Consult the PHRETS documentation. You have the second parameter as an integer. It should be a string. Also the comma needs to be removed after the last element in the array.
/* Search RETS server */
$search = $rets->SearchQuery(
'Property',
'3',
'(LastTransDate_f77=2013-01-01+)',
array(
'Format' => 'COMPACT-DECODED',
'Select' => 'AREA_f16',
'Count' => 1,
'Limit' => 20
));