<?php
$word = "rates";
$letters = str_split($word);

function makeCopy($inputArray) {
    $copyArray = [];

    foreach ($inputArray as $val) {
        array_push($copyArray, $val);
    }

    return $copyArray;
}

$found = [];

function combine($prefix = "", $inputArray) {
    global $found;

    foreach ($inputArray as $key => $currentLetter) {
        $copy = makeCopy($inputArray);
        unset($copy[$key]);
        $copy = array_values($copy);

        $currentWord = $prefix . $currentLetter . implode("", $copy);

        if (!in_array($currentWord, $found)) {
            array_push($found, $currentWord);
        }

        combine($prefix . $currentLetter, $copy);
    }
}

foreach ($letters as $key => $currentLetter) {
    $copy = makeCopy($letters);
    unset($copy[$key]);
    $copy = array_values($copy);

    combine($currentLetter, $copy);
}

echo print_r($found, true);