diff --git a/ILP/butadien/butadiensynthesis.py b/ILP/butadien/butadiensynthesis.py
new file mode 100644
index 0000000..e018ece
--- /dev/null
+++ b/ILP/butadien/butadiensynthesis.py
@@ -0,0 +1,281 @@
+import gurobipy as gp
+from gurobipy import GRB, Model, quicksum
+
+HYPEREDGES = {
+    4: (['Butadien', 'Butadien'], []), 
+    5: (['Butadien', 'Butadien'], ['Butadien', 'Butadien']), 
+    7: (['Butadien', 'Butadien'], []), 
+    9: (['p_{0,0}', 'p_{0,0}'], []), 
+    10: (['p_{0,0}', 'p_{0,1}'], ['Butadien', 'Butadien']), 
+    11: (['p_{0,0}', 'p_{0,1}'], []), 
+    13: (['p_{0,0}', 'p_{0,2}'], []), 
+    14: (['p_{0,0}', 'p_{0,2}'], []), 
+    15: (['Butadien', 'p_{0,0}'], ['Butadien']), 
+    16: (['p_{0,1}', 'p_{0,1}'], []), 
+    18: (['p_{0,1}', 'p_{0,1}'], ['Butadien']), 
+    20: (['p_{0,1}', 'p_{0,2}'], ['Butadien']), 
+    21: (['Butadien', 'p_{0,1}'], ['Butadien']), 
+    22: (['p_{0,1}', 'p_{0,2}'], []), 
+    23: (['Butadien', 'p_{0,1}'], []), 
+    24: (['p_{0,2}', 'p_{0,2}'], []), 
+    25: (['Butadien', 'p_{0,2}'], ['Butadien']), 
+    26: (['Butadien', 'p_{0,2}'], []), 
+    28: (['p_{0,0}', 'p_{0,1}'], []), 
+    30: (['Butadien', 'p_{0,0}'], []), 
+    32: (['Butadien', 'p_{0,1}'], []), 
+    33: (['Butadien', 'p_{0,1}'], []), 
+    35: (['Butadien', 'p_{0,1}'], []), 
+    37: (['Butadien', 'p_{0,1}'], []), 
+    38: (['p_{0,3}'], []), 
+    42: (['p_{0,4}'], []), 
+    50: (['p_{0,3}', 'p_{0,3}'], []), 
+    51: (['p_{0,3}', 'p_{0,4}'], []), 
+    52: (['p_{0,3}', 'p_{0,5}'], []), 
+    53: (['p_{0,3}', 'p_{0,6}'], []), 
+    54: (['p_{0,3}', 'p_{0,8}'], []), 
+    55: (['p_{0,3}', 'p_{0,9}'], []), 
+    56: (['p_{0,3}', 'p_{0,10}'], []), 
+    57: (['p_{0,2}', 'p_{0,3}'], []), 
+    58: (['p_{0,0}', 'p_{0,3}'], []), 
+    59: (['Butadien', 'p_{0,3}'], ['Butadien']), 
+    60: (['p_{0,1}', 'p_{0,3}'], []), 
+    61: (['p_{0,4}', 'p_{0,4}'], []), 
+    62: (['p_{0,4}', 'p_{0,5}'], []), 
+    64: (['p_{0,4}', 'p_{0,6}'], []), 
+    65: (['p_{0,2}', 'p_{0,4}'], []), 
+    66: (['p_{0,0}', 'p_{0,4}'], ['Butadien']), 
+    67: (['Butadien', 'p_{0,4}'], []), 
+    68: (['Butadien', 'p_{0,4}'], ['Butadien']), 
+    69: (['p_{0,1}', 'p_{0,4}'], []), 
+    70: (['p_{0,4}', 'p_{0,6}'], []), 
+    71: (['p_{0,4}', 'p_{0,8}'], []), 
+    72: (['p_{0,4}', 'p_{0,9}'], []), 
+    73: (['p_{0,4}', 'p_{0,10}'], []), 
+    74: (['p_{0,2}', 'p_{0,4}'], []), 
+    75: (['p_{0,0}', 'p_{0,4}'], []), 
+    76: (['p_{0,5}', 'p_{0,5}'], []), 
+    77: (['p_{0,5}', 'p_{0,6}'], []), 
+    78: (['p_{0,2}', 'p_{0,5}'], []), 
+    79: (['p_{0,0}', 'p_{0,5}'], ['Butadien']), 
+    80: (['Butadien', 'p_{0,5}'], []), 
+    81: (['Butadien', 'p_{0,5}'], ['Butadien']), 
+    82: (['p_{0,1}', 'p_{0,5}'], []), 
+    83: (['p_{0,1}', 'p_{0,5}'], []), 
+    84: (['p_{0,5}', 'p_{0,6}'], []), 
+    85: (['p_{0,5}', 'p_{0,8}'], []), 
+    86: (['p_{0,5}', 'p_{0,9}'], []), 
+    87: (['p_{0,5}', 'p_{0,10}'], []), 
+    88: (['p_{0,0}', 'p_{0,5}'], []), 
+    89: (['p_{0,6}', 'p_{0,6}'], []), 
