MAYBE

Problem:
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 1(1(0(2(0(2(0(2(1(1(1(1(1(2(1(0(0(1(0(0(x1))))))))))))))))))))
 0(0(0(0(1(1(1(0(1(0(0(1(0(1(0(2(1(1(1(2(x1)))))))))))))))))))) ->
 1(1(2(1(0(0(1(0(1(2(1(1(1(0(1(1(2(1(1(0(x1))))))))))))))))))))
 0(0(0(2(0(2(0(1(2(0(1(2(1(2(1(1(2(0(0(0(x1)))))))))))))))))))) ->
 1(0(2(0(0(2(2(0(2(1(0(0(2(1(0(1(1(1(1(0(x1))))))))))))))))))))
 0(0(1(0(0(2(0(1(1(1(1(0(1(1(2(1(2(0(2(1(x1)))))))))))))))))))) ->
 0(1(0(1(0(1(1(0(1(2(1(2(1(0(2(2(1(1(0(1(x1))))))))))))))))))))
 0(0(1(0(0(2(2(1(1(2(1(2(1(1(2(1(2(2(1(1(x1)))))))))))))))))))) ->
 0(0(2(0(1(0(0(1(0(2(0(0(2(0(1(1(2(1(0(1(x1))))))))))))))))))))
 0(0(1(0(2(0(0(2(2(1(2(1(1(1(2(1(0(0(2(0(x1)))))))))))))))))))) ->
 1(1(0(2(1(1(2(1(2(1(2(1(1(2(1(0(2(1(0(1(x1))))))))))))))))))))
 0(0(1(2(0(2(2(1(0(2(1(0(0(0(1(2(0(0(0(0(x1)))))))))))))))))))) ->
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 1(0(2(2(0(2(1(1(1(0(1(2(0(0(0(1(1(1(1(1(x1))))))))))))))))))))
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 0(0(2(2(1(0(1(1(0(1(0(2(1(1(2(1(0(1(0(0(x1))))))))))))))))))))
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 2(0(1(1(2(1(0(2(0(1(1(1(2(1(0(0(1(2(1(0(x1))))))))))))))))))))
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 1(1(1(0(2(2(1(1(1(1(0(2(2(0(1(0(2(0(2(1(x1))))))))))))))))))))
 1(0(0(0(0(1(2(0(1(0(1(0(1(1(0(0(0(1(2(1(x1)))))))))))))))))))) ->
 1(1(0(0(0(1(1(2(1(2(0(0(1(0(1(2(0(1(1(1(x1))))))))))))))))))))
 1(0(0(0(1(0(0(0(2(1(2(2(1(2(1(1(0(2(0(0(x1)))))))))))))))))))) ->
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 1(2(1(0(1(0(1(0(0(1(1(1(2(0(1(2(0(2(0(1(x1))))))))))))))))))))
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 1(1(0(0(0(0(0(1(1(0(1(0(1(0(2(0(1(2(0(1(x1))))))))))))))))))))
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 1(1(0(2(0(1(1(1(0(1(2(1(0(2(2(2(1(1(1(0(x1))))))))))))))))))))
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 2(1(1(1(0(1(1(2(2(0(1(0(1(2(1(1(0(0(0(0(x1))))))))))))))))))))
 2(1(1(2(1(2(1(1(0(1(0(1(0(0(2(0(0(0(1(0(x1)))))))))))))))))))) ->
 0(0(1(0(1(0(1(0(1(0(2(1(0(0(0(1(2(1(0(0(x1))))))))))))))))))))
