Backreferences, Redux

Many software tools for matching text support backreferences, which are able to match multiple occurrences of the same text. Consider the following extension to regular expressions to support backreferences. A capture operator stores matched text, and a backref operator matches the ith capture. Specifically, the operators in s$-$expression notation are:

$($capture e$)$ is a unary operator that takes a single expression e and stores the text from the input string that matches e$.$

$($backref i$)$ is a unary operator that takes a single non$-$negative integer i and matches the text of the ith capture in the overall expression.

For example:

$$ The expression $($concatenation $($capture a$)($capture b$)($backref $1))$ would match only the string $$abb$.$

$$ The expression $($concatenation $($capture $($union a b$))($backref $0))$ would match the text $$aa$$ and $$bb$,$ but it would not match the text $$ab$$ or $$ba$.$

Prove regular expressions extended with backreferences are not context$-$free.