+    90: (['p_{0,6}', 'p_{0,8}'], []), 
+    91: (['p_{0,6}', 'p_{0,9}'], []), 
+    92: (['p_{0,6}', 'p_{0,10}'], []), 
+    93: (['p_{0,2}', 'p_{0,6}'], []), 
+    94: (['p_{0,0}', 'p_{0,6}'], []), 
+    95: (['Butadien', 'p_{0,6}'], ['Butadien']), 
+    96: (['Butadien', 'p_{0,6}'], []), 
+    97: (['p_{0,1}', 'p_{0,6}'], ['Butadien']), 
+    98: (['p_{0,1}', 'p_{0,6}'], []), 
+    100: (['p_{0,0}', 'p_{0,6}'], []), 
+    102: (['p_{0,0}', 'p_{0,7}'], []), 
+    103: (['p_{0,8}', 'p_{0,8}'], []), 
+    104: (['p_{0,8}', 'p_{0,9}'], []), 
+    105: (['p_{0,8}', 'p_{0,10}'], []), 
+    106: (['p_{0,2}', 'p_{0,8}'], []), 
+    107: (['p_{0,0}', 'p_{0,8}'], []), 
+    108: (['Butadien', 'p_{0,8}'], ['Butadien']), 
+    109: (['p_{0,1}', 'p_{0,8}'], []), 
+    110: (['p_{0,9}', 'p_{0,9}'], []), 
+    111: (['p_{0,9}', 'p_{0,10}'], []), 
+    112: (['p_{0,2}', 'p_{0,9}'], []), 
+    113: (['p_{0,0}', 'p_{0,9}'], []), 
+    114: (['Butadien', 'p_{0,9}'], ['Butadien']), 
+    115: (['p_{0,1}', 'p_{0,9}'], []), 
+    116: (['p_{0,10}', 'p_{0,10}'], []), 
+    117: (['p_{0,2}', 'p_{0,10}'], []), 
+    118: (['p_{0,0}', 'p_{0,10}'], []), 
+    119: (['Butadien', 'p_{0,10}'], ['Butadien']), 
+    120: (['p_{0,1}', 'p_{0,10}'], []), 
+    121: (['p_{0,0}', 'p_{0,4}'], []), 
+    123: (['p_{0,0}', 'p_{0,4}'], []), 
+    125: (['Butadien', 'p_{0,7}'], []), 
+    130: (['p_{0,14}'], []), 
+    132: (['p_{0,15}'], []), 
+    135: (['p_{0,0}', 'p_{0,11}'], []), 
+    136: (['p_{0,12}', 'p_{0,12}'], []), 
+    137: (['p_{0,12}', 'p_{0,13}'], []), 
+    138: (['p_{0,12}', 'p_{0,14}'], []), 
+    139: (['p_{0,12}', 'p_{0,15}'], []),
+    140: (['p_{0,12}', 'p_{0,16}'], []), 
+    141: (['p_{0,8}', 'p_{0,12}'], []), 
+    142: (['p_{0,9}', 'p_{0,12}'], []), 
+    143: (['Butadien', 'p_{0,12}'], ['Butadien']), 
+    144: (['p_{0,10}', 'p_{0,12}'], []), 
+    145: (['p_{0,0}', 'p_{0,12}'], []), 
+    146: (['p_{0,1}', 'p_{0,12}'], []), 
+    147: (['p_{0,2}', 'p_{0,12}'], []), 
+    148: (['p_{0,3}', 'p_{0,12}'], []), 
+    149: (['p_{0,4}', 'p_{0,12}'], []), 
+    150: (['p_{0,5}', 'p_{0,12}'], []), 
+    151: (['p_{0,6}', 'p_{0,12}'], []), 
+    152: (['p_{0,13}', 'p_{0,13}'], []), 
+    153: (['Butadien', 'p_{0,13}'], []), 
+    154: (['Butadien', 'p_{0,13}'], ['Butadien']), 
+    155: (['p_{0,0}', 'p_{0,13}'], ['Butadien']), 
+    156: (['p_{0,1}', 'p_{0,13}'], []), 
+    157: (['p_{0,1}', 'p_{0,13}'], []), 
+    158: (['p_{0,2}', 'p_{0,13}'], []), 
+    159: (['p_{0,4}', 'p_{0,13}'], []), 
+    160: (['p_{0,5}', 'p_{0,13}'], []), 
+    161: (['p_{0,6}', 'p_{0,13}'], []), 
+    162: (['p_{0,13}', 'p_{0,14}'], []), 
+    163: (['p_{0,13}', 'p_{0,15}'], []), 
+    164: (['p_{0,13}', 'p_{0,16}'], []), 
+    165: (['p_{0,8}', 'p_{0,13}'], []), 
+    166: (['p_{0,9}', 'p_{0,13}'], []), 
+    167: (['p_{0,10}', 'p_{0,13}'], []), 
+    168: (['p_{0,0}', 'p_{0,13}'], []), 
+    169: (['p_{0,2}', 'p_{0,13}'], []), 
+    170: (['p_{0,3}', 'p_{0,13}'], []), 
+    171: (['p_{0,14}', 'p_{0,14}'], []), 
