Given a closed surface of genus $g\geq 2$, we know that the mapping class group $Mod(S)$ is generated by the Dehn twists. My question is 


**Given an element as a product of Dehn twist, is it possible to write down the corresponding Nielsen-Thurston decomposition?**


Explicitly, suppose $\phi\in Mod(S)$ such that $\phi=\prod\_{i=1}^nT\_{x\_i}^{k\_i}$ where $x\_i$'s are simple closed curves, $T\_{x\_i}$ is the left Dehn twist about $x\_i$ and $k\_i\in\mathbb{Z}$. Given this data, is it possible to write down the Nielsen-Thurston decomposition of $\phi.$


PS: Rivin's comment have helped me to find this [exact link](http://curver.readthedocs.io/en/master/). 



Nielsen-Thurston decomposition from the product of Dehn twists
There isn’t a simple recipe. Bell and Webb recently gave [a polynomial-time algorithm](http://arxiv.org/abs/1609.09392v2) to compute the Nielsen—Thurston type of a mapping class. Their paper also contains a summary of previously known algorithms.


