Compose melodious music utilizing the prescribed letter representation and integrating the given thematic element.
X:1
L:1/16
M:2/4
K:G
['G2AA B2B2', 'd2ed B2B2']  
X:1
L:1/16
M:2/4
K:G
 G2AA B2B2 | AGAB c2>c2 | G2AA B2B2 | AGAF G2 z2 | G2AA B2B2 | AGAB c2>c2 | d2ed B2B2 | 
 AGAF G2 z2 |: d2ed B2B2 | AGAA B2B2 | d2ed B2B2 | AGAF G2 z2 :|  