From 0963c445d3c521a25de21df62f4bf574a1eac9ad Mon Sep 17 00:00:00 2001
From: David Allemang <allemang.d@gmail.com>
Date: Thu, 12 Sep 2019 19:30:26 -0400
Subject: [PATCH 1/6] rows working correctly

---
 cosets/CMakeLists.txt |  2 ++
 cosets/src/main.cpp   | 18 ++++++-------
 cosets/src/tc.cpp     | 62 +++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 73 insertions(+), 9 deletions(-)
 create mode 100644 cosets/src/tc.cpp

diff --git a/cosets/CMakeLists.txt b/cosets/CMakeLists.txt
index dfa29e2..c8cf75b 100644
--- a/cosets/CMakeLists.txt
+++ b/cosets/CMakeLists.txt
@@ -15,3 +15,5 @@ add_custom_command(
             ${CMAKE_CURRENT_SOURCE_DIR}/src/shaders
             ${CMAKE_CURRENT_BINARY_DIR}/shaders
 )
+
+add_executable(coxeter src/tc.cpp)
diff --git a/cosets/src/main.cpp b/cosets/src/main.cpp
index 8531459..de0e007 100644
--- a/cosets/src/main.cpp
+++ b/cosets/src/main.cpp
@@ -29,16 +29,16 @@ public:
 
       program = build_program("main", vs, fs);
 
-      float verts_data[4 * VERTS_N]{
-         +.5f, +.5f, 0.f, 0.f,
-         +.5f, -.5f, 0.f, 0.f,
-         -.5f, -.5f, 0.f, -.1f,
-         -.5f, +.5f, 0.f, -.1f,
+      glm::vec4 verts_data[VERTS_N]{
+         {+0.5, +0.5, +0.5, +0.0},
+         {+0.5, -0.5, +0.5, +0.0},
+         {-0.5, -0.5, +0.5, +0.0},
+         {-0.5, +0.5, +0.5, +0.0},
 
-         +.5f, +.5f, 0.f, .1f,
-         +.5f, -.5f, 0.f, .1f,
-         -.5f, -.5f, 0.2f, .0f,
-         -.5f, +.5f, 0.2f, .0f,
+         {+0.5, +0.5, +0.5, -0.5},
+         {+0.5, -0.5, +0.5, -0.5},
+         {-0.5, -0.5, +0.5, +0.5},
+         {-0.5, +0.5, +0.5, +0.5},
       };
 
       glGenBuffers(1, &verts);
diff --git a/cosets/src/tc.cpp b/cosets/src/tc.cpp
new file mode 100644
index 0000000..fa2b5b7
--- /dev/null
+++ b/cosets/src/tc.cpp
@@ -0,0 +1,62 @@
+#include <iostream>
+#include <vector>
+
+struct Row {
+   std::vector<int>::const_iterator l;
+   std::vector<int>::const_iterator r;
+
+   int from;
+   int to;
+
+   Row(const std::vector<int> &vec, int from, int to) {
+      this->l = vec.begin();
+      this->r = vec.end();
+      this->from = from;
+      this->to = to;
+   }
+};
+
+std::ostream &operator<<(std::ostream &out, const Row &row) {
+   out << "[ " << row.from << " | ";
+   auto it = row.l;
+   while (it != row.r) {
+      out << *it << " ";
+      it++;
+   }
+   out << "| " << row.to << " ]";
+   return out;
+}
+
+int main(int argc, char *argv[]) {
+   int gens = 2;
+   std::vector<std::vector<int>> ids{
+      {0, 0},
+      {1, 1},
+      {0, 1, 0, 1, 0, 1}
+   };
+
+   std::vector<int> &id = ids[2];
+   Row row(id, 8, 9);
+
+   std::cout << row << std::endl;
+
+   row.l++;
+   row.from = 6;
+
+   std::cout << row << std::endl;
+
+//   std::vector<std::vector<char>> vecs{
+//      {'a', 'o', 'e', 'u'},
+//      {'p'},
+//      {'q', 'j', 'k'},
+//   };
+//
+//   for (const auto& vec : vecs) {
+//      for (const auto& ch : vec) {
+//         std::cout << ch;
+//      }
+//      std::cout << std::endl;
+//   }
+
+   return 0;
+}
\ No newline at end of file

