In the article [_Limit groups and groups acting freely on $\mathbb{R}^n$-trees_](http://msp.org/gt/2004/8-3/gt-v8-n3-p13-p.pdf) by Vincent Guirardel, after the statement of Theorem 7.1 on page 1430, the author concludes: "Hence, a limit group can be obtained from abelian and surface groups by a finite sequence of free products and amalgamations over Z".

**Question:** Why are HNN-extensions not necessary in this decomposition?

Here is the full reference to the cited article:  
Vincent Guirardel, [_Limit groups and groups acting freely on $\mathbb{R}^n$-trees_](http://msp.org/gt/2004/8-3/p13.xhtml), Geometry & Topology 8 (2004), pages 1427-1470  
DOI: [10.2140/gt.2004.8.1427](http://dx.doi.org/10.2140/gt.2004.8.1427), arXiv: [math/0306306](http://arxiv.org/abs/math/0306306) [math.GR]