\begin{scope}[xshift=0.5in, yshift=0in]
\node (a) {\small{
$\begin{aligned}
- & mark (((\epsilon|a^{0,\infty})(\epsilon|a)^{0,\infty} ))) = \big[ \\
- & \quad mark ( (\epsilon|a^{0,\infty})(\epsilon|a)^{0,\infty} ) ) = \big[ \\
+ & mark (((\epsilon|a^{0,\infty})(a|\epsilon)^{0,3} ))) = \big[ \\
+ & \quad mark ( (\epsilon|a^{0,\infty})(a|\epsilon)^{0,3} ) ) = \big[ \\
%
& \quad\quad mark ( (\epsilon|a^{0,\infty}) ) = \big[ \\
& \quad\quad mark ( \epsilon|a^{0,\infty} ) = \big[ \\
& \quad\quad\quad \big] = (0,0,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \\
& \quad\quad \big] = (1,1,(0,0,\epsilon)|(0,0,(0,0,a)^{0,\infty})) \\
%
- & \quad\quad mark ( (\epsilon|a)^{0,\infty} ) = \big[ \\
- & \quad\quad\quad mark ( (\epsilon|a) ) = \big[ \\
- & \quad\quad\quad\quad mark ( \epsilon|a ) = \big [ \\
- & \quad\quad\quad\quad\quad mark ( \epsilon ) = (0,0,\epsilon) \\
+ & \quad\quad mark ( (a|\epsilon)^{0,3} ) = \big[ \\
+ & \quad\quad\quad mark ( (a|\epsilon) ) = \big[ \\
+ & \quad\quad\quad\quad mark ( a|\epsilon ) = \big [ \\
& \quad\quad\quad\quad\quad mark ( a ) = (0,0,a) \\
- & \quad\quad\quad\quad \big] = (0,0,(0,0,\epsilon)|(0,0,a)) \\
- & \quad\quad\quad \big] = (1,1,(0,0,\epsilon) \mid (0,0,a)) \\
- & \quad\quad \big] = (1,0,(1,1,(0,0,\epsilon) \mid (0,0,a))^{0,\infty}) \\
+ & \quad\quad\quad\quad\quad mark ( \epsilon ) = (0,0,\epsilon) \\
+ & \quad\quad\quad\quad \big] = (0,0,(0,0,a) \mid (0,0,\epsilon)) \\
+ & \quad\quad\quad \big] = (1,1,(0,0,a) \mid (0,0,\epsilon)) \\
+ & \quad\quad \big] = (1,0,(1,1,(0,0,a) \mid (0,0,\epsilon))^{0,3}) \\
%
& \quad\big] = (1,0,
(1,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \\
- & \quad\quad\quad\quad \cdot (1,0,(1,1,(0,0,\epsilon) \mid (0,0,a))^{0,\infty})
+ & \quad\quad\quad\quad \cdot (1,0,(1,1,(0,0,a) \mid (0,0,\epsilon))^{0,3})
) \\
& \big] = (1,1,
(1,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \\
- & \quad\quad\quad \cdot (1,0,(1,1,(0,0,\epsilon) \mid (0,0,a))^{0,\infty})
+ & \quad\quad\quad \cdot (1,0,(1,1,(0,0,a) \mid (0,0,\epsilon))^{0,3})
)
\end{aligned}$
}};
$\begin{aligned}
& enum (1,1,(1,1,
(1,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \\
- & \quad\quad\quad\quad\quad \cdot (1,0,(1,1,(0,0,\epsilon) \mid (0,0,a))^{0,\infty}))) = \big[ \\
+ & \quad\quad\quad\quad\quad \cdot (1,0,(1,1,(0,0,a) \mid (0,0,\epsilon))^{0,3}))) = \big[ \\
& \quad enum (2,2,(1,1,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty}))) = \big[ \\