+    172: (['p_{0,14}', 'p_{0,15}'], []), 
+    173: (['p_{0,14}', 'p_{0,16}'], []), 
+    174: (['p_{0,8}', 'p_{0,14}'], []), 
+    175: (['p_{0,9}', 'p_{0,14}'], []), 
+    176: (['Butadien', 'p_{0,14}'], ['Butadien']), 
+    177: (['p_{0,10}', 'p_{0,14}'], []), 
+    178: (['p_{0,0}', 'p_{0,14}'], []), 
+    179: (['p_{0,1}', 'p_{0,14}'], []), 
+    180: (['p_{0,2}', 'p_{0,14}'], []), 
+    181: (['p_{0,3}', 'p_{0,14}'], []), 
+    182: (['p_{0,4}', 'p_{0,14}'], []), 
+    183: (['p_{0,5}', 'p_{0,14}'], []), 
+    184: (['p_{0,6}', 'p_{0,14}'], []), 
+    185: (['p_{0,15}', 'p_{0,15}'], []), 
+    186: (['p_{0,15}', 'p_{0,16}'], []), 
+    187: (['p_{0,8}', 'p_{0,15}'], []), 
+    188: (['p_{0,9}', 'p_{0,15}'], []), 
+    189: (['Butadien', 'p_{0,15}'], ['Butadien']), 
+    190: (['p_{0,10}', 'p_{0,15}'], []), 
+    191: (['p_{0,0}', 'p_{0,15}'], []), 
+    192: (['p_{0,1}', 'p_{0,15}'], []), 
+    193: (['p_{0,2}', 'p_{0,15}'], []), 
+    194: (['p_{0,3}', 'p_{0,15}'], []), 
+    195: (['p_{0,4}', 'p_{0,15}'], []), 
+    196: (['p_{0,5}', 'p_{0,15}'], []), 
+    197: (['p_{0,6}', 'p_{0,15}'], []), 
+    198: (['p_{0,16}', 'p_{0,16}'], []), 
+    199: (['p_{0,8}', 'p_{0,16}'], []), 
+    200: (['p_{0,9}', 'p_{0,16}'], []), 
+    201: (['Butadien', 'p_{0,16}'], ['Butadien']), 
+    202: (['p_{0,10}', 'p_{0,16}'], []), 
+    203: (['p_{0,0}', 'p_{0,16}'], []), 
+    204: (['p_{0,1}', 'p_{0,16}'], []), 
+    205: (['p_{0,2}', 'p_{0,16}'], []), 
+    206: (['p_{0,3}', 'p_{0,16}'], []), 
+    207: (['p_{0,4}', 'p_{0,16}'], []), 
+    208: (['p_{0,5}', 'p_{0,16}'], []), 
+    209: (['p_{0,6}', 'p_{0,16}'], []), 
+    211: (['Butadien', 'p_{0,11}'], []),
+}
+
+VERTICES = ['Butadien', 'p_{0,0}', 'p_{0,1}', 'p_{0,2}', 'p_{0,3}', 'p_{0,4}', 'p_{0,5}', 'p_{0,6}', 'p_{0,7}', 'p_{0,8}', 'p_{0,9}', 'p_{0,10}', 'p_{0,11}', 'p_{0,12}', 'p_{0,13}', 'p_{0,14}', 'p_{0,15}', 'p_{0,16}', 'p_{0,17}', 'p_{0,18}']
+
+VERTICESSMILES = ['C=CC=C', 'C=C', 'C=CC=CC=C', 'C1CCC(C=C)CC=1', 'C(CCC(C=C)CC=C)=C', 'C=CC=CC=CC=C', 'C1CCC(C=CC=C)CC=1', 'C=CC1C=CCCC1', 'C1CCCCC=1', 'C=CC1CC=CCC1C=C', 'C1CCC(C=C)C(C=C)C=1', 'C(C1CC(C=C)C=CC1)=C', 'C1C=CC=CC=1', 'C(CCC1C=CC=CC1)=C', 'C1C(C=CC=C)CCCC=1', 'C=CC(C=C)CCCC=C', 'C=CCCCCC=C', 'C=CC1C=CC(C=C)CC1', 'C1CC2CCCCC2CC=1', 'C1CC2C=CC=CC2CC=1']
+
+FIXED_FLOWS = {
+    #1: 1,
+}
+
+def build_model(name, hyperedges, vertices, nmrlikelihoods, excluded_support=None):
+    model = Model(name)
+
+    x = {e_id: model.addVar(vtype=GRB.INTEGER, lb = 0, name = f"x_{e_id}") for e_id in hyperedges}
+    b = {e_id: model.addVar(vtype=GRB.BINARY, name = f"b_{e_id}") for e_id in hyperedges}
+    n = model.addVars(vertices, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 1.0, name = "nmr")
+    
+
+    for v, nmr in zip(vertices, nmrlikelihoods):
+        n[v] = nmr
+
+    vertices = set(v for tails, heads in hyperedges.values() for v in tails + heads)
+
+    for v in vertices:
+        inflow = quicksum(x[e_id] for e_id, (_, heads) in hyperedges.items() if v in heads)
