眠い

How it works

This is two short plain-form clauses dropped side by side, the way you'd mutter to yourself. First the i-adjective 眠いねむい (sleepy) stands alone as a whole feeling — no subject, no copula needed. Then もう (already) sets up that the time has come, and the plain verb 寝るねる (sleep) states the plan. Plain form (no です (is) or ます (polite)) makes it sound casual and personal, almost like thinking out loud.