1 \begin{figure}[h!]

     2 \centering

     3 

     4 \subfigure[First possible way to split $x@z$]{\label{seq_first_split}

     5 \scalebox{0.7}{

     6 \begin{tikzpicture}

     7     \node[draw,minimum height=3.8ex] (xa) { $\hspace{4em}xa\hspace{4em}$ };

     8     \node[draw,minimum height=3.8ex, right=-0.03em of xa] (xxa) { $\hspace{0.5em}x - xa\hspace{0.5em}$ };

     9     \node[draw,minimum height=3.8ex, right=-0.03em of xxa] (z) { $\hspace{21em}$ };

    10 

    11     \draw[decoration={brace,transform={yscale=3}},decorate]

    12            (xa.north west) -- ($(xxa.north east)+(0em,0em)$)

    13                node[midway, above=0.5em]{$x$};

    14 

    15     \draw[decoration={brace,transform={yscale=3}},decorate]

    16            (z.north west) -- ($(z.north east)+(0em,0em)$)

    17                node[midway, above=0.5em]{$z$};

    18 

    19     \draw[decoration={brace,transform={yscale=3}},decorate]

    20            ($(xa.north west)+(0em,3ex)$) -- ($(z.north east)+(0em,3ex)$)

    21                node[midway, above=0.8em]{$x @ z \in L_1 ;; L_2$};

    22 

    23     \draw[decoration={brace,transform={yscale=3}},decorate]

    24            ($(z.south east)+(0em,0ex)$) -- ($(xxa.south west)+(0em,0ex)$)

    25                node[midway, below=0.5em]{$(x - xa) @ z \in L_2$};

    26 

    27     \draw[decoration={brace,transform={yscale=3}},decorate]

    28            ($(xa.south east)+(0em,0ex)$) -- ($(xa.south west)+(0em,0ex)$)

    29                node[midway, below=0.5em]{$xa \in L_1$};

    30 \end{tikzpicture}}}

    31 

    32 \subfigure[Transferred structure corresponding to the first way of splitting]{\label{seq_trans_first_split}

    33 \scalebox{0.7}{

    34 \begin{tikzpicture}

    35     \node[draw,minimum height=3.8ex] (xa) { $\hspace{4em}ya\hspace{4em}$ };

    36     \node[draw,minimum height=3.8ex, right=-0.03em of xa] (xxa) { $\hspace{0.5em}y - ya\hspace{0.5em}$ };

    37     \node[draw,minimum height=3.8ex, right=-0.03em of xxa] (z) { $\hspace{21em}$ };

    38 

    39     \draw[decoration={brace,transform={yscale=3}},decorate]

    40            (xa.north west) -- ($(xxa.north east)+(0em,0em)$)

    41                node[midway, above=0.5em]{$y$};

    42 

    43     \draw[decoration={brace,transform={yscale=3}},decorate]

    44            (z.north west) -- ($(z.north east)+(0em,0em)$)

    45                node[midway, above=0.5em]{$z$};

    46 

    47     \draw[decoration={brace,transform={yscale=3}},decorate]

    48            ($(xa.north west)+(0em,3ex)$) -- ($(z.north east)+(0em,3ex)$)

    49                node[midway, above=0.8em]{$y @ z \in L_1 ;; L_2$};

    50 

    51     \draw[decoration={brace,transform={yscale=3}},decorate]

    52            ($(z.south east)+(0em,0ex)$) -- ($(xxa.south west)+(0em,0ex)$)

    53                node[midway, below=0.5em]{$(y - ya) @ z \in L_2$};

    54 

    55     \draw[decoration={brace,transform={yscale=3}},decorate]

    56            ($(xa.south east)+(0em,0ex)$) -- ($(xa.south west)+(0em,0ex)$)

    57                node[midway, below=0.5em]{$ya \in L_1$};

    58 \end{tikzpicture}}}

    59 

    60 \subfigure[The second possible way to split $x@z$]{\label{seq_snd_split}

    61 \scalebox{0.7}{

    62 \begin{tikzpicture}

    63     \node[draw,minimum height=3.8ex] (x) { $\hspace{6.5em}x\hspace{6.5em}$ };

    64     \node[draw,minimum height=3.8ex, right=-0.03em of x] (za) { $\hspace{2em}za\hspace{2em}$ };

    65     \node[draw,minimum height=3.8ex, right=-0.03em of za] (zza) { $\hspace{6.1em}z - za\hspace{6.1em}$  };

    66 

    67     \draw[decoration={brace,transform={yscale=3}},decorate]

    68            ($(za.north west)+(0em,0ex)$) -- ($(zza.north east)+(0em,0ex)$)

    69                node[midway, above=0.8em]{$z$};

    70 

    71     \draw[decoration={brace,transform={yscale=3}},decorate]

    72            ($(x.north west)+(0em,3ex)$) -- ($(zza.north east)+(0em,3ex)$)

    73                node[midway, above=0.8em]{$x @ z \in L_1 ;; L_2$};

    74 

    75     \draw[decoration={brace,transform={yscale=3}},decorate]

    76            ($(za.south east)+(0em,0ex)$) -- ($(x.south west)+(0em,0ex)$)

    77                node[midway, below=0.5em]{$x @ za \in L_1$};

    78 \end{tikzpicture}}}

    79 

    80 

    81 \subfigure[Transferred structure corresponding to the second way of splitting]{\label{seq_trans_snd_split}

    82 \scalebox{0.7}{

    83 \begin{tikzpicture}

    84     \node[draw,minimum height=3.8ex] (x) { $\hspace{6.5em}y\hspace{6.5em}$ };

    85     \node[draw,minimum height=3.8ex, right=-0.03em of x] (za) { $\hspace{2em}za\hspace{2em}$ };

    86     \node[draw,minimum height=3.8ex, right=-0.03em of za] (zza) { $\hspace{6.1em}z - za\hspace{6.1em}$  };

    87 

    88     \draw[decoration={brace,transform={yscale=3}},decorate]

    89            ($(za.north west)+(0em,0ex)$) -- ($(zza.north east)+(0em,0ex)$)

    90                node[midway, above=0.8em]{$z$};

    91 

    92     \draw[decoration={brace,transform={yscale=3}},decorate]

    93            ($(x.north west)+(0em,3ex)$) -- ($(zza.north east)+(0em,3ex)$)

    94                node[midway, above=0.8em]{$y @ z \in L_1 ;; L_2$};

    95 

    96     \draw[decoration={brace,transform={yscale=3}},decorate]

    97            ($(za.south east)+(0em,0ex)$) -- ($(x.south west)+(0em,0ex)$)

    98                node[midway, below=0.5em]{$y @ za \in L_1$};

    99 \end{tikzpicture}}}

   100 

   101 \caption{The case for $SEQ$}

   102 \end{figure}