+        outflow = quicksum(x[e_id] for e_id, (tails, _) in hyperedges.items() if v in tails)
+        model.addConstr(inflow == outflow, name = f"flow_conservation_{v}")
+
+    for e_id, value in FIXED_FLOWS.items():
+        model.addConstr(x[e_id] == value, name = f"fixed_flow_{e_id}")
+
+    for e_id in hyperedges:
+        model.addGenConstrIndicator(b[e_id], 0, x[e_id] == 0, name = f"unused_implies_zero_{e_id}")
+        model.addConstr(x[e_id] >= b[e_id], name = f"used_implies_positive_flow_{e_id}")
+
+    reaction_path = {}
+
+
+    if excluded_support:
+        model.addConstr(quicksum(b[e_id] for e_id in excluded_support) <= len(excluded_support) - 1, name = "different_hyperedges",)
+    
+    #Multiplizier den node Wert mit infow + outflow
+    model.ModelSense = GRB.MAXIMIZE
+
+
+    #Multiply node value with infow or outflow
+    model.setObjectiveN(
+        quicksum(n[t_id[0]] * x[e_id] for e_id, (_, t_id) in hyperedges.items() if t_id != []),
+        index = 0,
+        priority = 2,
+        name = "maximize_nmr_similarity",
+    )    
+
+    model.setObjectiveN(
+        quicksum(-1 * x[e_id] for e_id in hyperedges),
+        index=1,
+        priority=1,
+        name="minimize_used_hyperedges",
+    )
+
+    return model, x, b
+
+
+def positive_entries(variable_dict, threshold = 0.5):
+    return {e_id: var.X for e_id, var in variable_dict.items() if var.X > threshold}
+
+def print_solution(title, flow_solution, binary_solution, hyperedges):
+    print(f"\n{title}:")
+    for e_id in sorted(flow_solution):
+        flow = flow_solution[e_id]
+        tails, heads = hyperedges[e_id]
+        print(f"Hyperedge {e_id}: Flow = {flow}, Tails = {tails}, Heads = {heads}")
+    print("\nBinary Variables:")
+    for e_id in sorted(binary_solution):
+        print(f"Binary Variable b_{e_id} = {binary_solution[e_id]}")
+
+    print(f"\nTotal flow: {sum(flow_solution.values())}")
+    print(f"Number of used hyperedges: {len(binary_solution)}")
+
+def main():
+    model, x, b = build_model("HypergraphFlow", HYPEREDGES, VERTICES, NMRLIKELYHOODS)
+    model.optimize()
+    if model.status != GRB.Status.OPTIMAL:
+        print("No optimal solution found for the first model.")
+        return
+    optimal_solution = positive_entries(x)
+    optimal_binary_solution = positive_entries(b)
+    print_solution("Optimal Solution", optimal_solution, optimal_binary_solution, HYPEREDGES)
+
+    """ excluded_support = list(optimal_binary_solution.keys())
+    second_model, x2, b2 = build_model("SecondBestHypergraphFlow", HYPEREDGES, excluded_support=excluded_support,)
+
+    second_model.optimize()
+    if second_model.status == GRB.Status.OPTIMAL:
+        second_solution = positive_entries(x2)
+        second_binary_solution = positive_entries(b2)
+        print_solution("Second Best Solution", second_solution, second_binary_solution, HYPEREDGES, VERTICES)
+    else:
+        print("No optimal solution found for the second best model.")
+ """
+if __name__ == "__main__":
+    main()
\ No newline at end of file