Domain Name Dispute: software patent eligibility after Alice

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Illustrative scenario prepared by my practice.
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Hypothetical question

EDIT: added more context below. 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 15 months 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?