what is the simplicial surface of the word $ab^{-1}c^{-1}a^{-1}cb$

Question

In order to study simplicial surfaces I saw the classification theorem and I'm trying to find a homomorphic surfaces for some words one of them is 1)$ab^{-1}c^{-1}a^{-1}cb$.
$a^{-1}$ is the opposite of the letter a. note that every letter is a edge and the word is some edges.
My attempt : $ab^{-1}c^{-1}a^{-1}cb$=$ac^{-1}b^{-1}a^{-1}cb$=$cbac^{-1}b^{-1}a^{-1}$=$DD^{-1}$
the first equal I used the assertion $AxBCx^{-1}D \longleftrightarrow AxCBx^{-1}D$ where $A,B,C,D $ is words and the second equal as a result of word is cyclic. so i can get that word is homomorphic to a sphere. is that correct?
please help me to find the homomorphic surface of the following words:
2) $abc^{-1}bca$
3) $ab^{-1}cedefa^{-1}bc^{-1}d^{-1}f$
4) $abcb^{-1}dc^{-1}d^{-1}a^{-1}$
5) $abec^{-1}ba^{-1}cd^{-1}ed$