  A magma (or groupoid) is a set with a binary operation $(A,f)$. Roughly
speaking, a magma is said to be lazy if compositions such as $f(x,f(f(y,z),u))$
depend on at most two variables. Recently, Kaprinai, Machida and Waldhauser
described the lattice of all the varieties of lazy groupoids.
  A forbidden structure theorem is one that charcaterizes a smaller class $A$
inside a larger class $B$ as all the elements in $B$ that avoid some
substructures. For example, a lattice is distributive (smaller class $A$) if
and only if it is a lattice (larger class $B$) and avoids the pentagon and the
diamond.
  In this paper we provide a characterization of all pairs of lazy groupoid
varieties $A\le B$ by forbidden substructure theorems. Some of the results are
straightforward, but some other are very involved. All of these results and
proofs were found using a computational tool that proves theorems of this type
(for many different classes of relational algebras) and that we make available
to every mathematician.
