Are Idempotent Commutative Operations Tractable? Edouard Bonnet, Ecole Normale Superieure de Cachan To tackle the dichotomy conjecture of Feder and Vardi about finite constraint satisfaction problems, the Galois correspondence between relations and operations (via invariants and polymorphisms) is a great help since it allows one to work only with operations and to use results of universal algebra. For instance, it is known that the CSP is tractable when the template has Maltsev, 2-semilattice, or Generalised Minority Majority operations as a polymorphism. Here, we formulate the following subconjecture: templates with a polymorphism which is idempotent and commutative, are tractable. We will test this conjecture by automatic means on small domain sizes. We will also discuss this exhaustive method itself, presenting its limit and its advantages.