From c9a50d540d01645f2bd27f3abf60341e287d7dca Mon Sep 17 00:00:00 2001
From: David Allemang <allemang.d@gmail.com>
Date: Thu, 12 Sep 2019 20:31:16 -0400
Subject: [PATCH 2/6] created table class

---
 cosets/src/tc.cpp | 65 +++++++++++++++++++++++++++++++----------------
 1 file changed, 43 insertions(+), 22 deletions(-)

diff --git a/cosets/src/tc.cpp b/cosets/src/tc.cpp
index fa2b5b7..63d0262 100644
--- a/cosets/src/tc.cpp
+++ b/cosets/src/tc.cpp
@@ -1,6 +1,11 @@
 #include <iostream>
 #include <vector>
 
+struct Row;
+
+template<int N>
+struct Table;
+
 struct Row {
    std::vector<int>::const_iterator l;
    std::vector<int>::const_iterator r;
@@ -16,6 +21,16 @@ struct Row {
    }
 };
 
+template<int N>
+struct Table {
+   std::vector<std::vector<int>> fwd;
+   std::vector<std::vector<int>> rev;
+
+   void add_row() {
+      fwd.push_back(std::vector<int>(N));
+   }
+};
+
 std::ostream &operator<<(std::ostream &out, const Row &row) {
    out << "[ " << row.from << " | ";
    auto it = row.l;
@@ -27,6 +42,28 @@ std::ostream &operator<<(std::ostream &out, const Row &row) {
    return out;
 }
 
+template<int N>
+std::ostream &operator<<(std::ostream &out, const Table<N> &table) {
+   out << "[";
+   for (int j = 0; j < table.fwd.size(); ++j) {
+      auto arr = table.fwd[j];
+      out << "[";
+      for (int i = 0; i < N; ++i) {
+         out << arr[i];
+
+         if (i < N - 1)
+            out << " ";
+      }
+
+      out << "]";
+      if (j < table.fwd.size() - 1)
+         out << "\n ";
+   }
+   out << "]\n";
+
+   return out;
+}
+
 int main(int argc, char *argv[]) {
    int gens = 2;
    std::vector<std::vector<int>> ids{
@@ -35,28 +72,12 @@ int main(int argc, char *argv[]) {
       {0, 1, 0, 1, 0, 1}
    };
 
-   std::vector<int> &id = ids[2];
-   Row row(id, 8, 9);
-
-   std::cout << row << std::endl;
-
-   row.l++;
-   row.from = 6;
-
-   std::cout << row << std::endl;
-
-//   std::vector<std::vector<char>> vecs{
-//      {'a', 'o', 'e', 'u'},
-//      {'p'},
-//      {'q', 'j', 'k'},
-//   };
-//
-//   for (const auto& vec : vecs) {
-//      for (const auto& ch : vec) {
-//         std::cout << ch;
-//      }
-//      std::cout << std::endl;
-//   }
+   Table<3> table;
+   table.add_row();
+   table.add_row();
+   table.add_row();
+   table.add_row();
+   std::cout << table;
 
    return 0;
 }
\ No newline at end of file

From f494025f6a740387c97ed47db1c775ba832ee5f7 Mon Sep 17 00:00:00 2001
From: allem <allemang.d@gmail.com>
Date: Thu, 12 Sep 2019 21:37:56 -0400
Subject: [PATCH 3/6] row learns from table

---
 .idea/cosets.iml  |  2 -
 .idea/misc.xml    | 15 --------
 .idea/modules.xml |  8 ----
 .idea/vcs.xml     |  6 ---
 cosets/src/tc.cpp | 98 ++++++++++++++++++++++++++++++++++++++++++-----
 5 files changed, 89 insertions(+), 40 deletions(-)
 delete mode 100644 .idea/cosets.iml
 delete mode 100644 .idea/misc.xml
 delete mode 100644 .idea/modules.xml
 delete mode 100644 .idea/vcs.xml

