The trace shows the current state of the input string to be parsed, and the current state of the stack.
Parsing... -> (the man saw) ((() s)) -> (the man saw) (((s) np vp) (() s)) -> (the man saw) (((np) n) ((s) np vp) (() s)) -> (the man saw) (((np) det n) ((s) np vp) (() s)) -> (man saw) (((det the)) ((np) det n) ((s) np vp) (() s)) -> (man saw) (((np (det the)) n) ((s) np vp) (() s)) -> (saw) (((n man)) ((np (det the)) n) ((s) np vp) (() s)) -> (saw) (((np (det the) (n man))) ((s) np vp) (() s)) -> (saw) (((s (np (det the) (n man))) vp) (() s)) -> (saw) (((vp) v) ((s (np (det the) (n man))) vp) (() s)) -> () (((v saw)) ((vp) v) ((s (np (det the) (n man))) vp) (() s)) -> () (((vp (v saw))) ((s (np (det the) (n man))) vp) (() s)) -> () (((s (np (det the) (n man)) (vp (v saw)))) (() s)) -> () ((((s (np (det the) (n man)) (vp (v saw)))))) ...
The trace output resulting from further backtracking has been omitted.