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A short proof that O 2 is an MCFL

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Figure

Figure 1second left-hand side argument into three parts.
Figure 2: Two strings xtogether represent a closed path, consisting of a pathfrom=a b a b a b and y=bato- ( 0, 0) to ( − 1, − 1) and a path from ( − 1, − 1) ( 0, 0) .
Figure 3: With xted) path=a b a b b and y=a a b , thebeginning of path A[ 0] and the beginning of (dot- B[ 0] have an 180◦ angle in P[ 0] , whichimplies x and y start with complementing symbols(here a and a ; the other possibility is b and b )
Figure 7: The excursion from Figure 6 truncatedin Q′1 and Q′2 on line m.
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