
    f(t - 1 - s_{k+2}, -1 - s_{k+2}), 
    \end{cases}
    &amp;
    \begin{array}{l}
    \text{if \(s_{k+2} \lt 0\)} \\
    \text{otherwise}
    \end{array}
    \\[1em]

    A_2 = &amp;
    \begin{cases}
    g(t, -s_{k+1}), \\
    f(t + s_{k+1}, 1 + s_{k+1}), 
    \end{cases}
    &amp;
    \begin{array}{l}
    \text{if \(s_{k+1} \lt 0\)} \\
    \text{otherwise}
    \end{array}
    \\[1em]

    A_3 = &amp;
    \begin{cases}
    h(t - 1, -s_{k+2}), \\
    f(t - 1 + s_{k+2}, 1 + s_{k+2}), \\
    0, 
    \end