assets/notebooks/ls-ses15-ex7-before.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "34ee827c-a326-436a-beec-b502b6798d8b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# This is my \"before\" half of L&S Session 15 Exercise 7\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cca580d9-1a58-441d-8c22-89e5e4da8bdc",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_nodes = [\"X\"+str(i) for i in range(9)]\n",
    "x_edges = [\n",
    "    (x_nodes[0],x_nodes[4]),\n",
    "    (x_nodes[1],x_nodes[5]),\n",
    "    (x_nodes[2],x_nodes[6]),\n",
    "    (x_nodes[3],x_nodes[8]),\n",
    "    (x_nodes[4],x_nodes[5]),\n",
    "    (x_nodes[5],x_nodes[6]),\n",
    "    (x_nodes[6],x_nodes[7]),\n",
    "    (x_nodes[7],x_nodes[5]),\n",
    "    (x_nodes[8],x_nodes[3])\n",
    "]\n",
    "XG = nx.DiGraph()\n",
    "XG.add_nodes_from(x_nodes)\n",
    "XG.add_edges_from(x_edges)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d12202a3-dce8-4cc7-b582-8156e08e39ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_nodes = [\"Y\"+y for y in [\"p\", \"q\", \"r\", \"s\", \"t\", \"v\", \"u\", \"m\", \"l\", \"w\", \"x\", \"y\", \"z\"]]\n",
    "\n",
    "y_edges = [\n",
    "    (y_nodes[0],y_nodes[2]),\n",
    "    (y_nodes[1],y_nodes[2]),\n",
    "    (y_nodes[2],y_nodes[4]),\n",
    "    (y_nodes[3],y_nodes[4]),\n",
    "    (y_nodes[4],y_nodes[5]),\n",
    "    (y_nodes[5],y_nodes[6]),\n",
    "    (y_nodes[6],y_nodes[3]),\n",
    "    (y_nodes[7],y_nodes[8]),\n",
    "    (y_nodes[8],y_nodes[7]),\n",
    "    (y_nodes[9],y_nodes[10]),\n",
    "    (y_nodes[10],y_nodes[11]),\n",
    "    (y_nodes[11],y_nodes[9]),\n",
    "    (y_nodes[12],y_nodes[11])\n",
    "]\n",
    "YG = nx.DiGraph()\n",
    "YG.add_nodes_from(y_nodes)\n",
    "YG.add_edges_from(y_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2d02c824-d4be-445b-98c2-b6c885455a0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "subax1 = plt.subplot(121)\n",
    "nx.draw(XG, with_labels=True, font_weight='bold')\n",
    "subax2 = plt.subplot(122)\n",
    "nx.draw_shell(YG, with_labels=True, font_weight='bold')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a77970b3-85b3-4413-bbcb-0e93a0edeeb5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_one_hot(idx,size):\n",
    "  return np.array([1 if idx == x else 0 for x in range(size)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "23c1c5c2-3298-48ba-8f13-69203602fc59",
   "metadata": {},
   "outputs": [],
   "source": [
    "def follow_endomap(G,n):\n",
    "  return list(G.successors(n))[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "72f1f67a-f70d-4e79-a578-fc6434648af4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_presentation(G):\n",
    "  G_nodes = list(G.nodes())\n",
    "  ones_G = np.full((len(G_nodes),),1)\n",
    "  GA =  nx.adjacency_matrix(G)\n",
    "  G_arrows_in =  np.matmul(ones_G,GA.toarray())\n",
    "  G_arrows_by_node = sorted(zip(range(len(G_nodes)),G_arrows_in), key=lambda x: x[1])\n",
    "  G_presentation = {}\n",
    "  G_relations = {}\n",
    "  for k,v in G_arrows_by_node:\n",
    "    print(f\"Checking node {k} with {v} arrows in\")\n",
    "    if v == 0:\n",
    "      print(f\"Adding root generator {G_nodes[k]}\")\n",
    "      G_presentation[G_nodes[k]] = (G_nodes[k],v)\n",
    "      next_node = follow_endomap(G,G_nodes[k])\n",
    "      steps = 1\n",
    "      while not next_node in G_presentation:\n",
    "        print(f\"Adding follow up node {next_node}: {steps} from {G_nodes[k]}\")\n",
    "        G_presentation[next_node] = (G_nodes[k],steps)\n",
    "        next_node = follow_endomap(G,next_node)\n",
    "        steps += 1\n",
    "      print(f\"next node {next_node} already has presentation\")\n",
    "      G_relations[G_nodes[k]] = ((G_nodes[k],steps),G_presentation[next_node])\n",
    "    elif v == 1:\n",
    "      print(f\"Only 1 way into node {k}\")\n",
    "      if G_nodes[k] in G_presentation:\n",
    "        print(\"already has a presentation\")\n",
    "      else:\n",
    "        print(\"Found potential loop\")\n",
    "        G_presentation[G_nodes[k]] = (G_nodes[k],0)\n",
    "        next_node = follow_endomap(G,G_nodes[k])\n",
    "        steps = 1\n",
    "        while not next_node in G_presentation:\n",
    "          print(f\"Adding follow up node {next_node}: {steps} from {G_nodes[k]}\")\n",
    "          G_presentation[next_node] = (G_nodes[k],steps)\n",
    "          next_node = follow_endomap(G,next_node)\n",
    "          steps += 1\n",
    "        print(f\"next node {next_node} already has presentation\")\n",
    "        G_relations[G_nodes[k]] = ((G_nodes[k],steps),G_presentation[next_node])\n",
    "    else:\n",
    "      print(f\"More than 1 way in\")\n",
    "\n",
    "  return {\n",
    "      \"generators\":list(G_relations.keys()),\n",
    "      \"relations\":list(G_relations.values())\n",
    "  }\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a223ee6d-2dd2-4683-b7ce-c5d4d01a1120",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checking node 0 with 0 arrows in\n",
      "Adding root generator X0\n",
      "Adding follow up node X4: 1 from X0\n",
      "Adding follow up node X5: 2 from X0\n",
      "Adding follow up node X6: 3 from X0\n",
      "Adding follow up node X7: 4 from X0\n",
      "next node X5 already has presentation\n",
      "Checking node 1 with 0 arrows in\n",
      "Adding root generator X1\n",
      "next node X5 already has presentation\n",
      "Checking node 2 with 0 arrows in\n",
      "Adding root generator X2\n",
      "next node X6 already has presentation\n",
      "Checking node 3 with 1 arrows in\n",
      "Only 1 way into node 3\n",
      "Found potential loop\n",
      "Adding follow up node X8: 1 from X3\n",
      "next node X3 already has presentation\n",
      "Checking node 4 with 1 arrows in\n",
      "Only 1 way into node 4\n",
      "already has a presentation\n",
      "Checking node 7 with 1 arrows in\n",
      "Only 1 way into node 7\n",
      "already has a presentation\n",
      "Checking node 8 with 1 arrows in\n",
      "Only 1 way into node 8\n",
      "already has a presentation\n",
      "Checking node 6 with 2 arrows in\n",
      "More than 1 way in\n",
      "Checking node 5 with 3 arrows in\n",
      "More than 1 way in\n",
      "{'generators': ['X0', 'X1', 'X2', 'X3'], 'relations': [(('X0', 5), ('X0', 2)), (('X1', 1), ('X0', 2)), (('X2', 1), ('X0', 3)), (('X3', 2), ('X3', 0))]}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_69979/1978947672.py:4: FutureWarning: adjacency_matrix will return a scipy.sparse array instead of a matrix in Networkx 3.0.\n",
