Currently in trigger xxxxxxTrigger, therefore it cannot recursively update itself: []

Question

I am working on the Custom Trigger and getting the following error:

ERROR Error: Update failed. First exception on row 0 with id a01c000000A8GvrAAF; first error: CANNOT_INSERT_UPDATE_ACTIVATE_ENTITY, XXXXTrigger: execution of BeforeUpdate caused by: System.DmlException: Update failed. First exception on row 0 with id a01c000000A8GvrAAF; first error: SELF_REFERENCE_FROM_TRIGGER, Object (id = a01c000000A8Gvr) is currently in trigger XXXXXTrigger, therefore it cannot recursively update itself: [] Class.XXXClass.XXXX: line 41, column 1 Trigger.XXXTrigger: line 3, column 1: []

I have the following code

trigger XXXTrigger on ServiceXXXX__c (before insert, before update, after insert, after update){
    XXXX.XXXX(Trigger.New)
}

Here is the helper class:

public class XXXX {
    public static void XXX(List<SObject> newSobjs){

        List<ServiceXXXX__c> newSI = (List<ServiceXXXX__c>) newSobjs;       
        List<ServiceXXXX__c> testlist = new List<ServiceXXXX__c>();

        Set<Id> caseIdSet = new Set<Id>();
        for(ServiceXXXX__c si : newSI){
            caseIdSet.add(si.Case__c);
        }

         Map<Id,Case> caseMap = new Map<Id,Case>([SELECT Id,Category,SubCategory
                                               FROM Case 
                                              WHERE Id IN :caseIdSet]);      

        for(ServiceXXXX__c si : newSI){
            if(caseMap.get(si.Case__c).Category__c == 'YYYY'){
                if(caseMap.get(si.Case__c).SubCategory__c == 'ZZZZ'){

                    if(si.XXX && si.XXX != null){
                        ServiceXXXX__c newSInfo = new ServiceXXXX__c();
                        newSInfo.Id = si.Id;
                        if(si.CCC == null){
                            newSInfo.CCC = 0;
                        }

                        if(newSInfo.CCCC > 0 && newSInfo.CCC <=2){
                            newSInfo.CCC++;
                        }
                        testlist.add(newSInfo);
                        System.debug('COUNTER :::==> '+newSInfo.CCC);
                    }
                }     
            }
        }
        update testlist;
    }
}