diff --git a/.idea/cosets.iml b/.idea/cosets.iml
deleted file mode 100644
index f08604b..0000000
--- a/.idea/cosets.iml
+++ /dev/null
@@ -1,2 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<module classpath="CMake" type="CPP_MODULE" version="4" />
\ No newline at end of file
diff --git a/.idea/misc.xml b/.idea/misc.xml
deleted file mode 100644
index 9bb8048..0000000
--- a/.idea/misc.xml
+++ /dev/null
@@ -1,15 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<project version="4">
-  <component name="CMakeWorkspace" PROJECT_DIR="$PROJECT_DIR$" />
-  <component name="CidrRootsConfiguration">
-    <sourceRoots>
-      <file path="$PROJECT_DIR$/cosets/src" />
-    </sourceRoots>
-    <libraryRoots>
-      <file path="$PROJECT_DIR$/vendor" />
-    </libraryRoots>
-  </component>
-  <component name="JavaScriptSettings">
-    <option name="languageLevel" value="ES6" />
-  </component>
-</project>
\ No newline at end of file
diff --git a/.idea/modules.xml b/.idea/modules.xml
deleted file mode 100644
index 44442b6..0000000
--- a/.idea/modules.xml
+++ /dev/null
@@ -1,8 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<project version="4">
-  <component name="ProjectModuleManager">
-    <modules>
-      <module fileurl="file://$PROJECT_DIR$/.idea/cosets.iml" filepath="$PROJECT_DIR$/.idea/cosets.iml" />
-    </modules>
-  </component>
-</project>
\ No newline at end of file
diff --git a/.idea/vcs.xml b/.idea/vcs.xml
deleted file mode 100644
index 94a25f7..0000000
--- a/.idea/vcs.xml
+++ /dev/null
@@ -1,6 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<project version="4">
-  <component name="VcsDirectoryMappings">
-    <mapping directory="$PROJECT_DIR$" vcs="Git" />
-  </component>
-</project>
\ No newline at end of file
diff --git a/cosets/src/tc.cpp b/cosets/src/tc.cpp
index 63d0262..63f83e1 100644
--- a/cosets/src/tc.cpp
+++ b/cosets/src/tc.cpp
@@ -1,11 +1,13 @@
 #include <iostream>
 #include <vector>
 
+template<int N>
 struct Row;
 
 template<int N>
 struct Table;
 
+template<int N>
 struct Row {
    std::vector<int>::const_iterator l;
    std::vector<int>::const_iterator r;
@@ -15,10 +17,37 @@ struct Row {
 
    Row(const std::vector<int> &vec, int from, int to) {
       this->l = vec.begin();
-      this->r = vec.end();
+      this->r = vec.end() - 1;
       this->from = from;
       this->to = to;
    }
+
+   bool learn(Table<N> &table) {
+      if (r - l == 0) {
+         return false;
+      }
+
+      while (r - l > 0) {
+         int next = table.get(from, *l);
+         if (next < 0) break;
+         l++;
+         from = next;
+      }
+
+      while (r - l > 0) {
+         int next = table.rget(*r, to);
+         if (next < 0) break;
+         r--;
+         to = next;
+      }
+
+      if (r - l == 0) {
+         table.set(from, *l, to);
+         return true;
+      }
+
+      return false;
+   }
 };
 
 template<int N>
@@ -26,15 +55,52 @@ struct Table {
    std::vector<std::vector<int>> fwd;
    std::vector<std::vector<int>> rev;
 
+   Table() {
+      add_row();
+   }
+
    void add_row() {
-      fwd.push_back(std::vector<int>(N));
+      fwd.push_back(std::vector<int>(N, -1));
+      rev.push_back(std::vector<int>(N, -1));
+   }
+
+   int add_coset() {
+      for (int from = 0; from < size(); ++from) {
+         for (int gen = 0; gen < N; ++gen) {
+            if (get(from, gen) < 0) {
+               int to = size();
+               add_row();
+               set(from, gen, to);
+               return to;
+            }
+         }
+      }
+      return 0;
+   }
+
+   [[nodiscard]] unsigned size() const {
+      return fwd.size();
+   }
+
+   void set(int from, int gen, int to) {
+      fwd[from][gen] = to;
+      rev[to][gen] = from;
+   }
+
+   [[nodiscard]] int get(int from, int gen) const {
+      return fwd[from][gen];
+   }
+
+   [[nodiscard]] int rget(int gen, int to) const {
+      return rev[to][gen];
    }
 };
 