      "  GA =  nx.adjacency_matrix(G)\n"
     ]
    }
   ],
   "source": [
    "endomap_alpha = make_presentation(XG)\n",
    "print(endomap_alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "dc070373-ac57-4f5f-8ac1-b024845e5ca6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checking node 0 with 0 arrows in\n",
      "Adding root generator Yp\n",
      "Adding follow up node Yr: 1 from Yp\n",
      "Adding follow up node Yt: 2 from Yp\n",
      "Adding follow up node Yv: 3 from Yp\n",
      "Adding follow up node Yu: 4 from Yp\n",
      "Adding follow up node Ys: 5 from Yp\n",
      "next node Yt already has presentation\n",
      "Checking node 1 with 0 arrows in\n",
      "Adding root generator Yq\n",
      "next node Yr already has presentation\n",
      "Checking node 12 with 0 arrows in\n",
      "Adding root generator Yz\n",
      "Adding follow up node Yy: 1 from Yz\n",
      "Adding follow up node Yw: 2 from Yz\n",
      "Adding follow up node Yx: 3 from Yz\n",
      "next node Yy already has presentation\n",
      "Checking node 3 with 1 arrows in\n",
      "Only 1 way into node 3\n",
      "already has a presentation\n",
      "Checking node 5 with 1 arrows in\n",
      "Only 1 way into node 5\n",
      "already has a presentation\n",
      "Checking node 6 with 1 arrows in\n",
      "Only 1 way into node 6\n",
      "already has a presentation\n",
      "Checking node 7 with 1 arrows in\n",
      "Only 1 way into node 7\n",
      "Found potential loop\n",
      "Adding follow up node Yl: 1 from Ym\n",
      "next node Ym already has presentation\n",
      "Checking node 8 with 1 arrows in\n",
      "Only 1 way into node 8\n",
      "already has a presentation\n",
      "Checking node 9 with 1 arrows in\n",
      "Only 1 way into node 9\n",
      "already has a presentation\n",
      "Checking node 10 with 1 arrows in\n",
      "Only 1 way into node 10\n",
      "already has a presentation\n",
      "Checking node 2 with 2 arrows in\n",
      "More than 1 way in\n",
      "Checking node 4 with 2 arrows in\n",
      "More than 1 way in\n",
      "Checking node 11 with 2 arrows in\n",
      "More than 1 way in\n",
      "{'generators': ['Yp', 'Yq', 'Yz', 'Ym'], 'relations': [(('Yp', 6), ('Yp', 2)), (('Yq', 1), ('Yp', 1)), (('Yz', 4), ('Yz', 1)), (('Ym', 2), ('Ym', 0))]}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_69979/1978947672.py:4: FutureWarning: adjacency_matrix will return a scipy.sparse array instead of a matrix in Networkx 3.0.\n",
      "  GA =  nx.adjacency_matrix(G)\n"
     ]
    }
   ],
   "source": [
    "endomap_beta = make_presentation(YG)\n",
    "print(endomap_beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e6762393-16c4-4da2-ba24-9b57bd922aec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['X8', 'X7', 'X6', 'X5', 'X4', 'X3', 'X2', 'X1', 'X0']\n",
      "Checking node 6 with 0 arrows in\n",
      "Adding root generator X2\n",
      "Adding follow up node X6: 1 from X2\n",
      "Adding follow up node X7: 2 from X2\n",
      "Adding follow up node X5: 3 from X2\n",
      "next node X6 already has presentation\n",
      "Checking node 7 with 0 arrows in\n",
      "Adding root generator X1\n",
      "next node X5 already has presentation\n",
      "Checking node 8 with 0 arrows in\n",
      "Adding root generator X0\n",
      "Adding follow up node X4: 1 from X0\n",
      "next node X5 already has presentation\n",
      "Checking node 0 with 1 arrows in\n",
      "Only 1 way into node 0\n",
      "Found potential loop\n",
      "Adding follow up node X3: 1 from X8\n",
      "next node X8 already has presentation\n",
      "Checking node 1 with 1 arrows in\n",
      "Only 1 way into node 1\n",
      "already has a presentation\n",
      "Checking node 4 with 1 arrows in\n",
      "Only 1 way into node 4\n",
      "already has a presentation\n",
      "Checking node 5 with 1 arrows in\n",
      "Only 1 way into node 5\n",
      "already has a presentation\n",
      "Checking node 2 with 2 arrows in\n",
      "More than 1 way in\n",
      "Checking node 3 with 3 arrows in\n",
      "More than 1 way in\n",
      "{'generators': ['X2', 'X1', 'X0', 'X8'], 'relations': [(('X2', 4), ('X2', 1)), (('X1', 1), ('X2', 3)), (('X0', 2), ('X2', 3)), (('X8', 2), ('X8', 0))]}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_69979/1978947672.py:4: FutureWarning: adjacency_matrix will return a scipy.sparse array instead of a matrix in Networkx 3.0.\n",
      "  GA =  nx.adjacency_matrix(G)\n"
     ]
    }
   ],
   "source": [
    "XG2 = nx.DiGraph()\n",
    "x2_nodes = [x_nodes[-1-i] for i in range(len(x_nodes))]\n",
    "print(x2_nodes)\n",
    "XG2.add_nodes_from(x2_nodes)\n",
    "XG2.add_edges_from(x_edges)\n",
    "endomap_alpha_prime = make_presentation(XG2)\n",
    "print(endomap_alpha_prime)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6f9d7158-79fa-462e-ae91-6a7c2d135df7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_map_info(endomap):\n",
    "  for idx,v in enumerate(endomap[\"relations\"]):\n",
    "    print(f\"Relation {idx} {v}\")\n",
    "    if v[0][0] == v[1][0]:\n",
    "      cl = abs(v[0][1] - v[1][1])\n",
    "      mins = min(v[0][1],v[1][1])\n",
    "      print(f\"{v[0][0]} leads to cycle of length {cl} after {mins} steps\")\n",
    "    else:\n",
    "      if v[0][1] > v[1][1]:\n",
    "          stdf = v[0][1] - v[1][1]\n",
    "          print(f\"{v[1][0]} leads to {v[0][0]} after {stdf} steps\")\n",
    "      else:\n",
    "          stdf = v[1][1] - v[0][1]\n",
    "          print(f\"{v[0][0]} leads to {v[1][0]} after {stdf} steps\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5dd48394-7d0b-4e5d-b92f-e8c175110d6e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relation 0 (('X0', 5), ('X0', 2))\n",
      "X0 leads to cycle of length 3 after 2 steps\n",
      "Relation 1 (('X1', 1), ('X0', 2))\n",
      "X1 leads to X0 after 1 steps\n",
      "Relation 2 (('X2', 1), ('X0', 3))\n",
      "X2 leads to X0 after 2 steps\n",
      "Relation 3 (('X3', 2), ('X3', 0))\n",
      "X3 leads to cycle of length 2 after 0 steps\n",
      "~~~~~~~~~~~~~~~~~~~\n",
      "Relation 0 (('Yp', 6), ('Yp', 2))\n",
      "Yp leads to cycle of length 4 after 2 steps\n",
      "Relation 1 (('Yq', 1), ('Yp', 1))\n",
      "Yq leads to Yp after 0 steps\n",
      "Relation 2 (('Yz', 4), ('Yz', 1))\n",
      "Yz leads to cycle of length 3 after 1 steps\n",
      "Relation 3 (('Ym', 2), ('Ym', 0))\n",
      "Ym leads to cycle of length 2 after 0 steps\n"
     ]
    }
   ],
   "source": [
    "print_map_info(endomap_alpha)\n",
    "print(\"~~~~~~~~~~~~~~~~~~~\")\n",
