diff --git a/causallearn/search/ConstraintBased/FCI.py b/causallearn/search/ConstraintBased/FCI.py
index 2738d769..ff3f92d0 100644
--- a/causallearn/search/ConstraintBased/FCI.py
+++ b/causallearn/search/ConstraintBased/FCI.py
@@ -2,7 +2,7 @@
 
 import warnings
 from queue import Queue
-from typing import List, Set, Tuple, Dict
+from typing import List, Set, Tuple, Dict, Generator
 from numpy import ndarray
 
 from causallearn.graph.Edge import Edge
@@ -17,6 +17,19 @@
 from causallearn.utils.PCUtils.BackgroundKnowledge import BackgroundKnowledge
 from itertools import combinations
 
+def is_uncovered_path(nodes: List[Node], G: Graph) -> bool:
+        """
+        Determines whether the given path is an uncovered path in this graph.
+
+        A path is an uncovered path if no two nonconsecutive nodes (Vi-1 and Vi+1) in the path are
+        adjacent.
+        """
+        for i in range(len(nodes) - 2):
+            if G.is_adjacent_to(nodes[i], nodes[i + 2]):
+                return False
+        return True
+
+
 def traverseSemiDirected(node: Node, edge: Edge) -> Node | None:
     if node == edge.get_node1():
         if edge.get_endpoint1() == Endpoint.TAIL or edge.get_endpoint1() == Endpoint.CIRCLE:
@@ -26,8 +39,17 @@ def traverseSemiDirected(node: Node, edge: Edge) -> Node | None:
             return edge.get_node1()
     return None
 
+def traverseCircle(node: Node, edge: Edge) -> Node | None:
+    if node == edge.get_node1():
+        if edge.get_endpoint1() == Endpoint.CIRCLE and edge.get_endpoint2() == Endpoint.CIRCLE:
+            return edge.get_node2()
+    elif node == edge.get_node2():
+        if edge.get_endpoint1() == Endpoint.CIRCLE and edge.get_endpoint2() == Endpoint.CIRCLE:
+            return edge.get_node1()
+    return None
+
 
-def existsSemiDirectedPath(node_from: Node, node_to: Node, G: Graph) -> bool:
+def existsSemiDirectedPath(node_from: Node, node_to: Node, G: Graph) -> bool: ## TODO: Now it does not detect whether the path is an uncovered path
     Q = Queue()
     V = set()
 
@@ -60,6 +82,42 @@ def existsSemiDirectedPath(node_from: Node, node_to: Node, G: Graph) -> bool:
 
     return False
 
+def GetUncoveredCirclePath(node_from: Node, node_to: Node, G: Graph, exclude_node: List[Node]) -> Generator[Node] | None:
+    Q = Queue()
+    V = set()
+
+    path = [node_from]
+
+    for node_u in G.get_adjacent_nodes(node_from):
+        if node_u in exclude_node:
+            continue
+        edge = G.get_edge(node_from, node_u)
+        node_c = traverseCircle(node_from, edge)
+
+        if node_c is None or node_c in exclude_node:
+            continue
+
+        if not V.__contains__(node_c):
+            V.add(node_c)
+            Q.put((node_c, path + [node_c]))
+
+    while not Q.empty():
+        node_t, path = Q.get_nowait()
+        if node_t == node_to and is_uncovered_path(path, G):
+            yield path
+
+        for node_u in G.get_adjacent_nodes(node_t):
+            edge = G.get_edge(node_t, node_u)
+            node_c = traverseCircle(node_t, edge)
+
+            if node_c is None or node_c in exclude_node:
+                continue
+
+            if not V.__contains__(node_c):
+                V.add(node_c)
+                Q.put((node_c, path + [node_c]))
+
+
 
 def existOnePathWithPossibleParents(previous, node_w: Node, node_x: Node, node_b: Node, graph: Graph) -> bool:
     if node_w == node_x:
@@ -371,6 +429,131 @@ def ruleR3(graph: Graph, sep_sets: Dict[Tuple[int, int], Set[int]], bk: Backgrou
                 changeFlag = True
     return changeFlag
 
