I think you could make an inner join with a similar
select p.id, p.pkg from package p inner join ad_frameworks adf on p.pkg like CONCAT('%', adf.path_fragment, '%')
or as you indicated
select * from package p inner join ad_frameworks adf on LOCATE(adf.fragment, p.pkg) > 0
or
select * from package p inner join ad_frameworks adf on INSTR( p.pkg,adf.fragment) > 0
or
select * from package p inner join ad_frameworks adf on POSITION(adf.fragment IN p.pkg) > 0
or
select * from package p inner join ad_frameworks adf on REPLACE(p.pkg, adf.fragemnt, '') <> p.pkg
Well, you have few options;)
SqlFiddle
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