 Pinch in an HNN extension

In $⟨G,t\mid ta{t}^{-1}=\varphi (a),a\in A⟩$, a pinch is a subword $ta{t}^{-1}$ with $a\in A$, or $t^{-1}bt$ with $b\in B=\varphi (A)$. It can be replaced by a base-group element, removing two stable letters. Britton's lemma asserts that every identity word with stable letters must have a pinch after base-group multiplication is performed.