They made little effort, despite the Jesuit presence in Asia, to convert local inhabitants to Christianity or to expand their territory into the interior.
( They ( ( ( ( ( ( made ( little effort ) ) , ) ( despite ( ( the ( Jesuit presence ) ) ( in Asia ) ) ) ) , ) ( ( ( to ( ( convert ( local inhabitants ) ) ( to Christianity ) ) ) or ) ( to ( ( expand ( their territory ) ) ( into ( the interior ) ) ) ) ) ) . ) )
(ROOT (S (NP (PRP They)) (VP (VBD made) (NP (JJ little) (NN effort)) (, ,) (PP (IN despite) (NP (NP (DT the) (NNP Jesuit) (NN presence)) (PP (IN in) (NP (NNP Asia))))) (, ,) (S (VP (VP (TO to) (VP (VB convert) (NP (JJ local) (NNS inhabitants)) (PP (TO to) (NP (NNP Christianity))))) (CC or) (VP (TO to) (VP (VB expand) (NP (PRP$ their) (NN territory)) (PP (IN into) (NP (DT the) (NN interior)))))))) (. .)))
The Jesuit presence in Asia helped to convert local residents to Christianity, allowing them to expand their territory. 
( ( ( The ( Jesuit presence ) ) ( in Asia ) ) ( ( ( ( helped ( to ( ( convert ( local residents ) ) ( to Christianity ) ) ) ) , ) ( allowing ( them ( to ( expand ( their territory ) ) ) ) ) ) . ) )
(ROOT (S (NP (NP (DT The) (NNP Jesuit) (NN presence)) (PP (IN in) (NP (NNP Asia)))) (VP (VBD helped) (S (VP (TO to) (VP (VB convert) (NP (JJ local) (NNS residents)) (PP (TO to) (NP (NNP Christianity)))))) (, ,) (S (VP (VBG allowing) (S (NP (PRP them)) (VP (TO to) (VP (VB expand) (NP (PRP$ their) (NN territory)))))))) (. .)))