    "print_map_info(endomap_beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "4e640c75-7a24-4eaf-a524-91c3e150802a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_cycles(endomap):\n",
    "  cycles_by_length = {}\n",
    "  cycles_by_generator = {}\n",
    "  for k,v in enumerate(endomap[\"relations\"]):\n",
    "    if v[0][0] == v[1][0]:\n",
    "      cl = abs(v[0][1] - v[1][1])\n",
    "      mins = min(v[0][1],v[1][1])\n",
    "      print(f\"{v[0][0]} leads to cycle of length {cl} after {mins} steps\")\n",
    "      if not cl in cycles_by_length:\n",
    "        cycles_by_length[cl] = {\n",
    "            \"primary_generators\":[k],\n",
    "            \"secondary_generators\":[]\n",
    "        }\n",
    "      else:\n",
    "        cycles_by_length[cl]['primary_generators'].append(k)\n",
    "      cycles_by_generator[v[0][0]] = cl\n",
    "    else:\n",
    "      cl = cycles_by_generator[v[1][0]]\n",
    "      cycles_by_length[cl]['secondary_generators'].append(k)\n",
    "      cycles_by_generator[v[0][0]] = cl\n",
    "  return {\n",
    "      \"cycles_by_length\":cycles_by_length, \n",
    "      \"cycles_by_generator\":cycles_by_generator\n",
    "  }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0ef57466-b3c1-40cf-beb2-fc16504cfacb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X0 leads to cycle of length 3 after 2 steps\n",
      "X3 leads to cycle of length 2 after 0 steps\n",
      "{'cycles_by_length': {3: {'primary_generators': [0], 'secondary_generators': [1, 2]}, 2: {'primary_generators': [3], 'secondary_generators': []}}, 'cycles_by_generator': {'X0': 3, 'X1': 3, 'X2': 3, 'X3': 2}}\n",
      "~~~~~~~~~~~~~~~~~~~~~~\n",
      "Yp leads to cycle of length 4 after 2 steps\n",
      "Yz leads to cycle of length 3 after 1 steps\n",
      "Ym leads to cycle of length 2 after 0 steps\n",
      "{'cycles_by_length': {4: {'primary_generators': [0], 'secondary_generators': [1]}, 3: {'primary_generators': [2], 'secondary_generators': []}, 2: {'primary_generators': [3], 'secondary_generators': []}}, 'cycles_by_generator': {'Yp': 4, 'Yq': 4, 'Yz': 3, 'Ym': 2}}\n"
     ]
    }
   ],
   "source": [
    "alpha_cycles = get_cycles(endomap_alpha)\n",
    "print(alpha_cycles)\n",
    "print(\"~~~~~~~~~~~~~~~~~~~~~~\")\n",
    "beta_cycles = get_cycles(endomap_beta)\n",
    "print(beta_cycles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ac9edd89-f346-4d1a-87c5-75aac32e13a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def iterate_endomap(endomap, start, steps):\n",
    "  out_val = start\n",
    "  for i in range(steps):\n",
    "    out_val = follow_endomap(endomap,out_val)\n",
    "  return out_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a340f69c-24ea-482a-a9df-10107978a237",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X6\n"
     ]
    }
   ],
   "source": [
    "print(iterate_endomap(XG,\"X1\",2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4e50a412-8f92-4bc0-896a-c9ff0b8ed213",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{'a': 'x'}, {'a': 'y'}, {'a': 'z'}]\n"
     ]
    }
   ],
   "source": [
    "def make_assignments(gen,poss_vals):\n",
    "  output = []\n",
    "  for v in poss_vals:\n",
    "    output.append({gen:v})\n",
    "  return output\n",
    "\n",
    "print(make_assignments(\"a\",[\"x\",\"y\",\"z\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3755a428-6ef0-410a-9535-b5f08445566c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'b': 'l', 'a': 'x'},\n",
       " {'b': 'l', 'a': 'y'},\n",
       " {'b': 'l', 'a': 'z'},\n",
       " {'b': 'm', 'a': 'x'},\n",
       " {'b': 'm', 'a': 'y'},\n",
       " {'b': 'm', 'a': 'z'}]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def join_assignments(ass1,ass2):\n",
    "  if len(ass2)<len(ass1):\n",
    "    return join_assignments(ass2,ass1)\n",
    "  if len(ass1) == 0:\n",
    "    return ass2\n",
    "\n",
    "  output = []\n",
    "  for a1 in ass1:\n",
    "    for a2 in ass2:\n",
    "      new_a1 = a1.copy()\n",
    "      for k,v in zip(a2.keys(),a2.values()):\n",
    "        new_a1[k] = v\n",
    "      output.append(new_a1)\n",
    "  return output\n",
    "join_assignments(make_assignments(\"a\",[\"x\",\"y\",\"z\"]),make_assignments(\"b\",[\"l\",\"m\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "3d746144-088f-4049-b018-58fbea3dc7ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_predecessors(endomap,target,steps=1):\n",
    "  preds = list(endomap.predecessors(target))\n",
    "  if steps > 1 and len(preds) > 0:\n",
    "    r_preds = []\n",
    "    for t in preds:\n",
    "      r_preds.extend(find_predecessors(endomap,t,steps-1))\n",
    "    return r_preds\n",
    "  else:\n",
    "    return preds\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "795b1cad-5888-433d-b46d-d058a7eb4cee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Yx', 'Yz']"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "find_predecessors(YG,\"Yw\",2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "f41efe03-2b88-4327-8af9-362b945b9811",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Attempting to match relation on: X0\n",
      "Cycle Length: 3\n",
      "Possible Generators: [0, 1, 2]\n",
      "Attempting to satisfy: (('X0', 5), ('X0', 2))\n",
      "In X: X5 = X5\n",
      "Testing generator: 0\n",
      "Trying to match up a loop\n",
      "Potential matches for X0: []\n",
      "New assignments: []\n",
      "Joined assignments: []\n",
      "Testing generator: 1\n",
      "Trying to match up a loop\n",
      "Potential matches for X0: []\n",
      "New assignments: []\n",
      "Joined assignments: []\n",
      "Testing generator: 2\n",
      "Trying to match up a loop\n",
      "Potential match at Yz! 0 from 2\n",
      "Potential match at Yy! 1 from 2\n",
      "Potential match at Yw! 2 from 2\n",
      "Potential match at Yx! 3 from 2\n",
      "Potential matches for X0: ['Yz', 'Yy', 'Yw', 'Yx']\n",
      "New assignments: [{'X0': 'Yz'}, {'X0': 'Yy'}, {'X0': 'Yw'}, {'X0': 'Yx'}]\n",
      "Joined assignments: [{'X0': 'Yz'}, {'X0': 'Yy'}, {'X0': 'Yw'}, {'X0': 'Yx'}]\n",
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Attempting to match relation on: X1\n",
      "Cycle Length: 3\n",
      "Possible Generators: [0, 1, 2]\n",
      "Attempting to satisfy: (('X1', 1), ('X0', 2))\n",
      "In X: X5 = X5\n",
      "Testing generator: 0\n",
      "Trying to match up a chain\n",
      "Existing Assignments: [{'X0': 'Yz'}, {'X0': 'Yy'}, {'X0': 'Yw'}, {'X0': 'Yx'}]\n",
      "* Checking {'X0': 'Yz'}\n",
      "\t Found assignment from X0 to Yz\n",
      "\tIn X: 1 steps from X1 is X5\n",
