  Compositionality supports the manipulation of large systems by working on
their components. For model-based testing, this means that large systems can be
tested by modelling and testing their components: passing tests for all
components implies passing tests for the whole system. In previous work [13],
we defined mutual acceptance for specification models and proved that this is a
sufficient condition for compositionality in model-based testing. In this
paper, we present an algorithm for verifying mutual acceptance on
specifications and a sound and exhaustive model-based test procedure for
checking mutual acceptance on black-box implementations, both inspired by the
idea of environmental conformance [7,8]. The result is that correctness of
large systems can be determined by testing the component implementations for
conformance to their component specification and for environmental conformance
to the specification of their environment.
