  We consider discriminating between bipartite boxes with 2 binary inputs and 2
binary outputs (2x2) using the class of completely locality preserving
operations i.e. those, which transform boxes with local hidden variable model
(LHVM) into boxes with LHVM, and have this property even when tensored with
identity operation. Following approach developed in entanglement theory we
derive linear program which gives an upper bound on the probability of success
of discrimination between different isotropic boxes. In particular we provide
an upper bound on the probability of success of discrimination between
isotropic boxes with the same mixing parameter. As a counterpart of
entanglement monotone we use the non-locality cost. Discrimination is
restricted by the fact that non-locality cost does not increase under
considered class of operations. We also show that with help of allowed class of
operations one can distinguish perfectly any two extremal boxes in 2x2 case and
any local extremal box from any other extremal box in case of two inputs and
two outputs of arbitrary cardinalities.