+def ruleR5(graph: Graph, changeFlag: bool,
+           verbose: bool = False) -> bool:
+    """
+    Rule R5 of the FCI algorithm. 
+    by Jiji Zhang, 2008, "On the completeness of orientation rules for causal discovery in the presence of latent confounders and selection bias"]
+
+    This function orients any edge that is part of an uncovered circle path between two nodes A and B,
+    if such a path exists. The path must start and end with a circle edge and must be uncovered, i.e. the
+    nodes on the path must not be adjacent to A or B. The orientation of the edges on the path is set to
+    double tail.
+    """
+    nodes = graph.get_nodes()
+    def orient_on_path_helper(path, node_A, node_B):
+        # orient A - C, D - B
+        edge = graph.get_edge(node_A, path[0])
+        graph.remove_edge(edge)
+        graph.add_edge(Edge(node_A, path[0], Endpoint.TAIL, Endpoint.TAIL))
+
+        edge = graph.get_edge(node_B, path[-1])
+        graph.remove_edge(edge)
+        graph.add_edge(Edge(node_B, path[-1], Endpoint.TAIL, Endpoint.TAIL))
+        if verbose:
+            print("Orienting edge A - C (Double tail): " + graph.get_edge(node_A, path[0]).__str__())
+            print("Orienting edge B - D (Double tail): " + graph.get_edge(node_B, path[-1]).__str__())
+
+        # orient everything on the path to both tails
+        for i in range(len(path) - 1):
+            edge = graph.get_edge(path[i], path[i + 1])
+            graph.remove_edge(edge)
+            graph.add_edge(Edge(path[i], path[i + 1], Endpoint.TAIL, Endpoint.TAIL))
+            if verbose:
+                print("Orienting edge (Double tail): " + graph.get_edge(path[i], path[i + 1]).__str__())
+    
+    for node_B in nodes:
+        intoBCircles = graph.get_nodes_into(node_B, Endpoint.CIRCLE)
+
+        for node_A in intoBCircles:
+            found_paths_between_AB = []
+            if graph.get_endpoint(node_B, node_A) != Endpoint.CIRCLE:
+                continue
+            else:
+                # Check if there is an uncovered circle path between A and B (A o-o C ..  D o-o B)
+                # s.t. A is not adjacent to D and B is not adjacent to C
+                a_node_idx = graph.node_map[node_A]
+                b_node_idx = graph.node_map[node_B]
+                a_adj_nodes = graph.get_adjacent_nodes(node_A)
+                b_adj_nodes = graph.get_adjacent_nodes(node_B)
+                
+                # get the adjacent nodes with circle edges of A and B
+                a_circle_adj_nodes_set = [node for node in a_adj_nodes if graph.node_map[node] != a_node_idx and graph.node_map[node]!= b_node_idx
+                                            and graph.get_endpoint(node, node_A) == Endpoint.CIRCLE and graph.get_endpoint(node_A, node) == Endpoint.CIRCLE]
+                b_circle_adj_nodes_set = [node for node in b_adj_nodes if graph.node_map[node] != a_node_idx and graph.node_map[node]!= b_node_idx 
+                                          and graph.get_endpoint(node, node_B) == Endpoint.CIRCLE and graph.get_endpoint(node_B, node) == Endpoint.CIRCLE]
+
+                #  get the adjacent nodes with circle edges of A and B that is non adjacent to B and A, respectively
