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.