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I think this is the correct logic for "remove lines that match 2013 and do not contain tttaaa". The way the line starts with < is just a coincidence:
$ sed "/2013/ { /tttaaa/ ! d }" file
<2013 abc...

awk '/2013/ && /tttaa/ || !/^</' file

In ksh93/bash:
x=(a b c)
y=(d e)
times=$((${#x } * ${#y }))
((xi=yi=0))
for((i=1;i<=times;i++,xi++,yi++))
do
if((xi>${#x }-1));then xi=0;fi
if((yi>${#y }-1));then yi=0;fi
print...

awk -F"|" '$1~/BELL-1180-1180-81/ && $2!~/:10[12]$/' file

Try,


$ sed -n '/Final/,/^<pg name="path" type="Path">$/p' file
Final
.....
.....
....
<pg name="path" type="Path">