Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
M:6/8
K:G
['BAG BdB A2 B GED G2 A', 'G2 A']  
X:1
L:1/8
M:6/8
K:G
 B3 BAG | BdB A2 B | GED G2 A | BAB GED | BAB BAG | BdB A2 B | GED G2 A | BGG G3 :| ege edB | 
 ege edB | ded dBA | ded dBA | G2 A B2 d | ege dBA | GED G2 A | BGG G3 | ege edB | ege dBA | 
 ded def | gfe dBA | G2 A B2 d | ege dBA | GED G2 A | BGG G3 ||  