Problem TRI-1. A 2-basis for the triangle algebra. Let T (for triangle) denote the 3-element algebra of type ⟨2, 2⟩ with two binary operations of join and meet defined on the set T = {0, 1, 2} with 0 < 1 < 2 < 0. The binary relation < is reflexive and antisymmetric but not transitive. Define x ∨ y = l.u.b.(x, y) and x ∧ y = g.l.b.(x, y). Thus both ∨ and ∧ are idempotent and commutative but not associative. If one draws the Hasse diagram of the algebra, it will be a triangle with 0 ∨ 1 = 1, 1 ∨ 2 = 2, 2 ∨ 0 = 0, etc. It is known that T is not 1-based. Find a simple 2-basis for the equational theory of T.