      "\tIn X: 2 steps from X0 is X5\n",
      "\tIn Y: 2 steps from Yz is Yw\n",
      "\tThis means X1 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yz', 'X1': 'Yy'}\n",
      "* Checking {'X0': 'Yy'}\n",
      "\t Found assignment from X0 to Yy\n",
      "\tIn X: 1 steps from X1 is X5\n",
      "\tIn X: 2 steps from X0 is X5\n",
      "\tIn Y: 2 steps from Yy is Yx\n",
      "\tThis means X1 needs to map to Yx after 1 steps\n",
      "\tPossible Predecessors: ['Yw']\n",
      "\tAdding new assignment: {'X0': 'Yy', 'X1': 'Yw'}\n",
      "* Checking {'X0': 'Yw'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X1 is X5\n",
      "\tIn X: 2 steps from X0 is X5\n",
      "\tIn Y: 2 steps from Yw is Yy\n",
      "\tThis means X1 needs to map to Yy after 1 steps\n",
      "\tPossible Predecessors: ['Yx', 'Yz']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx'}\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz'}\n",
      "* Checking {'X0': 'Yx'}\n",
      "\t Found assignment from X0 to Yx\n",
      "\tIn X: 1 steps from X1 is X5\n",
      "\tIn X: 2 steps from X0 is X5\n",
      "\tIn Y: 2 steps from Yx is Yw\n",
      "\tThis means X1 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yx', 'X1': 'Yy'}\n",
      "Done checking old assignments\n",
      "New assignments(5): [{'X0': 'Yz', 'X1': 'Yy'}, {'X0': 'Yy', 'X1': 'Yw'}, {'X0': 'Yw', 'X1': 'Yx'}, {'X0': 'Yw', 'X1': 'Yz'}, {'X0': 'Yx', 'X1': 'Yy'}]\n",
      "Testing generator: 1\n",
      "Trying to match up a chain\n",
      "Existing Assignments: [{'X0': 'Yz', 'X1': 'Yy'}, {'X0': 'Yy', 'X1': 'Yw'}, {'X0': 'Yw', 'X1': 'Yx'}, {'X0': 'Yw', 'X1': 'Yz'}, {'X0': 'Yx', 'X1': 'Yy'}]\n",
      "* Checking {'X0': 'Yz', 'X1': 'Yy'}\n",
      "\t Found assignment from X0 to Yz\n",
      "\tIn X: 1 steps from X1 is X5\n",
      "\tIn X: 2 steps from X0 is X5\n",
      "\tIn Y: 2 steps from Yz is Yw\n",
      "\tThis means X1 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yz', 'X1': 'Yy'}\n",
      "* Checking {'X0': 'Yy', 'X1': 'Yw'}\n",
      "\t Found assignment from X0 to Yy\n",
      "\tIn X: 1 steps from X1 is X5\n",
      "\tIn X: 2 steps from X0 is X5\n",
      "\tIn Y: 2 steps from Yy is Yx\n",
      "\tThis means X1 needs to map to Yx after 1 steps\n",
      "\tPossible Predecessors: ['Yw']\n",
      "\tAdding new assignment: {'X0': 'Yy', 'X1': 'Yw'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yx'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X1 is X5\n",
      "\tIn X: 2 steps from X0 is X5\n",
      "\tIn Y: 2 steps from Yw is Yy\n",
      "\tThis means X1 needs to map to Yy after 1 steps\n",
      "\tPossible Predecessors: ['Yx', 'Yz']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx'}\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yz'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X1 is X5\n",
      "\tIn X: 2 steps from X0 is X5\n",
      "\tIn Y: 2 steps from Yw is Yy\n",
      "\tThis means X1 needs to map to Yy after 1 steps\n",
      "\tPossible Predecessors: ['Yx', 'Yz']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx'}\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz'}\n",
      "* Checking {'X0': 'Yx', 'X1': 'Yy'}\n",
      "\t Found assignment from X0 to Yx\n",
      "\tIn X: 1 steps from X1 is X5\n",
      "\tIn X: 2 steps from X0 is X5\n",
      "\tIn Y: 2 steps from Yx is Yw\n",
      "\tThis means X1 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yx', 'X1': 'Yy'}\n",
      "Done checking old assignments\n",
      "New assignments(7): [{'X0': 'Yz', 'X1': 'Yy'}, {'X0': 'Yy', 'X1': 'Yw'}, {'X0': 'Yw', 'X1': 'Yx'}, {'X0': 'Yw', 'X1': 'Yz'}, {'X0': 'Yw', 'X1': 'Yx'}, {'X0': 'Yw', 'X1': 'Yz'}, {'X0': 'Yx', 'X1': 'Yy'}]\n",
      "Testing generator: 2\n",
      "Trying to match up a chain\n",
      "Existing Assignments: [{'X0': 'Yz', 'X1': 'Yy'}, {'X0': 'Yy', 'X1': 'Yw'}, {'X0': 'Yw', 'X1': 'Yx'}, {'X0': 'Yw', 'X1': 'Yz'}, {'X0': 'Yw', 'X1': 'Yx'}, {'X0': 'Yw', 'X1': 'Yz'}, {'X0': 'Yx', 'X1': 'Yy'}]\n",
      "* Checking {'X0': 'Yz', 'X1': 'Yy'}\n",
      "\t Found assignment from X0 to Yz\n",
      "\tIn X: 1 steps from X1 is X5\n",
      "\tIn X: 2 steps from X0 is X5\n",
      "\tIn Y: 2 steps from Yz is Yw\n",
      "\tThis means X1 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yz', 'X1': 'Yy'}\n",
      "* Checking {'X0': 'Yy', 'X1': 'Yw'}\n",
      "\t Found assignment from X0 to Yy\n",
      "\tIn X: 1 steps from X1 is X5\n",
      "\tIn X: 2 steps from X0 is X5\n",
      "\tIn Y: 2 steps from Yy is Yx\n",
      "\tThis means X1 needs to map to Yx after 1 steps\n",
      "\tPossible Predecessors: ['Yw']\n",
      "\tAdding new assignment: {'X0': 'Yy', 'X1': 'Yw'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yx'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X1 is X5\n",
      "\tIn X: 2 steps from X0 is X5\n",
      "\tIn Y: 2 steps from Yw is Yy\n",
      "\tThis means X1 needs to map to Yy after 1 steps\n",
      "\tPossible Predecessors: ['Yx', 'Yz']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx'}\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yz'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X1 is X5\n",
      "\tIn X: 2 steps from X0 is X5\n",
      "\tIn Y: 2 steps from Yw is Yy\n",
      "\tThis means X1 needs to map to Yy after 1 steps\n",
      "\tPossible Predecessors: ['Yx', 'Yz']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx'}\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yx'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X1 is X5\n",
      "\tIn X: 2 steps from X0 is X5\n",
      "\tIn Y: 2 steps from Yw is Yy\n",
      "\tThis means X1 needs to map to Yy after 1 steps\n",
      "\tPossible Predecessors: ['Yx', 'Yz']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx'}\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yz'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X1 is X5\n",
      "\tIn X: 2 steps from X0 is X5\n",
      "\tIn Y: 2 steps from Yw is Yy\n",
      "\tThis means X1 needs to map to Yy after 1 steps\n",
      "\tPossible Predecessors: ['Yx', 'Yz']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx'}\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz'}\n",
      "* Checking {'X0': 'Yx', 'X1': 'Yy'}\n",
      "\t Found assignment from X0 to Yx\n",
      "\tIn X: 1 steps from X1 is X5\n",
      "\tIn X: 2 steps from X0 is X5\n",
      "\tIn Y: 2 steps from Yx is Yw\n",
      "\tThis means X1 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yx', 'X1': 'Yy'}\n",
      "Done checking old assignments\n",
