\psset{unit=0.55cm}
%
\pspicture(0,0)(10,10)
% \showgrid
% The labeled grid
\psset{linewidth=0.01,linecolor=gray}
% horizontal grid lines:
\setcounter{dummycount}{5}
\multido{\ny=1+1}{9}{
	\psline(0.3,\ny)(9,\ny)
	\rput(0,\ny){$\scriptscriptstyle\arabic{dummycount}$}
	\stepcounter{dummycount}
}
% vertical grid lines:
\setcounter{dummycount}{-4}
\multido{\nx=1+1}{9}{
	\psline(\nx,0.3)(\nx,9)
	\rput(\nx,0){$\scriptscriptstyle\arabic{dummycount}$}
	\stepcounter{dummycount}
}
% Labels
%% Points x
%\rput(-11.5,1.5){$\scriptstyle r_4$}
%\rput(-10.5,1.5){$\scriptstyle r_3$}
%\rput(-9.5,1.5){$\scriptstyle r_2$}
%\rput(-8.5,1.5){$\scriptstyle r_1$}
%% Points y
%\rput(-8.5,7.5){$\scriptstyle s_4$}
%\rput(-6.5,7.5){$\scriptstyle s_3$}
%\rput(-3.5,7.5){$\scriptstyle s_2$}
%\rput(-0.5,7.5){$\scriptstyle s_1$}
%% Points z
%\rput(-0.5,13.5){$\scriptstyle t_4$}
%\rput(2.5,13.5){$\scriptstyle t_3$}
%\rput(6.5,13.5){$\scriptstyle t_2$}
%\rput(9.5,13.5){$\scriptstyle t_1$}
% The lattice paths
\psset{linewidth=0.15,fillstyle=none,linecolor=gray,linestyle=solid}
\psline(1,1)(1,6)(2,6)(2,7)(4,7)(4,8)(8,8)(8,9)(9,9)
\psline(1,1)(2,1)(2,2)(6,2)(6,3)(7,3)(7,5)(9,5)(9,9)
%\psline(1,1)(4,1)
% Starting point and ending point
\psset{linewidth=0.1,linecolor=black,fillstyle=solid,fillcolor=white}
\pscircle(1,1){0.3}
\pscircle(9,9){0.3}
% Labels
% lower path
\rput(1.5,1.35){$\scriptstyle x_5$}
\rput(2.5,2.35){$\scriptstyle x_6$}
\rput(3.5,2.35){$\scriptstyle x_6$}
\rput(4.5,2.35){$\scriptstyle x_6$}
\rput(5.5,2.35){$\scriptstyle x_6$}
\rput(6.5,3.35){$\scriptstyle x_7$}
\rput(7.5,5.35){$\scriptstyle x_9$}
\rput(8.5,5.35){$\scriptstyle x_9$}
% upper path
\rput(1.5,6.35){$\scriptstyle x_{10}$}
\rput(2.5,7.35){$\scriptstyle x_{11}$}
\rput(3.5,7.35){$\scriptstyle x_{11}$}
\rput(4.5,8.35){$\scriptstyle x_{12}$}
\rput(5.5,8.35){$\scriptstyle x_{12}$}
\rput(6.5,8.35){$\scriptstyle x_{12}$}
\rput(7.5,8.35){$\scriptstyle x_{12}$}
\rput(8.5,9.35){$\scriptstyle x_{13}$}

\endpspicture