+                for node_C in a_circle_adj_nodes_set:
+                    if graph.is_adjacent_to(node_B, node_C):
+                        continue
+                    for node_D in b_circle_adj_nodes_set:
+                        if graph.is_adjacent_to(node_A, node_D):
+                            continue
+                        paths = GetUncoveredCirclePath(node_from=node_C, node_to=node_D, G=graph, exclude_node=[node_A, node_B]) # get the uncovered circle path between C and D, excluding A and B
+                        found_paths_between_AB.append(paths)
+
+                # Orient the uncovered circle path between A and B
+                for paths in found_paths_between_AB:                    
+                    for path in paths:
+                        changeFlag = True
+                        if verbose:
+                            print("Find uncovered circle path between A and B: " + graph.get_edge(node_A, node_B).__str__())
+                        edge = graph.get_edge(node_A, node_B)
+                        graph.remove_edge(edge)
+                        graph.add_edge(Edge(node_A, node_B, Endpoint.TAIL, Endpoint.TAIL))
+                        orient_on_path_helper(path, node_A, node_B)
+
+    return changeFlag
+
+def ruleR6(graph: Graph, changeFlag: bool,
+           verbose: bool = False) -> bool:
+    nodes = graph.get_nodes()
+
+    for node_B in nodes:
+        # Find A - B
+        intoBTails = graph.get_nodes_into(node_B, Endpoint.TAIL)
+        exist = False
+        for node_A in intoBTails:
+            if graph.get_endpoint(node_B, node_A) == Endpoint.TAIL:
+                exist = True
+        if not exist:
+            continue
+        # Find B o-*C
+        intoBCircles = graph.get_nodes_into(node_B, Endpoint.CIRCLE)
+        for node_C in intoBCircles:
+            changeFlag = True
+            edge = graph.get_edge(node_B, node_C)
+            graph.remove_edge(edge)
+            graph.add_edge(Edge(node_B, node_C, Endpoint.TAIL, edge.get_proximal_endpoint(node_C)))
+            if verbose:
+                print("Orienting edge by rule 6): " + graph.get_edge(node_B, node_C).__str__())
+
+    return changeFlag
+
+
+def ruleR7(graph: Graph, changeFlag: bool,
+           verbose: bool = False) -> bool:
+    nodes = graph.get_nodes()
+
+    for node_B in nodes:
+        # Find A -o B
+        intoBCircles = graph.get_nodes_into(node_B, Endpoint.CIRCLE)
+        node_A_list = [node for node in intoBCircles if graph.get_endpoint(node_B, node) == Endpoint.TAIL]
+
+        # Find B o-*C
+        for node_C in intoBCircles:
+            # pdb.set_trace()
+            for node_A in node_A_list:
+                # pdb.set_trace()
+                if not graph.is_adjacent_to(node_A, node_C):
+                    changeFlag = True
+                    edge = graph.get_edge(node_B, node_C)
+                    graph.remove_edge(edge)
+                    graph.add_edge(Edge(node_B, node_C, Endpoint.TAIL, edge.get_proximal_endpoint(node_C)))
+                    if verbose:
+                        print("Orienting edge by rule 7): " + graph.get_edge(node_B, node_C).__str__())
+    return changeFlag
 
