The commutator length of \langle a,b|b^2=1\rangle is at least two, since there's an element of commutator length two in it.
In \langle a,b|b^2=1\rangle, the commutator length of aba^{-2}ba is two, since it equals (aba^{-1}b^{-1})(b^{-1}a^{-1}ba) but isn't a commutator.