-std::ostream &operator<<(std::ostream &out, const Row &row) {
+template<int N>
+std::ostream &operator<<(std::ostream &out, const Row<N> &row) {
    out << "[ " << row.from << " | ";
    auto it = row.l;
-   while (it != row.r) {
+   while (row.r - it > 0) {
       out << *it << " ";
       it++;
    }
@@ -45,7 +111,7 @@ std::ostream &operator<<(std::ostream &out, const Row &row) {
 template<int N>
 std::ostream &operator<<(std::ostream &out, const Table<N> &table) {
    out << "[";
-   for (int j = 0; j < table.fwd.size(); ++j) {
+   for (unsigned j = 0; j < table.size(); ++j) {
       auto arr = table.fwd[j];
       out << "[";
       for (int i = 0; i < N; ++i) {
@@ -65,19 +131,33 @@ std::ostream &operator<<(std::ostream &out, const Table<N> &table) {
 }
 
 int main(int argc, char *argv[]) {
-   int gens = 2;
    std::vector<std::vector<int>> ids{
       {0, 0},
       {1, 1},
       {0, 1, 0, 1, 0, 1}
    };
 
+   Row<3> row(ids[2], 0, 0);
    Table<3> table;
+
    table.add_row();
    table.add_row();
    table.add_row();
-   table.add_row();
-   std::cout << table;
+
+   table.set(0, 0, 1);
+   table.set(1, 1, 2);
+
+   std::cout << table << std::endl;
+   std::cout << row << std::endl;
+
+   row.learn(table);
+   std::cout << row << std::endl;
+
+//   std::cout << table << std::endl;
+//   table.add_coset();
+//   std::cout << table << std::endl;
+//
+//   row.learn(table);
 
    return 0;
-}
\ No newline at end of file
+}

From 30f77738773d531bb012dd0c9c657dd6e8ef468b Mon Sep 17 00:00:00 2001
From: allem <allemang.d@gmail.com>
Date: Thu, 12 Sep 2019 22:36:59 -0400
Subject: [PATCH 4/6] seems to be working

---
 cosets/src/tc.cpp | 179 +++++++++++++++++++++++++---------------------
 1 file changed, 99 insertions(+), 80 deletions(-)

diff --git a/cosets/src/tc.cpp b/cosets/src/tc.cpp
index 63f83e1..2de4e7c 100644
--- a/cosets/src/tc.cpp
+++ b/cosets/src/tc.cpp
@@ -1,67 +1,22 @@
 #include <iostream>
 #include <vector>
+#include <iomanip>
+#include <cmath>
 
-template<int N>
-struct Row;
 
-template<int N>
-struct Table;
-
-template<int N>
-struct Row {
-   std::vector<int>::const_iterator l;
-   std::vector<int>::const_iterator r;
-
-   int from;
-   int to;
-
-   Row(const std::vector<int> &vec, int from, int to) {
-      this->l = vec.begin();
-      this->r = vec.end() - 1;
-      this->from = from;
-      this->to = to;
-   }
-
-   bool learn(Table<N> &table) {
-      if (r - l == 0) {
-         return false;
-      }
-
-      while (r - l > 0) {
-         int next = table.get(from, *l);
-         if (next < 0) break;
-         l++;
-         from = next;
-      }
-
-      while (r - l > 0) {
-         int next = table.rget(*r, to);
-         if (next < 0) break;
-         r--;
-         to = next;
-      }
-
-      if (r - l == 0) {
-         table.set(from, *l, to);
-         return true;
-      }
-
-      return false;
-   }
-};
-
-template<int N>
 struct Table {
+   int N;
    std::vector<std::vector<int>> fwd;
    std::vector<std::vector<int>> rev;
 
-   Table() {
+   explicit Table(int N) {
       add_row();
+      this->N = N;
    }
 
    void add_row() {
-      fwd.push_back(std::vector<int>(N, -1));
-      rev.push_back(std::vector<int>(N, -1));
+      fwd.emplace_back(N, -1);
+      rev.emplace_back(N, -1);
    }
 
    int add_coset() {
@@ -96,8 +51,49 @@ struct Table {
    }
 };
 
