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this can be solved with sed and without recursion:
$ perl -e 'print "0"x10 . "1"x10 . "\n"' > x
$ cat x
00000000001111111111
$ cat x.sed
# match 0n1n
/^00*11*$/{
h
:again
/^00*11*$/{
s/01//
t again
}
/^$/{
x
p
}
}
$ sed -n -f x.sed x
00000000001111111111
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