[IP [DP_i [D' [D the] [NP dog]]]
  [VP [DP t_i] [V' [V saw] [DP [D the] [NP cat]]]]]

\Tree
[.TP
  [.T'
    [.T x-$\emptyset$-atin-$\emptyset_k$\\PAST-3S$_{A}$-BATH-INCHO ]
    [.AgrAP
      $t_i$
      [.AgrA'
        [.AgrA $t_k$ ]
        [.VP
          $t_i$
          [.V'
            [.V $t_k$ ]
            [.NP $t_k$ ]]]]]] !\sqtw{5cm}
  \qroof{achin$_i$\\MAN}.DP ]</pre>

\Tree [.CP \qroof{\node{1}{the article}}.DP_1
  [.C' [.C \node{2}{became-3s-pst_2} ]
    [.IP [.DP \node{3}{t_1} ]
      [.I' [.VP [.DP \node{5}{t_1} ]
        [.V' [.VP [.V' \qroof{the student}.DP [.V \node{7}{t_3} ]]
                  [.DP \node{8}{t_1} ]]
             [.V \node{6}{give-PRT_3} ]]]]]]]</pre>