& \quad\quad enum (3,3,(0,0,\epsilon)) = (3,3,(0,0,\epsilon)) \\
& \quad\quad enum (3,3,(0,0,(0,0,a)^{0,\infty})) = \big[ \\
& \quad\quad \big] = (3,3,(0,0,(0,0,a)^{0,\infty})) \\
& \quad \big] = (3,3,(2,2,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty}))) \\
%
- & \quad enum (3,3, (1,0,(1,1,(0,0,\epsilon) \mid (0,0,a))^{0,\infty}) ) = \big[ \\
- & \quad\quad enum (4,3, (1,1,(0,0,\epsilon) \mid (0,0,a)) ) = \big[ \\
- & \quad\quad\quad enum (5,4, (0,0,\epsilon) ) = (0,0,\epsilon) \\
+ & \quad enum (3,3, (1,0,(1,1,(0,0,a) \mid (0,0,\epsilon))^{0,3}) ) = \big[ \\
+ & \quad\quad enum (4,3, (1,1,(0,0,a) \mid (0,0,\epsilon)) ) = \big[ \\
& \quad\quad\quad enum (5,4, (0,0,a) ) = (0,0,a) \\
- & \quad\quad \big] = (5,4,(4,3,(0,0,\epsilon) \mid (0,0,a))) \\
- & \quad \big] = (5,4,(3,0,(4,3,(0,0,\epsilon) \mid (0,0,a))^{0,\infty})) \\
+ & \quad\quad\quad enum (5,4, (0,0,\epsilon) ) = (0,0,\epsilon) \\
+ & \quad\quad \big] = (5,4,(4,3,(0,0,a) \mid (0,0,\epsilon))) \\
+ & \quad \big] = (5,4,(3,0,(4,3,(0,0,a) \mid (0,0,\epsilon))^{0,3})) \\
%
& \big] = (5,4,(1,1,
(2,2,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \\
- & \quad\quad\quad\quad\quad \cdot (3,0,(4,3,(0,0,\epsilon) \mid (0,0,a))^{0,\infty})
+ & \quad\quad\quad\quad\quad \cdot (3,0,(4,3,(0,0,a) \mid (0,0,\epsilon))^{0,3})
)) \\
\\
\\
- & \IRE ((\epsilon|a^{0,\infty})(\epsilon|a)^{0,\infty} )) = \\
+ & \IRE ((\epsilon|a^{0,\infty})(a|\epsilon)^{0,3} )) = \\
& \quad\quad\quad = (1,1, (2,2,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \\
- & \quad\quad\quad\quad\quad\quad \cdot (3,0,(4,3,(0,0,\epsilon) \mid (0,0,a))^{0,\infty}))
+ & \quad\quad\quad\quad\quad\quad \cdot (3,0,(4,3,(0,0,a) \mid (0,0,\epsilon))^{0,3}))
\\
\\
\end{aligned}$
}};
\end{scope}
-\iffalse
-\begin{scope}[xshift=4in, yshift=-2in]
- \node[draw=none]
- {\small{
- $\begin{aligned}
- & \IRE ((\epsilon|a^{0,\infty})(\epsilon|a)^{0,\infty} )) = \\
- & \quad\quad\quad = (1,1, (2,2,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty})) \\
- & \quad\quad\quad\quad\quad\quad \cdot (3,0,(4,3,(0,0,\epsilon) \mid (0,0,a))^{0,\infty}))
- \end{aligned}$
- }};
-\end{scope}
-\fi
-
\begin{scope}[xshift=2.5in, yshift=-2.4in]
\graph [tree layout, grow=down, fresh nodes] {
"${(1, 1, \cdot)}_{\Lambda}$" -- {
"${(0, 0, a)}_{1.2.1}$"[draw=none]
}
},
- "${(3, 0, \{0,\infty\})}_{2}$" -- {
+ "${(3, 0, \{0,3\})}_{2}$" -- {
"${(4, 3, |)}_{2.1}$" -- {
"${(0, 0, a)}_{2.1.1}$"[draw=none],
"${(0, 0, \epsilon)}_{2.1.2}$"[draw=none]