      "New assignments(11): [{'X0': 'Yz', 'X1': 'Yy'}, {'X0': 'Yy', 'X1': 'Yw'}, {'X0': 'Yw', 'X1': 'Yx'}, {'X0': 'Yw', 'X1': 'Yz'}, {'X0': 'Yw', 'X1': 'Yx'}, {'X0': 'Yw', 'X1': 'Yz'}, {'X0': 'Yw', 'X1': 'Yx'}, {'X0': 'Yw', 'X1': 'Yz'}, {'X0': 'Yw', 'X1': 'Yx'}, {'X0': 'Yw', 'X1': 'Yz'}, {'X0': 'Yx', 'X1': 'Yy'}]\n",
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Attempting to match relation on: X2\n",
      "Cycle Length: 3\n",
      "Possible Generators: [0, 1, 2]\n",
      "Attempting to satisfy: (('X2', 1), ('X0', 3))\n",
      "In X: X6 = X6\n",
      "Testing generator: 0\n",
      "Trying to match up a chain\n",
      "Existing Assignments: [{'X0': 'Yz', 'X1': 'Yy'}, {'X0': 'Yy', 'X1': 'Yw'}, {'X0': 'Yw', 'X1': 'Yx'}, {'X0': 'Yw', 'X1': 'Yz'}, {'X0': 'Yw', 'X1': 'Yx'}, {'X0': 'Yw', 'X1': 'Yz'}, {'X0': 'Yw', 'X1': 'Yx'}, {'X0': 'Yw', 'X1': 'Yz'}, {'X0': 'Yw', 'X1': 'Yx'}, {'X0': 'Yw', 'X1': 'Yz'}, {'X0': 'Yx', 'X1': 'Yy'}]\n",
      "* Checking {'X0': 'Yz', 'X1': 'Yy'}\n",
      "\t Found assignment from X0 to Yz\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yz is Yx\n",
      "\tThis means X2 needs to map to Yx after 1 steps\n",
      "\tPossible Predecessors: ['Yw']\n",
      "\tAdding new assignment: {'X0': 'Yz', 'X1': 'Yy', 'X2': 'Yw'}\n",
      "* Checking {'X0': 'Yy', 'X1': 'Yw'}\n",
      "\t Found assignment from X0 to Yy\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yy is Yy\n",
      "\tThis means X2 needs to map to Yy after 1 steps\n",
      "\tPossible Predecessors: ['Yx', 'Yz']\n",
      "\tAdding new assignment: {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}\n",
      "\tAdding new assignment: {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yx'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yz'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yx'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yz'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yx'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yz'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yx'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yz'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yx', 'X1': 'Yy'}\n",
      "\t Found assignment from X0 to Yx\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yx is Yx\n",
      "\tThis means X2 needs to map to Yx after 1 steps\n",
      "\tPossible Predecessors: ['Yw']\n",
      "\tAdding new assignment: {'X0': 'Yx', 'X1': 'Yy', 'X2': 'Yw'}\n",
      "Done checking old assignments\n",
      "New assignments(12): [{'X0': 'Yz', 'X1': 'Yy', 'X2': 'Yw'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yx', 'X1': 'Yy', 'X2': 'Yw'}]\n",
      "Testing generator: 1\n",
      "Trying to match up a chain\n",
      "Existing Assignments: [{'X0': 'Yz', 'X1': 'Yy', 'X2': 'Yw'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yx', 'X1': 'Yy', 'X2': 'Yw'}]\n",
      "* Checking {'X0': 'Yz', 'X1': 'Yy', 'X2': 'Yw'}\n",
      "\t Found assignment from X0 to Yz\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yz is Yx\n",
      "\tThis means X2 needs to map to Yx after 1 steps\n",
      "\tPossible Predecessors: ['Yw']\n",
      "\tAdding new assignment: {'X0': 'Yz', 'X1': 'Yy', 'X2': 'Yw'}\n",
      "* Checking {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}\n",
      "\t Found assignment from X0 to Yy\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yy is Yy\n",
      "\tThis means X2 needs to map to Yy after 1 steps\n",
      "\tPossible Predecessors: ['Yx', 'Yz']\n",
      "\tAdding new assignment: {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}\n",
      "\tAdding new assignment: {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}\n",
      "* Checking {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}\n",
      "\t Found assignment from X0 to Yy\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yy is Yy\n",
      "\tThis means X2 needs to map to Yy after 1 steps\n",
      "\tPossible Predecessors: ['Yx', 'Yz']\n",
      "\tAdding new assignment: {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}\n",
      "\tAdding new assignment: {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yx', 'X1': 'Yy', 'X2': 'Yw'}\n",
      "\t Found assignment from X0 to Yx\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yx is Yx\n",
      "\tThis means X2 needs to map to Yx after 1 steps\n",
      "\tPossible Predecessors: ['Yw']\n",
      "\tAdding new assignment: {'X0': 'Yx', 'X1': 'Yy', 'X2': 'Yw'}\n",
      "Done checking old assignments\n",
      "New assignments(14): [{'X0': 'Yz', 'X1': 'Yy', 'X2': 'Yw'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yx', 'X1': 'Yy', 'X2': 'Yw'}]\n",
      "Testing generator: 2\n",
      "Trying to match up a chain\n",
      "Existing Assignments: [{'X0': 'Yz', 'X1': 'Yy', 'X2': 'Yw'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yx', 'X1': 'Yy', 'X2': 'Yw'}]\n",
      "* Checking {'X0': 'Yz', 'X1': 'Yy', 'X2': 'Yw'}\n",
      "\t Found assignment from X0 to Yz\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yz is Yx\n",
      "\tThis means X2 needs to map to Yx after 1 steps\n",
      "\tPossible Predecessors: ['Yw']\n",
      "\tAdding new assignment: {'X0': 'Yz', 'X1': 'Yy', 'X2': 'Yw'}\n",
      "* Checking {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}\n",
      "\t Found assignment from X0 to Yy\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yy is Yy\n",
      "\tThis means X2 needs to map to Yy after 1 steps\n",
      "\tPossible Predecessors: ['Yx', 'Yz']\n",
      "\tAdding new assignment: {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}\n",
      "\tAdding new assignment: {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}\n",
      "* Checking {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}\n",
      "\t Found assignment from X0 to Yy\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yy is Yy\n",
      "\tThis means X2 needs to map to Yy after 1 steps\n",
      "\tPossible Predecessors: ['Yx', 'Yz']\n",
      "\tAdding new assignment: {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}\n",
      "\tAdding new assignment: {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}\n",
      "* Checking {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}\n",
      "\t Found assignment from X0 to Yy\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yy is Yy\n",
      "\tThis means X2 needs to map to Yy after 1 steps\n",
      "\tPossible Predecessors: ['Yx', 'Yz']\n",
      "\tAdding new assignment: {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}\n",
      "\tAdding new assignment: {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}\n",
      "* Checking {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}\n",