-template<int N>
-std::ostream &operator<<(std::ostream &out, const Row<N> &row) {
+struct Row {
+   std::vector<int>::const_iterator l;
+   std::vector<int>::const_iterator r;
+
+   int from;
+   int to;
+
+   Row(const std::vector<int> &vec, int cos) {
+      this->l = vec.begin();
+      this->r = vec.end() - 1;
+      this->from = cos;
+      this->to = cos;
+   }
+
+   bool learn(Table *table) {
+      if (r - l == 0) {
+         return false;
+      }
+
+      while (r - l > 0) {
+         int next = table->get(from, *l);
+         if (next < 0) break;
+         l++;
+         from = next;
+      }
+
+      while (r - l > 0) {
+         int next = table->rget(*r, to);
+         if (next < 0) break;
+         r--;
+         to = next;
+      }
+
+      if (r - l == 0) {
+         table->set(from, *l, to);
+         return true;
+      }
+
+      return false;
+   }
+};
+
+std::ostream &operator<<(std::ostream &out, const Row &row) {
    out << "[ " << row.from << " | ";
    auto it = row.l;
    while (row.r - it > 0) {
@@ -108,16 +104,17 @@ std::ostream &operator<<(std::ostream &out, const Row<N> &row) {
    return out;
 }
 
-template<int N>
-std::ostream &operator<<(std::ostream &out, const Table<N> &table) {
+std::ostream &operator<<(std::ostream &out, const Table &table) {
+   int k = ceil(log10(table.size()));
+
    out << "[";
    for (unsigned j = 0; j < table.size(); ++j) {
       auto arr = table.fwd[j];
-      out << "[";
-      for (int i = 0; i < N; ++i) {
+      out << " " << std::setw(k) << j << " [";
+      for (int i = 0; i < table.N; ++i) {
          out << arr[i];
 
-         if (i < N - 1)
+         if (i < table.N - 1)
             out << " ";
       }
 
@@ -130,34 +127,56 @@ std::ostream &operator<<(std::ostream &out, const Table<N> &table) {
    return out;
 }
 
+Table *solve(int gens, const std::vector<int> &subgens, const std::vector<std::vector<int>> &rels) {
+   auto *table = new Table(gens);
+
+   for (int gen : subgens)
+      table->set(0, gen, 0);
+
+   std::vector<Row> rows;
+   rows.reserve(rels.size());
+   for (const auto &rel : rels)
+      rows.emplace_back(rel, 0);
+
+   while (!rows.empty()) {
+      while (true) {
+         bool learned = false;
+         for (int i = (int) rows.size() - 1; i >= 0; i--) {
+            if (rows[i].learn(table)) {
+               learned = true;
+               rows.erase(rows.begin() + i);
+            }
+         }
+         if (!learned)
+            break;
+      }
+
+      int i = (int) table->size();
+      if (table->add_coset() > 0) {
+         for (const auto &rel : rels)
+            rows.emplace_back(rel, i);
+      } else {
+         break;
+      }
+   }
+
+   return table;
+}
+
 int main(int argc, char *argv[]) {
    std::vector<std::vector<int>> ids{
       {0, 0},
       {1, 1},
-      {0, 1, 0, 1, 0, 1}
+      {2, 2},
+      {0, 1, 0, 1, 0, 1, 0, 1},
+      {1, 2, 1, 2, 1, 2},
+      {0, 2, 0, 2}
    };
 
-   Row<3> row(ids[2], 0, 0);
-   Table<3> table;
+   Table *table = solve(3, {}, ids);
 
-   table.add_row();
-   table.add_row();
-   table.add_row();
-
-   table.set(0, 0, 1);
-   table.set(1, 1, 2);
-
-   std::cout << table << std::endl;
-   std::cout << row << std::endl;
-
-   row.learn(table);
-   std::cout << row << std::endl;
-
-//   std::cout << table << std::endl;
-//   table.add_coset();
-//   std::cout << table << std::endl;
-//
-//   row.learn(table);
+   std::cout << table->size() << std::endl;
+   std::cout << *table << std::endl;
 
    return 0;
 }

From 0543907571e6c40eaef3ba0bc3e0ee91772b7fc7 Mon Sep 17 00:00:00 2001
From: allem <allemang.d@gmail.com>
Date: Thu, 12 Sep 2019 22:37:26 -0400
Subject: [PATCH 5/6] fix unsigned to signed cast

---
 cosets/src/tc.cpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/cosets/src/tc.cpp b/cosets/src/tc.cpp
index 2de4e7c..7b2bb83 100644
--- a/cosets/src/tc.cpp
+++ b/cosets/src/tc.cpp
@@ -20,10 +20,10 @@ struct Table {
    }
 
    int add_coset() {
-      for (int from = 0; from < size(); ++from) {
+      for (int from = 0; from < (int) size(); ++from) {
          for (int gen = 0; gen < N; ++gen) {
             if (get(from, gen) < 0) {
-               int to = size();
+               int to = (int) size();
                add_row();
                set(from, gen, to);
                return to;

