  We compare two natural bases for the invariant space of a tensor product of
irreducible representations of A_2, or sl(3). One basis is the web basis,
defined from a skein theory called the combinatorial A_2 spider. The other
basis is the dual canonical basis, the dual of the basis defined by Lusztig and
Kashiwara. For sl(2) or A_1, the web bases have been discovered many times and
were recently shown to be dual canonical by Frenkel and Khovanov.
  We prove that for sl(3), the two bases eventually diverge even though they
agree in many small cases. The first disagreement comes in the invariant space
Inv((V^+ tensor V^+ tensor V^- tensor V^-)^{tensor 3}), where V^+ and V^- are
the two 3-dimensional representations of sl(3). If the tensor factors are
listed in the indicated order, only 511 of the 512 invariant basis vectors
coincide.