      "\t Found assignment from X0 to Yy\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yy is Yy\n",
      "\tThis means X2 needs to map to Yy after 1 steps\n",
      "\tPossible Predecessors: ['Yx', 'Yz']\n",
      "\tAdding new assignment: {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}\n",
      "\tAdding new assignment: {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "\t Found assignment from X0 to Yw\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yw is Yw\n",
      "\tThis means X2 needs to map to Yw after 1 steps\n",
      "\tPossible Predecessors: ['Yy']\n",
      "\tAdding new assignment: {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\n",
      "* Checking {'X0': 'Yx', 'X1': 'Yy', 'X2': 'Yw'}\n",
      "\t Found assignment from X0 to Yx\n",
      "\tIn X: 1 steps from X2 is X6\n",
      "\tIn X: 3 steps from X0 is X6\n",
      "\tIn Y: 3 steps from Yx is Yx\n",
      "\tThis means X2 needs to map to Yx after 1 steps\n",
      "\tPossible Predecessors: ['Yw']\n",
      "\tAdding new assignment: {'X0': 'Yx', 'X1': 'Yy', 'X2': 'Yw'}\n",
      "Done checking old assignments\n",
      "New assignments(18): [{'X0': 'Yz', 'X1': 'Yy', 'X2': 'Yw'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X0': 'Yx', 'X1': 'Yy', 'X2': 'Yw'}]\n",
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Attempting to match relation on: X3\n",
      "Cycle Length: 2\n",
      "Possible Generators: [3]\n",
      "Attempting to satisfy: (('X3', 2), ('X3', 0))\n",
      "In X: X3 = X3\n",
      "Testing generator: 3\n",
      "Trying to match up a loop\n",
      "Potential match at Ym! 0 from 3\n",
      "Potential match at Yl! 1 from 3\n",
      "Potential matches for X3: ['Ym', 'Yl']\n",
      "New assignments: [{'X3': 'Ym'}, {'X3': 'Yl'}]\n",
      "Joined assignments: [{'X3': 'Ym', 'X0': 'Yz', 'X1': 'Yy', 'X2': 'Yw'}, {'X3': 'Ym', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X3': 'Ym', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X3': 'Ym', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X3': 'Ym', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X3': 'Ym', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X3': 'Ym', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X3': 'Ym', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X3': 'Ym', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X3': 'Ym', 'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X3': 'Ym', 'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X3': 'Ym', 'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X3': 'Ym', 'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X3': 'Ym', 'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X3': 'Ym', 'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X3': 'Ym', 'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X3': 'Ym', 'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X3': 'Ym', 'X0': 'Yx', 'X1': 'Yy', 'X2': 'Yw'}, {'X3': 'Yl', 'X0': 'Yz', 'X1': 'Yy', 'X2': 'Yw'}, {'X3': 'Yl', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X3': 'Yl', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X3': 'Yl', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X3': 'Yl', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X3': 'Yl', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X3': 'Yl', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X3': 'Yl', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}, {'X3': 'Yl', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}, {'X3': 'Yl', 'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X3': 'Yl', 'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X3': 'Yl', 'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X3': 'Yl', 'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X3': 'Yl', 'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X3': 'Yl', 'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X3': 'Yl', 'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}, {'X3': 'Yl', 'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}, {'X3': 'Yl', 'X0': 'Yx', 'X1': 'Yy', 'X2': 'Yw'}]\n",
      "Pre-dupe removal: 36\n",
      "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
      "Final assignment count: 12\n",
      "{\"{'X3': 'Yl', 'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\", \"{'X3': 'Ym', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}\", \"{'X3': 'Ym', 'X0': 'Yw', 'X1': 'Yz', 'X2': 'Yy'}\", \"{'X3': 'Yl', 'X0': 'Yx', 'X1': 'Yy', 'X2': 'Yw'}\", \"{'X3': 'Yl', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}\", \"{'X3': 'Yl', 'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\", \"{'X3': 'Ym', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yz'}\", \"{'X3': 'Ym', 'X0': 'Yw', 'X1': 'Yx', 'X2': 'Yy'}\", \"{'X3': 'Ym', 'X0': 'Yz', 'X1': 'Yy', 'X2': 'Yw'}\", \"{'X3': 'Yl', 'X0': 'Yz', 'X1': 'Yy', 'X2': 'Yw'}\", \"{'X3': 'Yl', 'X0': 'Yy', 'X1': 'Yw', 'X2': 'Yx'}\", \"{'X3': 'Ym', 'X0': 'Yx', 'X1': 'Yy', 'X2': 'Yw'}\"}\n"
     ]
    }
   ],
   "source": [
    "assignments = []\n",
    "\n",
    "for idx,rel in enumerate(endomap_alpha['relations']):\n",
    "  print(\"~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\")\n",
    "  x_gen = rel[0][0]\n",
    "  print(f'Attempting to match relation on: {x_gen}')\n",
    "  cl = alpha_cycles['cycles_by_generator'][x_gen]\n",
    "  print(f'Cycle Length: {cl}')\n",
    "  y_cycles = alpha_cycles['cycles_by_length'][cl]\n",
    "  poss_y_gen = y_cycles['primary_generators']+y_cycles['secondary_generators']\n",
    "  print(f\"Possible Generators: {poss_y_gen}\")\n",
    "\n",
    "    \n",
    "  print(f\"Attempting to satisfy: {rel}\")\n",
    "  rel_lhs = iterate_endomap(XG,rel[0][0],rel[0][1])\n",
    "  rel_rhs = iterate_endomap(XG,rel[1][0],rel[1][1])\n",
    "  print(f\"In X: {rel_lhs} = {rel_rhs}\")\n",
    "    \n",
    "  for gen in poss_y_gen:\n",
    "    print(f\"Testing generator: {gen}\")\n",
    "    if rel[0][0]==rel[1][0]:\n",
    "      print(\"Trying to match up a loop\")\n",
    "      seen_in_Y = set([])\n",
    "      eligible_subs = {}\n",
    "      cur_y = endomap_beta['generators'][gen]\n",
    "      y_steps = 0\n",
    "      found_pairs = []\n",
    "      while not cur_y in seen_in_Y:\n",
    "        lhs = iterate_endomap(YG,cur_y,rel[0][1])\n",
    "        rhs = iterate_endomap(YG,cur_y,rel[1][1])\n",
    "        if lhs == rhs:\n",
    "          print(f\"Potential match at {cur_y}! {y_steps} from {gen}\")\n",
    "          found_pairs.append(cur_y)\n",
    "        seen_in_Y.add(cur_y)\n",
    "        y_steps += 1\n",
    "        cur_y = iterate_endomap(YG,cur_y,1)\n",
    "\n",
    "      print(f\"Potential matches for {x_gen}: {found_pairs}\")\n",
