Thanks for your interest in the Nest Learning Thermostat. I'd be happy to take a look into this for you.
It appears that your system is compatible with the Nest Thermostats. Wires labeled S1 or S2 can be indicator lights or sensor wires. The Nest thermostat does not need these wires. Install your Nest thermostat without these wires and the jumper wire.
Here's a wiring diagram for you to follow:
If there’s anything else I can help you with, please let me know.
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