A software for calculations in free Lie algebras

Question

I am interested to expand the symmetrised tensor products of several elements of the Philip Hall basis of a free Lie algebra in tensor form. For example, if the algebra has two generators $x$ and $y$, then we have $\ell_1=x$, $\ell_2=y$, $\ell_3=[x,y]$, and so on. It is easy to calculate by hand that $$ (\ell_1,\ell_2,\ell_2)=\frac{1}{3}(x\otimes y\otimes y+y\otimes x\otimes y+y\otimes x\otimes x), $$ but the calculation of,say, $(\ell_1,\ell_2,\ell_5)$ is more boring. Do there exist a software which may do such calculations?