module sender {
  var st : boolean; // Sender toggle bit
  var message1 : boolean; // Message sent to message channel

  input ack : boolean; // Acknowledgement from acknowledgement channel

  init {
    st = false;
    message1 = false;
  }

  next {
    if (ack == st) {
      st' = !st;
      message1' = !message1; // Assuming message content toggles for demonstration
    } else {
      message1' = message1;
    }
  }
}

module receiver {
  var rt : boolean; // Receiver toggle bit
  var message2 : boolean; // Acknowledgement sent to acknowledgement channel

  input msg : boolean; // Message from message channel
  input control_bit : boolean; // Control bit from message channel

  init {
    rt = false;
    message2 = false;
  }

  next {
    if (control_bit == rt) {
      rt' = !rt;
      message2' = rt;
    } else {
      message2' = message2;
    }
  }
}

module main {
  var ack : boolean;
  var msg : boolean;
  var control_bit : boolean;

  instance s : sender(ack);
  instance r : receiver(msg, control_bit);

  init {
    ack = false;
    msg = false;
    control_bit = false;
  }

  next {
    // Simulate message channel
    msg' = s.message1;
    control_bit' = s.st;

    // Simulate acknowledgement channel
    ack' = r.message2;
  }

  // Properties to verify
  invariant correct_acknowledgement : (s.st == !r.rt);
}
