Helper Class:
public void setMaintenanceDateAfterUpdate(){
        list<Id> assetIds =new list<Id>();
        list<sls_Asset__c> assetList = new List<sls_Asset__c>();
        for(sls_Asset__c a:newList){
            if((trgOldMap.get(a.Id).sls_StartDate__c == null && trgNewMap.get(a.Id).sls_StartDate__c !=null)||
                (trgOldMap.get(a.Id).sls_StartDate__c <> trgNewMap.get(a.Id).sls_StartDate__c) ){
                  assetIds.add(a.Id);
               }      
        }
        if(!assetIds.isEmpty()){
            for(sls_Asset__c a : [select id,sls_startdate__c,sls_MaintenanceDate__c,sls_CheckDate__c,sls_OrderProduct__c,sls_OrderProduct__r.BProduct2__c,sls_OrderProduct__r.BProduct2__r.name,sls_OrderProduct__r.BProduct2__r.sls_InspectionPeriodMonths__c,sls_OrderProduct__r.BProduct2__r.sls_UsefulLifeMonths__c from sls_Asset__c where id =: assetIds]){
               integer inspect  = Integer.valueOf( a.sls_OrderProduct__r.BProduct2__r.sls_InspectionPeriodMonths__c);
                integer useful = Integer.valueOf(a.sls_OrderProduct__r.BProduct2__r.sls_UsefulLifeMonths__c);
                a.sls_MaintenanceDate__c = trgNewMap.get(a.Id).sls_StartDate__c.addmonths(inspect);
                a.sls_CheckDate__c = trgNewMap.get(a.Id).sls_StartDate__c.addmonths(useful);
                 assetList.add(a);

             }
        }
        if(!assetList.isEmpty()){
             system.debug('assetList:'+assetList);
            update assetList;
        }
           
    }

test Class:
static testMethod void setMaintenanceDateTest01(){
         BCMNTestDataUtil.loadBProfitStandard();
         User user = BCMNTestDataUtil.newUser(false);
         user.Department = '営業統括部';
         insert user;
         Account acc = BCMNTestDataUtil.newAccount('account01', '01234', true);
         Product2 product = BCMNTestDataUtil.newProduct2('Product1', 'PRODUCT1', 'AEDオプション', false);
         product.sls_InspectionPeriodMonths__c = 12; //点検月数
         product.sls_UsefulLifeMonths__c = 24;       //耐用月数
         insert product;
         PricebookEntry pbe = BCMNTestDataUtil.newStandardPricebookEntry(product, 20000, 10000, true);
         Opportunity opp = BCMNTestDataUtil.newOpportunity('opp01', user.Id, acc.Id, pbe.Pricebook2Id, false);
         opp.BSalesForm__c = '常駐警備';
         insert opp;
         BOrder__c order = BCMNTestDataUtil.newBOrder(opp.Id, true);
         BOrderProduct__c orderProduct =BCMNTestDataUtil.newBOrderProduct(order.Id, false);
         orderProduct.BProduct2__c = product.id;
         orderProduct.BUnitPrice__c = 20000;
         orderProduct.BQuantity__c = 2;
          insert orderProduct;
         Test.startTest();
         sls_Asset__c asset1 = new sls_Asset__c();
         asset1.sls_OrderProduct__c = orderProduct.Id;
         asset1.sls_Status__c = '保証書受領待ち';
         asset1.sls_StartDate__c = system.today();
         sls_Asset__c asset2 = new sls_Asset__c();
         asset2.sls_OrderProduct__c = orderProduct.Id;
         asset2.sls_Status__c = '保証書受領待ち';
         asset2.sls_StartDate__c = system.today();
         insert new List<sls_Asset__c>{asset1, asset2};
         Test.stopTest();
         //交換したレコードのステータスが更新されていること
         asset1 = [SELECT Id, sls_Status__c, sls_StartDate__c, sls_MaintenanceDate__c, sls_CheckDate__c FROM sls_Asset__c WHERE Id =: asset1.Id];
         system.assertEquals(asset1.sls_StartDate__c.addMonths(integer.valueOf(product.sls_InspectionPeriodMonths__c)), asset1.sls_MaintenanceDate__c);   //交換期限
         system.assertEquals(asset1.sls_StartDate__c.addMonths(integer.valueOf(product.sls_UsefulLifeMonths__c)), asset1.sls_CheckDate__c);         //点検期限
         asset2 = [SELECT Id, sls_Status__c, sls_StartDate__c, sls_MaintenanceDate__c, sls_CheckDate__c FROM sls_Asset__c WHERE Id =: asset2.Id];
         system.assertEquals(asset2.sls_StartDate__c.addMonths(integer.valueOf(product.sls_InspectionPeriodMonths__c)), asset2.sls_MaintenanceDate__c);
         system.assertEquals(asset2.sls_StartDate__c.addMonths(integer.valueOf(product.sls_UsefulLifeMonths__c)), asset2.sls_CheckDate__c);
     }

Error:
System.DmlException: Insert failed. First exception on row 0; first error: CANNOT_INSERT_UPDATE_ACTIVATE_ENTITY, sls_AssetTrigger: execution of AfterInsert

caused by: System.NullPointerException: Argument cannot be null.