----------------------------------------
|context> => |context: binary tree>


text |x> => |start node>
left |x> => |0>
right |x> => |1>


text |0> => |first child node>
left |0> => |00>
right |0> => |10>
inverse-left |0> => |x>


text |1> => |second child node>
left |1> => |01>
right |1> => |11>
inverse-right |1> => |x>


text |00> => |third child node>
left |00> => |000>
right |00> => |100>
inverse-left |00> => |0>


text |10> => |fourth child node>
left |10> => |010>
right |10> => |110>
inverse-right |10> => |0>


text |01> => |fifth child node>
left |01> => |001>
right |01> => |101>
inverse-left |01> => |1>


text |11> => |sixth child node>
left |11> => |011>
right |11> => |111>
inverse-right |11> => |1>


child |*> #=> left |_self> + right |_self>
parent |*> #=> inverse-left |_self> + inverse-right |_self>


inverse-supported-ops |op: text> => |x> + |0> + |1> + |00> + |10> + |01> + |11>


inverse-supported-ops |op: left> => |x> + |0> + |1> + |00> + |10> + |01> + |11>


inverse-supported-ops |op: right> => |x> + |0> + |1> + |00> + |10> + |01> + |11>


inverse-text |start node> => |x>


inverse-supported-ops |op: inverse-left> => |0> + |00> + |01> + |000> + |010> + |001> + |011>


inverse-text |first child node> => |0>


inverse-supported-ops |op: inverse-right> => |1> + |10> + |11> + |100> + |110> + |101> + |111>


inverse-text |second child node> => |1>


inverse-text |third child node> => |00>


inverse-left |000> => |00>


inverse-right |100> => |00>


inverse-text |fourth child node> => |10>


inverse-left |010> => |10>


inverse-right |110> => |10>


inverse-text |fifth child node> => |01>


inverse-left |001> => |01>


inverse-right |101> => |01>


inverse-text |sixth child node> => |11>


inverse-left |011> => |11>


inverse-right |111> => |11>


inverse-supported-ops |op: child> => |*>


inverse-supported-ops |op: inverse-supported-ops> => |op: text> + |op: left> + |op: right> + |op: inverse-left> + |op: inverse-right> + |op: child> + |op: inverse-supported-ops> + |op: inverse-text>


inverse-supported-ops |op: inverse-text> => |start node> + |first child node> + |second child node> + |third child node> + |fourth child node> + |fifth child node> + |sixth child node>
----------------------------------------

-- some post processing:

child |x> => child |_self>
child |0> => child |_self>
child |1> => child |_self>
child |00> => child |_self>
child |10> => child |_self>
child |01> => child |_self>
child |11> => child |_self>
child |000> => child |_self>
child |100> => child |_self>
child |010> => child |_self>
child |110> => child |_self>
child |001> => child |_self>
child |101> => child |_self>
child |011> => child |_self>
child |111> => child |_self>

parent |x> => parent |_self>
parent |0> => parent |_self>
parent |1> => parent |_self>
parent |00> => parent |_self>
parent |10> => parent |_self>
parent |01> => parent |_self>
parent |11> => parent |_self>
parent |000> => parent |_self>
parent |100> => parent |_self>
parent |010> => parent |_self>
parent |110> => parent |_self>
parent |001> => parent |_self>
parent |101> => parent |_self>
parent |011> => parent |_self>
parent |111> => parent |_self>