Tolarian Terror

• WOTC Official Reminder Textofficial rules
  Ward — Whenever this permanent becomes the target of a spell or ability an opponent controls, counter it unless that player pays [cost].

• WWizards of the Coast2024-11-08
  Official Ruling
  Tolarian Terror's first ability can't reduce its cost below .
• WWizards of the Coast2024-11-08
  Official Ruling
  To determine the total cost of a spell, start with the mana cost or alternative cost you're paying, add any cost increases, then apply any cost reductions (such as that of Tolarian Terror). The mana value of the spell is determined by only its mana cost, no matter what the total cost to cast that spell was.

Rulings via Scryfall