Let A = {p | ∃x(p(x)↓)}.

A is certainly nontrivial, since some programs terminate on some input, and some programs fail to terminate on all inputs.

A also respects equivalence. Suppose that p and q are two equivalent programs.

  p ∈ A ⇒ ∃x(p(x)↓)
        ⇒ ∃x(q(x)↓)      since q is equivalent to p
        ⇒ q ∈ A

By Rice's Theorem, A is uncomputable.