Dic: inroad(s) into something

1. In Italy, as elsewhere, television has made deep inroads into cinema.
2. This deal is their first major inroad into the American market.
3. George was unable to make inroads into solving the problem.
3. We are making no inroads into the high-priority project.

1. If one thing makes inroads into another, the first thing starts affecting or destroying the second.
2. inroad into sth: something that is achieved, especially by reducing the power or success of sth else
3. Fig. to succeed in getting something done or at least started.

.... Cobuild, OALD, http://idioms.thefreedictionary.com/inroad

CF. make inroads in/into something:

1.reduce the amount of something

• Repairs to the house had made deep inroads into their savings.  

2.advance successfully into a new area

• Doctors are making great inroads in the fight against cancer.  
• Their products are already making inroads in these new markets.  

.... Oxford Idioms Dictionary for Learners of English