Isomorphism between two finitley presented groups which are not finite I am looking for an isomorphism between the two following groups (infinite groups) ( probably by GAP to show that there is an isomorphism between $f$ and $g$)

$$f=\langle  a,b,c ~| ~ bab^{-1}a^{-1},cac^{-1}a^{-1}\rangle $$

$$g=\langle a,b,c ~|~ bcb^{-1}c^{-1},cac^{-1}a^{-1}\rangle$$

The generators $a$, $b$, $c$ are the same in two groups, I am not sure but guess, there should be an isomorphism which takes $a$ to $c$?
Sure $$&lt;a,b,c|bcb^{-1}c^{-1},cac^{-1}a^{-1}&gt;\ =\ &lt;a,b,c|bcb^{-1}c^{-1}, (cac^{-1}a^{-1})^{-1}&gt;$$
Sure $$&lt;a,b,c|bcb^{-1}c^{-1},cac^{-1}a^{-1}&gt;\ =\ &lt;a,b,c|bcb^{-1}c^{-1}, (cac^{-1}a^{-1})^{-1}&gt;$$