requirement is when we insert record into account object then status field will be success and if it find duplicate then status will be error .
below is my code . it is executong but fields are not updating .

global class insertrecord implements Database.Batchable<sObject>, Database.Stateful {
String Query = 'select name , phone, fax, BillingStreet from Account ';
global Database.QueryLocator start(Database.BatchableContext BC)  {
      return Database.getQueryLocator(query);
      }
global void execute(Database.BatchableContext BC, List<sObject> scope) {
       List<Account > AccList = [Select name,BillingStreet,fax from Account ];
         Set<string> name= new Set<string>();
         Set<string> BillingStreet= new Set<string>();
         Set<string> fax= new Set<string>();
        for(Account Acc : AccList)
         {
           name.add(Acc.name );
           BillingStreet.add(Acc.BillingStreet);
           fax.add(Acc.fax);
         } 
       List<Account > duplicateAccountList = [Select name,BillingStreet from Account where name=:name and BillingStreet=:BillingStreet];
       List<Account > duplicateAccountList1 = [Select name,fax from Account where name=:name and fax=:fax];
       Set<string > duplicateAccountIds = new Set<string >();
       for(Account dup: duplicateAccountList )
       {
         duplicateAccountIds.add(dup.name);
         duplicateAccountIds.add(dup.BillingStreet);  
       }
       for(Account a : duplicateAccountList )
       {
            if(a.name!=null & a.BillingStreet!=null )
            {
               if(duplicateAccountIds.contains(a.name) & duplicateAccountIds.contains(a.BillingStreet))
               {
                 a.status1__c = 'Error';
               }
               else{
               a.status1__c = 'Success';
               }
            }
       }
             for(Account dup: duplicateAccountList1 )
       {
         duplicateAccountIds.add(dup.name);
         duplicateAccountIds.add(dup.fax);  
       }
       for(Account a1 : duplicateAccountList1 )
       {
            if(a1.name!=null & a1.fax!=null )
            {
               if(duplicateAccountIds.contains(a1.name) & duplicateAccountIds.contains(a1.fax))
               {
                 a1.status1__c = 'Duplicate';
               }
            }
       }       
}
global void finish(Database.BatchableContext BC)
    {

    }

}




TRIGGER :

trigger testbatch on Account (before insert) {

Database.executeBatch(new insertrecord());


}