From 163f4f7a82ceda6a0e9075245bee67a4cc714029 Mon Sep 17 00:00:00 2001
From: allem <allemang.d@gmail.com>
Date: Thu, 12 Sep 2019 23:00:29 -0400
Subject: [PATCH 6/6] word enumeration

---
 cosets/src/tc.cpp | 88 ++++++++++++++++++++++++++++++++++-------------
 1 file changed, 64 insertions(+), 24 deletions(-)

diff --git a/cosets/src/tc.cpp b/cosets/src/tc.cpp
index 7b2bb83..12ca511 100644
--- a/cosets/src/tc.cpp
+++ b/cosets/src/tc.cpp
@@ -1,6 +1,7 @@
 #include <iostream>
 #include <vector>
 #include <iomanip>
+#include <algorithm>
 #include <cmath>
 
 
@@ -49,6 +50,37 @@ struct Table {
    [[nodiscard]] int rget(int gen, int to) const {
       return rev[to][gen];
    }
+
+   std::vector<std::vector<int>> words() {
+      std::vector<std::vector<int> *> vecs(size());
+      vecs[0] = new std::vector<int>();
+
+      while (std::find(vecs.begin(), vecs.end(), nullptr) != vecs.end()) {
+         for (int from = 0; from < (int) vecs.size(); ++from) {
+            std::vector<int> *word = vecs[from];
+            if (word == nullptr) {
+               continue;
+            }
+
+            for (int gen = 0; gen < (int) N; ++gen) {
+               int to = get(from, gen);
+               if (vecs[to] != nullptr) {
+                  continue;
+               }
+
+               vecs[to] = new std::vector<int>(*word);
+               vecs[to]->push_back(gen);
+            }
+         }
+      }
+
+      std::vector<std::vector<int>> res(size());
+      for (int i = 0; i < (int) size(); ++i) {
+         res[i] = *vecs[i];
+      }
+
+      return res;
+   }
 };
 
 struct Row {
@@ -104,29 +136,6 @@ std::ostream &operator<<(std::ostream &out, const Row &row) {
    return out;
 }
 
-std::ostream &operator<<(std::ostream &out, const Table &table) {
-   int k = ceil(log10(table.size()));
-
-   out << "[";
-   for (unsigned j = 0; j < table.size(); ++j) {
-      auto arr = table.fwd[j];
-      out << " " << std::setw(k) << j << " [";
-      for (int i = 0; i < table.N; ++i) {
-         out << arr[i];
-
-         if (i < table.N - 1)
-            out << " ";
-      }
-
-      out << "]";
-      if (j < table.fwd.size() - 1)
-         out << "\n ";
-   }
-   out << "]\n";
-
-   return out;
-}
-
 Table *solve(int gens, const std::vector<int> &subgens, const std::vector<std::vector<int>> &rels) {
    auto *table = new Table(gens);
 
@@ -163,6 +172,29 @@ Table *solve(int gens, const std::vector<int> &subgens, const std::vector<std::v
    return table;
 }
 
+std::ostream &operator<<(std::ostream &out, const Table &table) {
+   int k = ceil(log10(table.size()));
+
+   out << "[";
+   for (unsigned j = 0; j < table.size(); ++j) {
+      auto arr = table.fwd[j];
+      out << " " << std::setw(k) << j << " [";
+      for (int i = 0; i < table.N; ++i) {
+         out << arr[i];
+
+         if (i < table.N - 1)
+            out << " ";
+      }
+
+      out << "]";
+      if (j < table.fwd.size() - 1)
+         out << "\n ";
+   }
+   out << "]\n";
+
+   return out;
+}
+
 int main(int argc, char *argv[]) {
    std::vector<std::vector<int>> ids{
       {0, 0},
@@ -173,10 +205,18 @@ int main(int argc, char *argv[]) {
       {0, 2, 0, 2}
    };
 
-   Table *table = solve(3, {}, ids);
+   Table *table = solve(3, {0, 1}, ids);
 
    std::cout << table->size() << std::endl;
    std::cout << *table << std::endl;
 
+   for (const auto &v : table->words()) {
+      std::cout << "[ ";
+      for (auto e : v) {
+         std::cout << e << " ";
+      }
+      std::cout << "]\n";
+   }
+
    return 0;
 }