 def getPath(node_c: Node, previous) -> List[Node]:
     l = []
@@ -544,9 +727,8 @@ def ruleR4B(graph: Graph, maxPathLength: int, data: ndarray, independence_test_m
 
 
 
-def rule8(graph: Graph, nodes: List[Node]):
-    nodes = graph.get_nodes()
-    changeFlag = False
+def rule8(graph: Graph, nodes: List[Node], changeFlag):
+    nodes = graph.get_nodes() if nodes is None else nodes
     for node_B in nodes:
         adj = graph.get_adjacent_nodes(node_B)
         if len(adj) < 2:
@@ -601,9 +783,9 @@ def find_possible_children(graph: Graph, parent_node, en_nodes=None):
 
     return potential_child_nodes
 
-def rule9(graph: Graph, nodes: List[Node]):
-    changeFlag = False
-    nodes = graph.get_nodes()
+def rule9(graph: Graph, nodes: List[Node], changeFlag):
+    # changeFlag = False
+    nodes = graph.get_nodes() if nodes is None else nodes
     for node_C in nodes:
         intoCArrows = graph.get_nodes_into(node_C, Endpoint.ARROW)
         for node_A in intoCArrows:
@@ -629,8 +811,8 @@ def rule9(graph: Graph, nodes: List[Node]):
     return changeFlag
 
