diff --git a/algorithm/italiano.h b/algorithm/italiano.h
index 662fe66..ddc8e8d 100644
--- a/algorithm/italiano.h
+++ b/algorithm/italiano.h
@@ -38,7 +38,6 @@ private:
   std::map<T, Edges> E;
 };
 
-
 template<typename T>
 void Italiano<T>::init() {
   for (const auto& u : std::views::keys(G.adjMatrix)) {
@@ -62,21 +61,45 @@ bool Italiano<T>::query(const T& u, const T& v) {
 
 template<typename T>
 void Italiano<T>::remove(const T& u, const T& v) {
-  std::map<T, std::set<T>> R;
+  std::map<T, std::forward_list<T>> R;
   for (const auto& w : std::views::keys(G.adjMatrix)) {
-    if (RT[w].contains(u, v)) {
-      R[w].insert(v);
+    if (RT[w].contains(u, v) &&
+        std::distance(E[w].inc.begin(), E[w].inc.end()) > 1) {
+      if (E[v].inc.front() == u) {
+        E[v].inc.pop_front();
+        R[w].push_front(E[v].inc.front());
+        E[v].inc.push_front(u);
+      } else {
+        R[w].push_front(E[v].inc.front());
+      }
     }
-    E[u].inc.remove(v);
-    E[u].out.remove(u);
-    G.remove(u, v);
   }
+  E[u].inc.remove(v);
+  E[u].out.remove(u);
+  G.remove(u, v);
 
-  //for (const auto& w : std::views::keys(G.adjMatrix)) {
-  //  while (R[w].size() > 0) {
-  //    auto pop = R[w].
-  //  }
-  //}
+  for (const auto& w : std::views::keys(G.adjMatrix)) {
+    bool hooked = false;
+    // R contains all vertices that need a hook-parent
+    while (!R[w].empty()) {
+      // z is a candidate hook-parent if it is in RT[w]
+      const auto& toHook = R[w].front();
+      for (const auto& z : E[toHook].inc) {
+        if (RT[w].contains(u, z)) {
+          R[w].remove(toHook);
+          hooked = true;
+          break;
+        }
+      }
+      if (!hooked) {
+        TC[w][toHook] = false;
+        for (const auto& z : E[toHook].out) {
+          if (RT[w].contains(toHook, z))
+            R[w].push_front(z);
+        }
+      }
+    }
+  }
 }
 
 } // namespace algo
diff --git a/benchmark/decremental_bench.cc b/benchmark/decremental_bench.cc
index edb607f..b43f352 100644
--- a/benchmark/decremental_bench.cc
+++ b/benchmark/decremental_bench.cc
@@ -4,6 +4,7 @@
 #include "algorithm/decremental_scc.h"
 #include "algorithm/italiano.h"
 #include "algorithm/frigioni.h"
+#include "algorithm/tarjan.h"
 
 #include <fstream>
 
@@ -12,9 +13,22 @@ using namespace graph;
 TEST_SUITE("Decremental algorithms") {
   
   TEST_CASE("Decremental maintenance of SCCs 1") {
-    std::ifstream infile("resources/data.txt");
+    std::ifstream infile("resources/dag.txt");
     std::uint16_t u, v;
+    Digraph<std::uint16_t> G;
 
-    //while (infile >> u >> v) {}
+    while (infile >> u >> v)
+      G.insert(u, v);
+
+    auto SCCs = algo::Tarjan<std::uint16_t>(G.adjMatrix).execute();
+
+    // Testing whether an scc is a 1-vertex scc which after the normalization
+    // has no edges, in this case we know tgat there exist no 2-vertex sccs
+    for (auto& scc : SCCs) {
+      CHECK_EQ(std::all_of(scc.adjMatrix.begin(), scc.adjMatrix.end(),
+                           [](const auto& p) {
+                             return p.second.size() == 0;
+                           }), true);
+    }
   }
 }
\ No newline at end of file
diff --git a/test/decremental_test.cc b/test/decremental_test.cc
index dc741cc..7a7885b 100644
--- a/test/decremental_test.cc
+++ b/test/decremental_test.cc
@@ -65,48 +65,50 @@ TEST_SUITE("Decremental algorithms") {
   }
 
   TEST_CASE("Italiano") {
-    // 1 --> 2 --> 3 --> 1
-    //             3 --> 4 --> 5 --> 3
-    //       2 --> 6 --> 7 --> 8 --> 6
-    //                   7 --> 9
-    //             6 --> 9 --> 10 --> 11 --> 12 --> 13 --> 9
-    //                                       12 --> 10
+    // 1 --> 2 --> 4 --> 6 --> 8 --> 9
+    //             4 --> 5 --> 7 --> 8
+    //                         7 --> 9
+    // 1 --> 3 --> 9
+    //       3 --> 5 --> 6
     Digraph<std::uint16_t> G;
     G.insert(1, 2);
-    G.insert(2, 3);
-    G.insert(3, 1);
-    G.insert(3, 4);
+    G.insert(1, 3);
+    G.insert(2, 4);
+    G.insert(3, 5);
+    G.insert(3, 9);
     G.insert(4, 5);
-    G.insert(5, 3);
-    G.insert(2, 6);
-    G.insert(6, 7);
+    G.insert(4, 6);
+    G.insert(5, 6);
+    G.insert(5, 7);
+    G.insert(6, 8);
     G.insert(7, 8);
     G.insert(7, 9);
-    G.insert(8, 6);
-    G.insert(6, 9);
-    G.insert(9, 10);
-    G.insert(10, 11);
-    G.insert(11, 12);
-    G.insert(12, 13);
-    G.insert(13, 9);
-    G.insert(12, 10);
+    G.insert(8, 9);
 
-    REQUIRE_EQ(G.adjMatrix.size(), 13);
+    REQUIRE_EQ(G.adjMatrix.size(), 9);
 
     algo::Italiano<std::uint16_t> italiano(G);
     italiano.init();
 
     SUBCASE("Italiano::query") {
-      CHECK_EQ(italiano.query(1, 13), true);
-      CHECK_EQ(italiano.query(6, 10), true);
-      CHECK_EQ(italiano.query(9, 11), true);
-      CHECK_EQ(italiano.query(8, 2), false);
-      CHECK_EQ(italiano.query(9, 3), false);
-      CHECK_EQ(italiano.query(9, 8), false);
+      CHECK_EQ(italiano.query(1, 9), true);
+      CHECK_EQ(italiano.query(2, 8), true);
+      CHECK_EQ(italiano.query(3, 7), true);
+      CHECK_EQ(italiano.query(4, 3), false);
+      CHECK_EQ(italiano.query(5, 4), false);
+      CHECK_EQ(italiano.query(6, 1), false);
     }
 
     SUBCASE("Italiano::remove") {
+      italiano.remove(4, 6);
 
+      CHECK_EQ(italiano.query(1, 8), true);
+      CHECK_EQ(italiano.query(3, 6), true);
+
+      italiano.remove(5, 6);
+
+      CHECK_EQ(italiano.query(1, 9), true);
+      CHECK_EQ(italiano.query(1, 6), false);
     }
   }