 2(1(2(0(2(0(2(1(0(0(1(1(0(0(2(1(0(1(0(0(x1)))))))))))))))))))) ->
 1(1(1(0(2(0(0(2(0(1(0(0(1(1(1(0(0(0(0(0(x1))))))))))))))))))))
 2(1(2(1(0(0(1(1(0(2(0(0(2(0(1(0(1(0(2(1(x1)))))))))))))))))))) ->
 1(2(1(0(1(1(1(1(1(2(1(1(1(1(1(2(2(1(1(0(x1))))))))))))))))))))
 2(1(2(1(0(0(2(0(1(1(2(0(1(0(0(1(2(1(1(2(x1)))))))))))))))))))) ->
 0(2(1(0(1(1(0(0(2(1(2(2(1(0(1(1(0(2(2(0(x1))))))))))))))))))))
 2(1(2(1(1(2(0(0(2(2(1(0(2(1(1(1(0(1(0(0(x1)))))))))))))))))))) ->
 1(1(1(1(1(2(1(0(0(1(2(1(1(1(0(2(1(2(1(0(x1))))))))))))))))))))
 2(1(2(1(2(0(1(2(0(1(1(1(0(2(2(1(0(2(0(2(x1)))))))))))))))))))) ->
 2(0(0(0(2(1(0(0(1(1(2(1(1(0(2(0(0(0(2(0(x1))))))))))))))))))))
 2(1(2(2(0(1(2(2(1(0(1(0(0(1(2(1(1(2(1(1(x1)))))))))))))))))))) ->
 0(1(0(1(2(0(0(1(0(1(0(1(1(2(1(1(0(1(0(2(x1))))))))))))))))))))
 2(2(0(0(1(0(1(1(1(2(1(0(2(1(2(0(2(1(0(1(x1)))))))))))))))))))) ->
 0(0(0(1(0(1(0(0(1(0(2(1(0(1(2(0(1(0(2(1(x1))))))))))))))))))))
 2(2(0(0(1(1(1(0(0(2(2(1(2(1(1(1(0(0(2(1(x1)))))))))))))))))))) ->
 2(0(1(1(1(0(1(0(1(1(0(1(2(0(1(2(2(0(0(1(x1))))))))))))))))))))
 2(2(0(0(2(0(1(1(0(0(0(1(2(1(1(2(1(2(1(1(x1)))))))))))))))))))) ->
 1(1(1(1(2(2(0(2(1(1(1(2(0(2(0(1(0(1(1(1(x1))))))))))))))))))))
 2(2(0(0(2(1(0(1(0(1(2(0(1(2(1(2(0(1(0(1(x1)))))))))))))))))))) ->
 0(0(0(1(0(0(1(1(1(2(1(0(0(2(0(2(1(2(0(1(x1))))))))))))))))))))
 2(2(0(1(2(2(2(1(0(1(0(0(0(1(2(1(1(2(1(1(x1)))))))))))))))))))) ->
 2(0(0(1(1(1(0(1(0(0(2(1(2(0(1(0(1(2(2(1(x1))))))))))))))))))))
 2(2(1(1(1(0(2(2(1(0(2(1(0(2(1(1(0(0(1(2(x1)))))))))))))))))))) ->
 1(2(1(2(1(0(1(0(0(0(1(0(2(1(0(1(0(0(1(0(x1))))))))))))))))))))
 2(2(1(2(0(2(0(2(0(2(2(1(1(1(2(1(1(0(1(1(x1)))))))))))))))))))) ->
 0(1(0(0(0(0(1(1(0(1(0(0(2(0(0(0(0(2(1(1(x1))))))))))))))))))))
 2(2(1(2(1(1(0(2(0(0(1(2(0(0(1(2(1(1(0(0(x1)))))))))))))))))))) ->
 0(2(1(1(0(2(0(0(1(1(2(0(0(0(2(0(1(1(1(0(x1))))))))))))))))))))
 2(2(2(0(1(0(0(0(1(1(1(2(0(0(2(1(2(0(1(1(x1)))))))))))))))))))) ->
 2(1(0(2(1(0(1(0(0(0(1(1(2(1(0(2(0(2(0(1(x1))))))))))))))))))))
 2(2(2(1(1(1(1(1(2(0(0(0(0(0(1(2(0(1(2(1(x1)))))))))))))))))))) ->
 1(2(0(0(1(1(0(1(1(1(2(1(1(2(2(1(1(1(2(2(x1))))))))))))))))))))

Proof:
 Open