```uclid
module main {
  // Define an enumeration type for status
  type status_t = enum { ready, busy };

  // Declare the variables with their respective types
  var request : boolean;
  var status : status_t;

  // Initialize the variables
  init {
    status = status_t.ready;   // status begins as ready
  }

  // The transition relation
  next {
    if (request) {
      status' = status_t.busy; // status becomes busy when request is true
    } else {
      // Removing erroneous nondeterministic update
      status' = status;
    }
  }

  // Define an auxiliary variable to monitor if 'status' has been 'busy' after 'request' is true
  var ever_busy : boolean;
  
  init {
    ever_busy = false;
  }
  
  next {
    ever_busy' = ever_busy || (request && status == status_t.busy);
  }

  // Safety property to ensure that if request is true, status eventually becomes busy
  property request_implies_eventually_busy = [](request -> <>(status == status_t.busy));

  // Liveness property to verify using auxiliary variable
  property liveness_property = [](request -> <>ever_busy);

  // Add control statements for execution
  control {
    // Run BMC to check safety property
    check;
    // Run induction to verify the liveness property
    check;
    print_results;
  }
}
```