info = oe.contract_path(eq, *arrays, optimize="greedy")
     if info.largest_intermediate > 2**20:
@@ -253,8 +253,7 @@ def test_contract_expression(
     sort_contraction_indices,
 ):
     inputs, output, shapes, size_dict = ctg.utils.lattice_equation([4, 8])
-
-    eq = f"{','.join(map(''.join, inputs))}->{''.join(output)}"
+    eq = ctg.utils.inputs_output_to_eq(inputs, output)
     arrays = [np.random.rand(*s) for s in shapes]
     x0 = oe.contract(eq, *arrays)
 
diff --git a/tests/test_paths_basic.py b/tests/test_paths_basic.py
index a72169b..578f523 100644
--- a/tests/test_paths_basic.py
+++ b/tests/test_paths_basic.py
@@ -121,7 +121,7 @@ def test_basic_rand(seed, which):
         d_max=3,
         seed=seed,
     )
-    eq = ",".join(map("".join, inputs)) + "->" + "".join(output)
+    eq = ctg.utils.inputs_output_to_eq(inputs, output)
 
     path = {
         "greedy": pb.optimize_greedy,
@@ -137,6 +137,27 @@ def test_basic_rand(seed, which):
     )
 
 
+@pytest.mark.parametrize("seed", range(10))
+@pytest.mark.parametrize("which", ["greedy", "optimal"])
+def test_basic_perverse(seed, which):
+    inputs, output, shapes, size_dict = ctg.utils.perverse_equation(
+        10, seed=seed
+    )
+    eq = ctg.utils.inputs_output_to_eq(inputs, output)
+    print(eq)
+    path = {
+        "greedy": pb.optimize_greedy,
+        "optimal": pb.optimize_optimal,
+    }[
+        which
+    ](inputs, output, size_dict)
+    tree = ctg.ContractionTree.from_path(inputs, output, size_dict, path=path)
+    arrays = [np.random.randn(*s) for s in shapes]
+    assert_allclose(
+        tree.contract(arrays), np.einsum(eq, *arrays, optimize=True)
+    )
+
+
 def test_optimal_lattice_eq():
     inputs, output, _, size_dict = ctg.utils.lattice_equation(
         [4, 5], d_max=3, seed=42