    "      new_assignments = make_assignments(x_gen,found_pairs)\n",
    "      print(f\"New assignments: {new_assignments}\")\n",
    "      assignments = join_assignments(assignments,new_assignments)\n",
    "      print(f\"Joined assignments: {assignments}\")\n",
    "    else:\n",
    "      print(\"Trying to match up a chain\")\n",
    "      new_assignments = []\n",
    "      print(f\"Existing Assignments: {assignments}\")\n",
    "      for ass in assignments:\n",
    "        print(f\"* Checking {ass}\")\n",
    "        if rel[1][0] in ass.keys():\n",
    "          print(f\"\\t Found assignment from {rel[1][0]} to {ass[rel[1][0]]}\")\n",
    "          y_target = ass[rel[1][0]]\n",
    "\n",
    "          x_lhs = iterate_endomap(XG,rel[0][0],rel[0][1])\n",
    "          print(f\"\\tIn X: {rel[0][1]} steps from {rel[0][0]} is {x_lhs}\")\n",
    "          x_rhs = iterate_endomap(XG,rel[1][0],rel[1][1])\n",
    "          print(f\"\\tIn X: {rel[1][1]} steps from {rel[1][0]} is {x_rhs}\")\n",
    "\n",
    "\n",
    "          y_rhs = iterate_endomap(YG,y_target,rel[1][1])\n",
    "          print(f\"\\tIn Y: {rel[1][1]} steps from {y_target} is {y_rhs}\")\n",
    "\n",
    "          print(f\"\\tThis means {rel[0][0]} needs to map to {y_rhs} after {rel[0][1]} steps\")\n",
    "          poss_vals = find_predecessors(YG,y_rhs,rel[0][1])\n",
    "          print(f\"\\tPossible Predecessors: {poss_vals}\")\n",
    "\n",
    "          for v in poss_vals:\n",
    "            new_ass = ass.copy()\n",
    "            new_ass[rel[0][0]] = v\n",
    "            print(f\"\\tAdding new assignment: {new_ass}\")\n",
    "            new_assignments.append(new_ass)\n",
    "      print(\"Done checking old assignments\")\n",
    "      print(f\"New assignments({len(new_assignments)}): {new_assignments}\")\n",
    "\n",
    "      assignments = new_assignments\n",
    "\n",
    "print(f\"Pre-dupe removal: {len(assignments)}\")\n",
    "    \n",
    "remove_dupes = set([str(x) for x in assignments])    \n",
    "print(\"~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\")\n",
    "print(f\"Final assignment count: {len(remove_dupes)}\")\n",
    "print(remove_dupes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "8511e31c-d8bb-4905-9417-a441274e89ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "#ok, we're supposed to have 14... where's the missing one?\n",
    "#let's try smaller systems\n",
    "sm_x_nodes = [\"a\", \"b\", \"c\", \"α a\", \"α^2 a\", \"α^3 a\", \"α^4 a\"]\n",
    "sm_x_edges = [\n",
    "    (sm_x_nodes[0],sm_x_nodes[3]),\n",
    "    (sm_x_nodes[1],sm_x_nodes[4]),\n",
    "    (sm_x_nodes[2],sm_x_nodes[5]),\n",
    "    (sm_x_nodes[3],sm_x_nodes[4]),\n",
    "    (sm_x_nodes[4],sm_x_nodes[5]),\n",
    "    (sm_x_nodes[5],sm_x_nodes[6]),\n",
    "    (sm_x_nodes[6],sm_x_nodes[4])\n",
    "    \n",
    "]\n",
    "sm_XG = nx.DiGraph()\n",
    "sm_XG.add_nodes_from(sm_x_nodes)\n",
    "sm_XG.add_edges_from(sm_x_edges)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "625fad79-8b78-4262-b033-c4bf808d0e72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(sm_XG, with_labels=True, font_weight='bold')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "29e4678a-c823-49c9-bf3b-48ecd34a5729",
   "metadata": {},
   "outputs": [],
   "source": [
    "#let's try smaller systems\n",
    "sm_y_nodes = [\"w\",\"x\",\"y\",\"z\"]\n",
    "sm_y_edges = [\n",
    "    (sm_y_nodes[0],sm_y_nodes[1]),\n",
    "    (sm_y_nodes[1],sm_y_nodes[2]),\n",
    "    (sm_y_nodes[2],sm_y_nodes[0]),\n",
    "    (sm_y_nodes[3],sm_y_nodes[2])\n",
    "]\n",
    "sm_YG = nx.DiGraph()\n",
    "sm_YG.add_nodes_from(sm_y_nodes)\n",
    "sm_YG.add_edges_from(sm_y_edges)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "70a41408-7aa8-4bdd-b48a-68f0288e6bde",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(sm_YG, with_labels=True, font_weight='bold')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "0a51f754-8b41-46b7-a61d-cf0afd143be1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checking node 0 with 0 arrows in\n",
      "Adding root generator a\n",
      "Adding follow up node α a: 1 from a\n",
      "Adding follow up node α^2 a: 2 from a\n",
      "Adding follow up node α^3 a: 3 from a\n",
      "Adding follow up node α^4 a: 4 from a\n",
      "next node α^2 a already has presentation\n",
      "Checking node 1 with 0 arrows in\n",
      "Adding root generator b\n",
      "next node α^2 a already has presentation\n",
      "Checking node 2 with 0 arrows in\n",
      "Adding root generator c\n",
      "next node α^3 a already has presentation\n",
      "Checking node 3 with 1 arrows in\n",
      "Only 1 way into node 3\n",
      "already has a presentation\n",
      "Checking node 6 with 1 arrows in\n",
      "Only 1 way into node 6\n",
      "already has a presentation\n",
      "Checking node 5 with 2 arrows in\n",
      "More than 1 way in\n",
      "Checking node 4 with 3 arrows in\n",
      "More than 1 way in\n",
      "Checking node 3 with 0 arrows in\n",
      "Adding root generator z\n",
      "Adding follow up node y: 1 from z\n",
      "Adding follow up node w: 2 from z\n",
      "Adding follow up node x: 3 from z\n",
      "next node y already has presentation\n",
      "Checking node 0 with 1 arrows in\n",
      "Only 1 way into node 0\n",
      "already has a presentation\n",
      "Checking node 1 with 1 arrows in\n",
      "Only 1 way into node 1\n",
      "already has a presentation\n",
      "Checking node 2 with 2 arrows in\n",
      "More than 1 way in\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_69979/1978947672.py:4: FutureWarning: adjacency_matrix will return a scipy.sparse array instead of a matrix in Networkx 3.0.\n",
      "  GA =  nx.adjacency_matrix(G)\n"
     ]
    }
   ],
   "source": [
    "sm_X_alpha = make_presentation(sm_XG)\n",
    "sm_Y_beta = make_presentation(sm_YG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "a94525b8-a698-445e-ad6b-9a634a2cf0ae",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'generators': ['a', 'b', 'c'], 'relations': [(('a', 5), ('a', 2)), (('b', 1), ('a', 2)), (('c', 1), ('a', 3))]}\n",
      "~~~~~~~~~~~~~~~~~~~\n",
      "{'generators': ['z'], 'relations': [(('z', 4), ('z', 1))]}\n"
     ]
    }
   ],
   "source": [
    "\n",
    "print(sm_X_alpha)\n",
    "print(\"~~~~~~~~~~~~~~~~~~~\")\n",
    "print(sm_Y_beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "cf3576d9-9a8d-4d0f-b8d0-4ae33bd59eac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16384"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "4**7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "4c64e569-f195-4e56-b30c-3af1481abe9f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# okay, stepping back -- lets check ALL MAPS\n",
