We're writing a requirements document for our client and need to include the use cases of the system. We're following this template:

ID
Description
Actors
Precondition
Basic Steps
Alternate Steps
Exceptions
Business validations/Rules
Postconditions

In the Basic Steps section, should we include steps that the system performs in the back end or should we only include steps that the user directly interacts with?

Example:

Basic Steps for Search 1:

User goes to search page
User enters term
User presses search
System matches search term with database entries
System displays results

vs

Basic Steps for Search 2:

User goes to search page
User enters term
User presses search
System displays results