 
-def rule10(graph: Graph):
-    changeFlag = False
+def rule10(graph: Graph, changeFlag):
+    # changeFlag = False
     nodes = graph.get_nodes()
     for node_C in nodes:
         intoCArrows = graph.get_nodes_into(node_C, Endpoint.ARROW)
@@ -895,6 +1077,7 @@ def fci(dataset: ndarray, independence_test_method: str=fisherz, alpha: float =
     graph, sep_sets, test_results = fas(dataset, nodes, independence_test_method=independence_test_method, alpha=alpha,
                                         knowledge=background_knowledge, depth=depth, verbose=verbose, show_progress=show_progress)
 
+    # pdb.set_trace()
     reorientAllWith(graph, Endpoint.CIRCLE)
 
     rule0(graph, nodes, sep_sets, background_knowledge, verbose)
@@ -925,12 +1108,22 @@ def fci(dataset: ndarray, independence_test_method: str=fisherz, alpha: float =
             if verbose:
                 print("Epoch")
 
+        # rule 5
+        change_flag = ruleR5(graph, change_flag, verbose)
+        
+        # rule 6
+        change_flag = ruleR6(graph, change_flag, verbose)
+        
+        # rule 7
+        change_flag = ruleR7(graph, change_flag, verbose)
+        
         # rule 8
-        change_flag = rule8(graph,nodes)
+        change_flag = rule8(graph,nodes, change_flag)
+        
         # rule 9
-        change_flag = rule9(graph, nodes)
+        change_flag = rule9(graph, nodes, change_flag)
         # rule 10
-        change_flag = rule10(graph)
+        change_flag = rule10(graph, change_flag)
 
     graph.set_pag(True)
 
diff --git a/causallearn/utils/DAG2PAG.py b/causallearn/utils/DAG2PAG.py
index 9980b96b..2a091f72 100644
--- a/causallearn/utils/DAG2PAG.py
+++ b/causallearn/utils/DAG2PAG.py
@@ -10,10 +10,11 @@
 from causallearn.graph.Endpoint import Endpoint
 from causallearn.graph.GeneralGraph import GeneralGraph
 from causallearn.graph.Node import Node
-from causallearn.search.ConstraintBased.FCI import rule0, rulesR1R2cycle, ruleR3, ruleR4B
+from causallearn.search.ConstraintBased.FCI import rule0, rulesR1R2cycle, ruleR3, ruleR4B, ruleR5, ruleR6, ruleR7, rule8, rule9, rule10
 from causallearn.utils.cit import CIT, d_separation
 
-def dag2pag(dag: Dag, islatent: List[Node]) -> GeneralGraph:
+
+def dag2pag(dag: Dag, islatent: List[Node], isselection: List[Node] = []) -> GeneralGraph:
     """
     Convert a DAG to its corresponding PAG
     Parameters
@@ -27,8 +28,8 @@ def dag2pag(dag: Dag, islatent: List[Node]) -> GeneralGraph:
     dg = nx.DiGraph()
     true_dag = nx.DiGraph()
     nodes = dag.get_nodes()
-    observed_nodes = list(set(nodes) - set(islatent))
-    mod_nodes = observed_nodes + islatent
+    observed_nodes = list(set(nodes) - set(islatent) - set(isselection))
+    mod_nodes = observed_nodes + islatent + isselection
     nodes = dag.get_nodes()
     nodes_ids = {node: i for i, node in enumerate(nodes)}
     mod_nodeids = {node: i for i, node in enumerate(mod_nodes)}
@@ -65,7 +66,7 @@ def dag2pag(dag: Dag, islatent: List[Node]) -> GeneralGraph:
             for Z in combinations(observed_nodes, l):
                 if nodex in Z or nodey in Z:
                     continue
-                if d_separated(dg, {nodes_ids[nodex]}, {nodes_ids[nodey]}, set(nodes_ids[z] for z in Z)):
+                if d_separated(dg, {nodes_ids[nodex]}, {nodes_ids[nodey]}, set(nodes_ids[z] for z in Z) | set([nodes_ids[s] for s in isselection])):
                     if edge:
                         PAG.remove_edge(edge)
                     sepset[(nodes_ids[nodex], nodes_ids[nodey])] |= set(Z)
@@ -105,6 +106,13 @@ def dag2pag(dag: Dag, islatent: List[Node]) -> GeneralGraph:
         change_flag = ruleR4B(PAG, -1, data, independence_test_method, 0.05, sep_sets=sepset_reindexed,
                           change_flag=change_flag,
                           bk=None, verbose=False)
+        change_flag = ruleR5(PAG, changeFlag=change_flag, verbose=True)
+        change_flag = ruleR6(PAG, changeFlag=change_flag)
+        change_flag = ruleR7(PAG, changeFlag=change_flag)
+        change_flag = rule8(PAG, nodes=observed_nodes, changeFlag=change_flag)
+        change_flag = rule9(PAG, nodes=observed_nodes, changeFlag=change_flag)
+        change_flag = rule10(PAG, changeFlag=change_flag)
+
     return PAG
 
