Trigger to update related Account record type when Contract status = Activated

Question

I need to write a trigger so that when a new Contract (standard object) is created and activated e.g Contract.Status = Activated, the related Account record types update like this:

Vendor Prospect -> Vendor Or Client Prospect -> Client

Here is my code so far:

trigger contractStatus on Contract (after insert, after update)
{ 
    List <Account> accs = new List <Account>();
    List <Account> newAcc = new List <Account>();
    List <Contract> cons = new List <Contract>();
    Id accRecordTypeIdVP = Schema.SObjectType.Account.getRecordTypeInfosByName().get('Vendor-Prospect').getRecordTypeId();
    Id accRecordTypeIdCP = Schema.SObjectType.Account.getRecordTypeInfosByName().get('Client-Prospect').getRecordTypeId();
    Id vendorRecordTypeId = Schema.SObjectType.Account.getRecordTypeInfosByName().get('Vendor').getRecordTypeId();
    Id clientRecordTypeId = Schema.SObjectType.Account.getRecordTypeInfosByName().get('Client').getRecordTypeId();

    for(Contract con : trigger.new)
    { 
        if (Con.Status == 'Activated')
        {
            cons.add(con);
        }

        for(Account acc :accs)
        {

            if(acc.RecordTypeId == accRecordTypeIdVP)
            {
                acc.RecordTypeId = vendorRecordTypeId;
            }
            else if(acc.RecordTypeId == accRecordTypeIdCP)
            {
                acc.RecordTypeId = clientRecordTypeId;
            }

            newAcc.add(acc);

        }

        if (accs.size() > 0)
        {
            Database.update(accs);
        }
    }
}

The problem is, is that now when I test it (Create a Contract with status = activated) and check the account recordtype, the record type does not change. If somebody could help me figure out what I am doing wrong I would greatly appreciate it. Thanks.