  It was conjectured in \texttt{\small arXiv:1606.02521} that a Nichols algebra
of diagonal type with finite Gelfand-Kirillov dimension has finite
(generalized) root system. We prove the conjecture assuming that the rank is 2.
We also show that a Nichols algebra of affine Cartan type has infinite
Gelfand-Kirillov dimension.
