  In this paper, we investigate the complexity growth of the tensionless limit
of string in the neutral BTZ black hole horizon in massive gravity. When the
string approaches the horizon, we observe a novel phenomenon for the Nambu-Goto
action growth that produces significant difference from tensile string
geometry. The string's tension is then suggested to partially contribute to the
growth of the action. We also argue a potential proposal that reconstructs the
complexity from the renormalization group (RG) flow.
