Domain Name Dispute — software patent eligibility after Alice

I publish illustrative scenarios prepared by my practice. All participants and conversations are fictional. The fictional posts are not posts by real users, accounts of client experiences, or reports of actual results.
Illustrative scenario prepared by my practice.
For informational purposes only. This is not legal advice. Laws vary by jurisdiction. Consult a qualified attorney for advice specific to your situation.
Hypothetical question

I've been trying to resolve this on my own but I'm stuck.

software patent eligibility after Alice. I've been dealing with this for about 4 weeks now and the situation isn't improving.

I have already done some research online but the other party is not cooperating.

Do I have a strong case? What should my next steps be?

Illustrative response

Important clarification on arbitration: if your contract has a mandatory arbitration clause, you generally CAN'T sue in court. But here's the thing — filing for arbitration is often MORE intimidating to companies because they have to pay the arbitration fees (often $3,000-5,000 for the company's share). Use this to your advantage just saying.