  In some maps the existence of an attractor with a positive Lyapunov exponent
can be proved by constructing a trapping region in phase space and an invariant
expanding cone in tangent space. If this approach fails it may be possible to
adapt the strategy by considering an induced map (a first return map for a
well-chosen subset of phase space). In this paper we show that such a
construction can be applied to the two-dimensional border-collision normal form
(a continuous piecewise-linear map) if a certain set of conditions are
satisfied and develop an algorithm for checking these conditions. The algorithm
requires relatively few computations, so it is a more efficient method than,
for example, estimating the Lyapunov exponent from a single orbit in terms of
speed, numerical accuracy, and rigor. The algorithm is used to prove the
existence of an attractor with a positive Lyapunov exponent numerically in an
area of parameter space where the map has strong rotational characteristics and
the consideration of an induced map is critical for the proof of robust chaos.
