Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
M:4/4
K:G
['dedB cBAB G2 BG DGBG A^GAB', 'dggf gdBd eaa^g a=geg']  
X:1
L:1/8
M:4/4
K:G
 dedB cBAB | G2 BG DGBG | A^GAB cBA=G | EAA^G ABcA | dedB cBAB | G2 BG DGBG | A^GAB cdef | 
 gdcA BG G2 :| dggf gdBd | eaa^g a=geg | (3fed ad bdad | gage dcBc | dggf gdBd | eaa^g a=geg | 
 gage dcBc | (3ded cA BG G2 :|  