diff --git a/pytensor/graph/basic.py b/pytensor/graph/basic.py
index fc85209236..42a117b690 100644
--- a/pytensor/graph/basic.py
+++ b/pytensor/graph/basic.py
@@ -1615,34 +1615,66 @@ def expand(o: Apply) -> List[Apply]:
     )
 
 
-def is_in_ancestors(l_apply: Apply, f_node: Apply) -> bool:
-    """Determine if `f_node` is in the graph given by `l_apply`.
+def is_in_ancestors(
+    l_apply: Apply,
+    f_apply: Union[Apply, Collection[Apply]],
+    *,
+    known_dependent: Optional[Set[Apply]] = None,
+    known_independent: Optional[Set[Apply]] = None,
+    eager=True,
+) -> bool:
+    """Determine if `f_apply` is in the graph given by (any of) `l_apply`.
 
     Parameters
     ----------
     l_apply : Apply
         The node to walk.
-    f_apply : Apply
+    f_apply : Union[Apply, Collection[Apply]]
         The node to find in `l_apply`.
+    known_dependent: Optional[Set[Apply]]
+        Cache information about intermediate Applys that depend on f_apply
+    known_independent: Optional[Set[Apply]]
+        Cache information about intermediate Applys that do not depend on f_apply
+    eager: bool
+        return on first match (True) or traverse the whole graph (False)
 
     Returns
     -------
     bool
 
     """
-    computed = set()
-    todo = [l_apply]
-    while todo:
-        cur = todo.pop()
-        if cur.outputs[0] in computed:
-            continue
-        if all(i in computed or i.owner is None for i in cur.inputs):
-            computed.update(cur.outputs)
-            if cur is f_node:
-                return True
+    if known_dependent is None:
+        known_dependent = set()
+    if known_independent is None:
+        known_independent = set()
+    if not isinstance(f_apply, Collection):
+        f_apply = {f_apply}
+    if l_apply in known_dependent:
+        return True
+    elif l_apply in f_apply:
+        known_dependent.add(l_apply)
+        return True
+    else:
+        search = (
+            is_in_ancestors(
+                inp.owner,
+                f_apply,
+                known_dependent=known_dependent,
+                known_independent=known_independent,
+                eager=eager,
+            )
+            for inp in l_apply.inputs
+            if inp.owner
+        )
+        if not eager:
+            dependent = any(list(search))
         else:
-            todo.append(cur)
-            todo.extend(i.owner for i in cur.inputs if i.owner)
+            dependent = any(search)
+        if dependent:
+            known_dependent.add(l_apply)
+            return True
+
+    known_independent.add(l_apply)
     return False
 
 
diff --git a/tests/graph/test_basic.py b/tests/graph/test_basic.py
index f9b4fed79a..b5f55c7f76 100644
--- a/tests/graph/test_basic.py
+++ b/tests/graph/test_basic.py
@@ -512,6 +512,48 @@ def test_is_in_ancestors():
     assert is_in_ancestors(o2.owner, o1.owner)
 
 
+def test_is_in_ancestors_complete():
+
+    r1, r2, r3 = MyVariable(1), MyVariable(2), MyVariable(3)
+    o0 = MyOp(r2, r2)
+    o1 = MyOp(r1, r2)
+    o1.name = "o1"
+    o2 = MyOp(r3, o1)
+    o2.name = "o2"
+    o3 = MyOp(o2, o0)
+    o3.name = "o3"
+    dependent = set()
+    independent = set()
+    assert is_in_ancestors(
+        o3.owner,
+        o1.owner,
+        known_dependent=dependent,
+        known_independent=independent,
+        # o0 should not fall into independent with
+        # eager=True default
+        # because it is the second input in o3
+    )
+    assert o1.owner in dependent
+    assert o2.owner in dependent
+    assert o3.owner in dependent
+    assert o0.owner not in independent
+    dependent = set()
+    independent = set()
+    assert is_in_ancestors(
+        o3.owner,
+        o1.owner,
+        known_dependent=dependent,
+        known_independent=independent,
+        # o0 should not fall into independent with
+        eager=False
+        # because it is supposed to be the complete traverse
+    )
+    assert o1.owner in dependent
+    assert o2.owner in dependent
+    assert o3.owner in dependent
+    assert o0.owner in independent
+
+
 @pytest.mark.xfail(reason="Not implemented")
 def test_io_connection_pattern():
     raise AssertionError()