    "def make_all_maps(xs,ys):\n",
    "    x_size = len(xs)\n",
    "    y_size = len(ys)\n",
    "    total = y_size**x_size\n",
    "    all_assignments = []\n",
    "    for x in xs:\n",
    "        new_maps = []\n",
    "        for y in ys:\n",
    "            new_maps.append({x:y})\n",
    "        all_assignments = join_assignments(all_assignments,new_maps) \n",
    "    return all_assignments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "4b4f36c9-e0ee-4c0c-aee4-e1269839f1c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "sm_maps = make_all_maps(sm_x_nodes,sm_y_nodes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "287ba7b4-60fc-418c-90c7-5fde117affd6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16384\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[{'α^4 a': 'z',\n",
       "  'α^3 a': 'z',\n",
       "  'α^2 a': 'z',\n",
       "  'α a': 'z',\n",
       "  'c': 'z',\n",
       "  'a': 'z',\n",
       "  'b': 'w'},\n",
       " {'α^4 a': 'z',\n",
       "  'α^3 a': 'z',\n",
       "  'α^2 a': 'z',\n",
       "  'α a': 'z',\n",
       "  'c': 'z',\n",
       "  'a': 'z',\n",
       "  'b': 'x'},\n",
       " {'α^4 a': 'z',\n",
       "  'α^3 a': 'z',\n",
       "  'α^2 a': 'z',\n",
       "  'α a': 'z',\n",
       "  'c': 'z',\n",
       "  'a': 'z',\n",
       "  'b': 'y'},\n",
       " {'α^4 a': 'z',\n",
       "  'α^3 a': 'z',\n",
       "  'α^2 a': 'z',\n",
       "  'α a': 'z',\n",
       "  'c': 'z',\n",
       "  'a': 'z',\n",
       "  'b': 'z'}]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(len(sm_maps))\n",
    "sm_maps[-4:]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "47de2d13-33c2-43ff-9ac6-dc5954e49169",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'α^4 a': 'w',\n",
       " 'α^3 a': 'w',\n",
       " 'α^2 a': 'w',\n",
       " 'α a': 'w',\n",
       " 'c': 'w',\n",
       " 'a': 'w',\n",
       " 'b': 'w'}"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm_maps[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "4a60da1b-b6f8-4ff7-8070-8a67b79258f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def preserves_structure(f,x_graph,y_graph):\n",
    "    for k,v in zip(f.keys(),f.values()):\n",
    "        #print(f\"f({k}) = {v}\")\n",
    "        alpha_x = follow_endomap(x_graph,k)\n",
    "        f_alpha_x = f[alpha_x]\n",
    "        #print(f\"alpha({k}) = {alpha_x}\")\n",
    "        #print(f\"f({alpha_x}) = {f_alpha_x}\")\n",
    "        beta_y = follow_endomap(y_graph,v)\n",
    "        #print(f\"beta({v}) = {beta_y}\")\n",
    "        if beta_y != f_alpha_x:\n",
    "              #print(\"fails to preserve structure\")\n",
    "              return False\n",
    "    return True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "6429b7db-5eea-4a93-9821-a53f309a0b0a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preserves_structure(sm_maps[0],sm_XG, sm_YG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "532091dd-380a-4339-b086-d4f84ac195f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "sm_evaluations = list(filter(lambda x: preserves_structure(x,sm_XG,sm_YG),sm_maps))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "dc731d2a-a730-4784-9b98-585ea2649083",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n",
      "[{'α^4 a': 'w', 'α^3 a': 'y', 'α^2 a': 'x', 'α a': 'w', 'c': 'x', 'a': 'y', 'b': 'w'}, {'α^4 a': 'w', 'α^3 a': 'y', 'α^2 a': 'x', 'α a': 'w', 'c': 'z', 'a': 'y', 'b': 'w'}, {'α^4 a': 'x', 'α^3 a': 'w', 'α^2 a': 'y', 'α a': 'x', 'c': 'y', 'a': 'w', 'b': 'x'}, {'α^4 a': 'x', 'α^3 a': 'w', 'α^2 a': 'y', 'α a': 'x', 'c': 'y', 'a': 'w', 'b': 'z'}, {'α^4 a': 'y', 'α^3 a': 'x', 'α^2 a': 'w', 'α a': 'y', 'c': 'w', 'a': 'x', 'b': 'y'}, {'α^4 a': 'y', 'α^3 a': 'x', 'α^2 a': 'w', 'α a': 'y', 'c': 'w', 'a': 'z', 'b': 'y'}]\n"
     ]
    }
   ],
   "source": [
    "print(len(sm_evaluations))\n",
    "print(sm_evaluations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "b1f0973f-f25f-4df3-9283-e4b6fad3374d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(X1) edge (X4)\n",
      "(X2) edge (X5)\n",
      "(X3) edge (X6)\n",
      "(X4) edge (X5)\n",
      "(X5) edge (X6)\n",
      "(X6) edge (X7)\n",
      "(X7) edge (X5)\n",
      "(X8) edge (X1)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# IDEA: extend tail of 'a'\n",
    "\n",
    "\n",
    "sm_z_nodes = [\"X\"+str(i+1) for i in range(8)]\n",
    "sm_z_edges = [\n",
    "    (sm_z_nodes[0],sm_z_nodes[3]),\n",
    "    (sm_z_nodes[1],sm_z_nodes[4]),\n",
    "    (sm_z_nodes[2],sm_z_nodes[5]),\n",
    "    (sm_z_nodes[3],sm_z_nodes[4]),\n",
    "    (sm_z_nodes[4],sm_z_nodes[5]),\n",
    "    (sm_z_nodes[5],sm_z_nodes[6]),\n",
    "    (sm_z_nodes[6],sm_z_nodes[4]),\n",
    "    (sm_z_nodes[7],sm_z_nodes[0])\n",
    "    \n",
    "]\n",
    "sm_ZG = nx.DiGraph()\n",
    "sm_ZG.add_nodes_from(sm_z_nodes)\n",
    "sm_ZG.add_edges_from(sm_z_edges)\n",
    "\n",
    "# make my latex easier\n",
    "print(\"\\n\".join([\"(\"+e[0]+\") edge (\"+e[1]+\")\" for e in sm_z_edges]))\n",
    "\n",
    "nx.draw(sm_ZG, with_labels=True, font_weight='bold')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "caff54bb-2507-44ef-949a-48fee8a754bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "my_missing_maps = make_all_maps(sm_z_nodes,sm_y_nodes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "2cd9797a-cdbb-46f5-8e47-91ac8113ccd5",
   "metadata": {},
   "outputs": [],
   "source": [
    "missing_map_evaluations = list(filter(lambda x: preserves_structure(x,sm_ZG,sm_YG),my_missing_maps))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "a92de802-5516-4680-a9e4-e4726ab546b3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n",
      "[{'X8': 'w', 'X7': 'y', 'X6': 'x', 'X5': 'w', 'X4': 'y', 'X3': 'w', 'X1': 'x', 'X2': 'y'}, {'X8': 'x', 'X7': 'w', 'X6': 'y', 'X5': 'x', 'X4': 'w', 'X3': 'x', 'X1': 'y', 'X2': 'w'}, {'X8': 'x', 'X7': 'w', 'X6': 'y', 'X5': 'x', 'X4': 'w', 'X3': 'z', 'X1': 'y', 'X2': 'w'}, {'X8': 'y', 'X7': 'x', 'X6': 'w', 'X5': 'y', 'X4': 'x', 'X3': 'y', 'X1': 'w', 'X2': 'x'}, {'X8': 'y', 'X7': 'x', 'X6': 'w', 'X5': 'y', 'X4': 'x', 'X3': 'y', 'X1': 'w', 'X2': 'z'}, {'X8': 'z', 'X7': 'w', 'X6': 'y', 'X5': 'x', 'X4': 'w', 'X3': 'x', 'X1': 'y', 'X2': 'w'}, {'X8': 'z', 'X7': 'w', 'X6': 'y', 'X5': 'x', 'X4': 'w', 'X3': 'z', 'X1': 'y', 'X2': 'w'}]\n"
     ]
    }
   ],
   "source": [
    "print(len(missing_map_evaluations))\n",
    "print(missing_map_evaluations)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}