The Scenario

You have built a Multi-Agent System (MAS) to book flights:

1. BookingAgent: Finds flights and asks PaymentAgent to pay.
2. PaymentAgent: Needs an Invoice ID before paying.
3. BookingAgent: Cannot generate Invoice ID until payment is confirmed.

The Loop:

• BookingAgent: "Please pay."
• PaymentAgent: "I need an Invoice ID first."
• BookingAgent: "I cannot generate ID until you pay."
• PaymentAgent: "I need an Invoice ID first."

They are polite, functional, and stuck forever.

The Goal

Implement a Deadlock Detector:

1. Track the conversation hash (or state history).
2. Detect Semantic Repetition: If the same exchange happens 3 times, intervene.
3. Circuit Break: Raise a DeadlockError to stop the madness.

Requirements:

• Implement run_multi_agent_system(agent_a, agent_b).
• Maintain a history of interactions.
• If a circular pattern is detected, stop execution.