 
diff --git a/tests/TestDAG2PAG.py b/tests/TestDAG2PAG.py
index 569fc945..004ea897 100644
--- a/tests/TestDAG2PAG.py
+++ b/tests/TestDAG2PAG.py
@@ -72,3 +72,17 @@ def test_case3(self):
         print(pag)
         graphviz_pag = GraphUtils.to_pgv(pag)
         graphviz_pag.draw("pag.png", prog='dot', format='png')
+
+    def test_case_selection(self):
+        nodes = []
+        for i in range(5):
+            nodes.append(GraphNode(str(i)))
+        dag = Dag(nodes)
+        dag.add_directed_edge(nodes[0], nodes[1])
+        dag.add_directed_edge(nodes[1], nodes[2])
+        dag.add_directed_edge(nodes[2], nodes[3])
+        # Selection nodes
+        dag.add_directed_edge(nodes[3], nodes[4])
+        dag.add_directed_edge(nodes[0], nodes[4])
+        pag = dag2pag(dag, islatent=[], isselection=[nodes[4]])
+        print(pag)
diff --git a/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_alarm_fci_chisq_0.05.txt b/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_alarm_fci_chisq_0.05.txt
index 2430e1de..ce08eb4f 100644
--- a/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_alarm_fci_chisq_0.05.txt
+++ b/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_alarm_fci_chisq_0.05.txt
@@ -3,7 +3,7 @@
 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 -1 -1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-2 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+2 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0
 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
@@ -12,7 +12,7 @@
 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2
+0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0
@@ -20,9 +20,9 @@
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
-0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 2 0 2 0 0 0 0 2 -1 0 0 0 0 0
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 -1 0 0 0 0 2 -1 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -1 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0
diff --git a/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_andes_fci_chisq_0.05.txt b/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_andes_fci_chisq_0.05.txt
index a9f9886f..934b13bd 100644
--- a/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_andes_fci_chisq_0.05.txt
+++ b/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_andes_fci_chisq_0.05.txt
@@ -39,8 +39,8 @@
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
diff --git a/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_hepar2_fci_chisq_0.05.txt b/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_hepar2_fci_chisq_0.05.txt
index 9e6c7aac..0569bd1b 100644
--- a/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_hepar2_fci_chisq_0.05.txt
+++ b/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_hepar2_fci_chisq_0.05.txt
@@ -40,7 +40,7 @@
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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-0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
diff --git a/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_insurance_fci_chisq_0.05.txt b/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_insurance_fci_chisq_0.05.txt
index 80a266db..4d6a5b4a 100644
--- a/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_insurance_fci_chisq_0.05.txt
+++ b/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_insurance_fci_chisq_0.05.txt
@@ -2,7 +2,7 @@
 -1 0 1 1 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
 1 1 0 1 1 0 0 0 -1 0 0 0 0 0 0 0 0 -1 1 0 0 1 0 0 0 0 0
 0 1 1 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 -1 -1 0 0 0 0 0 0 0 -1
-0 0 2 0 0 0 2 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0
+0 0 2 0 0 0 -1 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 0 0 0 -1 0 0
 0 0 0 0 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0
 0 0 0 0 0 -1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 -1 0
diff --git a/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_water_fci_chisq_0.05.txt b/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_water_fci_chisq_0.05.txt
index cee53cda..bd9c2aec 100644
--- a/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_water_fci_chisq_0.05.txt
+++ b/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_water_fci_chisq_0.05.txt
@@ -1,4 +1,4 @@
-0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+0 0 0 0 0 0 0 0 2 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
@@ -14,12 +14,12 @@
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0
-0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0
+0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 -1 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 1 0 0 0 0
 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 0 0
 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 0
 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1
-0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
+0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0
 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1
 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
diff --git a/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_win95pts_fci_chisq_0.05.txt b/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_win95pts_fci_chisq_0.05.txt
index b971fb87..8bc6b692 100644
--- a/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_win95pts_fci_chisq_0.05.txt
+++ b/tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_win95pts_fci_chisq_0.05.txt
@@ -8,7 +8,7 @@
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0
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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+0 0 0 2 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
@@ -34,7 +34,7 @@
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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-0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
@@ -50,7 +50,7 @@
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
diff --git a/tests/TestData/benchmark_returned_results/linear_10_fci_fisherz_0.05.txt b/tests/TestData/benchmark_returned_results/linear_10_fci_fisherz_0.05.txt
index 046443a3..07a248fb 100644
--- a/tests/TestData/benchmark_returned_results/linear_10_fci_fisherz_0.05.txt
+++ b/tests/TestData/benchmark_returned_results/linear_10_fci_fisherz_0.05.txt
@@ -5,7 +5,7 @@
 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1
 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
-0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 2 2 0
+0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 0 0 0 2 -1 0
 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 -1 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0
diff --git a/tests/TestFCI.py b/tests/TestFCI.py
index 7884cbde..e2fb683c 100644
--- a/tests/TestFCI.py
+++ b/tests/TestFCI.py
@@ -10,8 +10,11 @@
 import pandas as pd
 
