Thread[(a _ # & /@ Rg[12]) -> Gs ] // List // TF
a _ 1 -> 1 a _ 2 -> x a _ 3 -> y a _ 4 -> y x a _ 5 -> x y a _ 6 -> x^2 a _ 7 -> x y x a _ 8 -> y x y a _ 9 -> x^2 y a _ 10 -> y x^2 a _ 11 -> x^2 y x a _ 12 -> x y x^2

arl = Reverse @ Thread[Gs -> (a _ # & /@ Rg[12])]

set = {1, x y x^2, y x, x^2 y, y, x y, y x^2} ; Table[set [[ i ]] set [[ j ]], {i, Length[set]}, {j, Length[set]}] /. Reverse @ Thread[Gs -> (a _ # & /@ Rg[12])] // MF

( a a a a a a a ) 1 12 4 9 3 5 10 a a a a a a a 12 1 8 10 11 2 9 a a a a a a a 4 5 9 1 8 7 11 a a a a a a a 9 7 1 4 6 12 2 a a a a a a a 3 11 2 7 1 8 6 a a a a a a a 5 4 6 11 2 10 1 a a a a a a a 10 6 12 8 7 1 5

Converted by Mathematica  (October 16, 2002)