In the article Limit groups and groups acting freely on $\mathbb{R}^n$-trees 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, Geometry & Topology 8 (2004), pages 1427-1470
DOI: 10.2140/gt.2004.8.1427, arXiv: math/0306306 [math.GR]