Our efforts having been in vain, we had abandoned the matter, hoping that it might turn up of itself one day. 
( ( ( Our efforts ) ( having ( been ( in vain ) ) ) ) ( , ( we ( ( had ( ( ( abandoned ( the matter ) ) , ) ( hoping ( that ( it ( might ( ( ( turn up ) ( of itself ) ) ( one day ) ) ) ) ) ) ) ) . ) ) ) )
(ROOT (S (S (NP (PRP$ Our) (NNS efforts)) (VP (VBG having) (VP (VBN been) (PP (IN in) (NP (JJ vain)))))) (, ,) (NP (PRP we)) (VP (VBD had) (VP (VBN abandoned) (NP (DT the) (NN matter)) (, ,) (S (VP (VBG hoping) (SBAR (IN that) (S (NP (PRP it)) (VP (MD might) (VP (VB turn) (PRT (RP up)) (PP (IN of) (NP (PRP itself))) (NP (CD one) (NN day)))))))))) (. .)))
We were no longer trying to solve the problem.
( We ( ( ( were ( no longer ) ) ( trying ( to ( solve ( the problem ) ) ) ) ) . ) )
(ROOT (S (NP (PRP We)) (VP (VBD were) (ADVP (RB no) (RB longer)) (VP (VBG trying) (S (VP (TO to) (VP (VB solve) (NP (DT the) (NN problem))))))) (. .)))