 from causallearn.graph.Dag import Dag
+from causallearn.graph.Edge import Edge
+from causallearn.graph.Endpoint import Endpoint
+from causallearn.graph.GeneralGraph import GeneralGraph
 from causallearn.graph.GraphNode import GraphNode
-from causallearn.search.ConstraintBased.FCI import fci
+from causallearn.search.ConstraintBased.FCI import fci, ruleR5
 from causallearn.utils.cit import chisq, fisherz, kci, d_separation
 from causallearn.utils.DAG2PAG import dag2pag
 from causallearn.utils.GraphUtils import GraphUtils
@@ -30,21 +33,21 @@
 ######################################### Test Notes ###########################################
 
 BENCHMARK_TXTFILE_TO_MD5 = {
-    "tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_asia_fci_chisq_0.05.txt": "65f54932a9d8224459e56c40129e6d8b",
-    "tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_cancer_fci_chisq_0.05.txt": "0312381641cb3b4818e0c8539f74e802",
-    "tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_earthquake_fci_chisq_0.05.txt": "a1160b92ce15a700858552f08e43b7de",
-    "tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_sachs_fci_chisq_0.05.txt": "dced4a202fc32eceb75f53159fc81f3b",
-    "tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_survey_fci_chisq_0.05.txt": "b1a28eee1e0c6ea8a64ac1624585c3f4",
-    "tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_alarm_fci_chisq_0.05.txt": "c3bbc2b8aba456a4258dd071a42085bc",
-    "tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_barley_fci_chisq_0.05.txt": "4a5000e7a582083859ee6aef15073676",
-    "tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_child_fci_chisq_0.05.txt": "6b7858589e12f04b0f489ba4589a1254",
-    "tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_insurance_fci_chisq_0.05.txt": "9975942b936aa2b1fc90c09318ca2d08",
-    "tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_water_fci_chisq_0.05.txt": "48eee804d59526187b7ecd0519556ee5",
-    "tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_hailfinder_fci_chisq_0.05.txt": "6b9a6b95b6474f8530e85c022f4e749c",
-    "tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_hepar2_fci_chisq_0.05.txt": "4aae21ff3d9aa2435515ed2ee402294c",
-    "tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_win95pts_fci_chisq_0.05.txt": "648fdf271e1440c06ca2b31b55ef1f3f",
-    "tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_andes_fci_chisq_0.05.txt": "04092ae93e54c727579f08bf5dc34c77",
-    "tests/TestData/benchmark_returned_results/linear_10_fci_fisherz_0.05.txt": "289c86f9c665bf82bbcc4c9e1dcec3e7"
+    'tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_asia_fci_chisq_0.05.txt': '4b014aa90aee456bc02dddd008d8be1f',
+    'tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_cancer_fci_chisq_0.05.txt': '0312381641cb3b4818e0c8539f74e802',
+    'tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_earthquake_fci_chisq_0.05.txt': 'a1160b92ce15a700858552f08e43b7de',
+    'tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_sachs_fci_chisq_0.05.txt': 'dced4a202fc32eceb75f53159fc81f3b',
+    'tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_survey_fci_chisq_0.05.txt': 'b1a28eee1e0c6ea8a64ac1624585c3f4',
+    'tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_alarm_fci_chisq_0.05.txt': '4b06f6ea7fefe66255a3d16cb8a3711f',
+    'tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_barley_fci_chisq_0.05.txt': 'a926e329b2bf2b397d3676e9d2020483',
+    'tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_child_fci_chisq_0.05.txt': '5eff3ea6ce2e2daa53d6b649bd9c31fe',
+    'tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_insurance_fci_chisq_0.05.txt': '55eed065b8dfc6a21610d3d6e18423c6',
+    'tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_water_fci_chisq_0.05.txt': '48917f914c8f80684ae2abde87417d5c',
+    'tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_hailfinder_fci_chisq_0.05.txt': 'bcffe793866db6ddfe9cc602081789cd',
+    'tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_hepar2_fci_chisq_0.05.txt': '3558683a485588a41493b1a2f2c1d370',
+    'tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_win95pts_fci_chisq_0.05.txt': '52596ace09c45656f61c70d0e66bdd6a',
+    'tests/TestData/benchmark_returned_results/bnlearn_discrete_10000_andes_fci_chisq_0.05.txt': '4b7e2ecba5eb50c7266f24670d0d0ae9',
+    'tests/TestData/benchmark_returned_results/linear_10_fci_fisherz_0.05.txt': 'eaabd1fbb16bc152b45e456c30166c55'
 }
 #
 INCONSISTENT_RESULT_GRAPH_ERRMSG = "Returned graph is inconsistent with the benchmark. Please check your code with the commit 5918419."
@@ -211,3 +214,23 @@ def test_er_graph(self):
             print(G)
             print(f'fci(data, d_separation, 0.05):')
             self.run_simulate_data_test(pag, G)
+
+    def test_rule5(self):
+        nodes = []
+        for i in range(7):
+            nodes.append(GraphNode(str(i)))
+        g = GeneralGraph(nodes)
+        g.add_edge(Edge(nodes[0], nodes[1], Endpoint.CIRCLE, Endpoint.CIRCLE))
+        g.add_edge(Edge(nodes[0], nodes[2], Endpoint.CIRCLE, Endpoint.CIRCLE))
+        g.add_edge(Edge(nodes[0], nodes[5], Endpoint.CIRCLE, Endpoint.CIRCLE))
+        g.add_edge(Edge(nodes[0], nodes[6], Endpoint.CIRCLE, Endpoint.CIRCLE))
+        g.add_edge(Edge(nodes[1], nodes[3], Endpoint.CIRCLE, Endpoint.CIRCLE))
+        g.add_edge(Edge(nodes[2], nodes[4], Endpoint.CIRCLE, Endpoint.CIRCLE))
+        g.add_edge(Edge(nodes[3], nodes[5], Endpoint.CIRCLE, Endpoint.CIRCLE))
+        g.add_edge(Edge(nodes[4], nodes[6], Endpoint.CIRCLE, Endpoint.CIRCLE))
+
+        ruleR5(g, changeFlag=True, verbose=True)
+
+        for edge in g.get_graph_edges():
+            assert edge.get_endpoint1() == Endpoint.TAIL
+            assert edge.get_endpoint2() == Endpoint.TAIL