Complex sentence: Some argue that she lost considerable credibility in the run-up to the 2003 election, when she resinged as mayor, but since then she has become leader of the Alliance after a heated election between her and the sitting leader Össur Skarphéðinsson.
Split into simpler sentences: Some argue that she lost considerable credibility in the run-up to the 2003 election, when she resinged as mayor. Since then she has become leader of the Alliance after a heated election between her and the sitting party leader Össur Skarphéðinsson.