Time range clashing scenarios

time-range-clashes.php

<?php

// Assumes that the lower and upper bounds are exclusive

$scenarios = [

    // [AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA]
    // [BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB]
    ['14:00', '15:00', '14:00', '15:00', true],

    //         [AAAAAAAAAAAAAAAAAAAAA]
    // [BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB]
    ['14:20', '14:40', '14:00', '15:00', true],

    // [AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA]
    //         [BBBBBBBBBBBBBBBBBBBBB]
    ['14:00', '15:00', '14:20', '14:40', true],

    // [AAAAAAAAAAA]
    // [BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB]
    ['14:00', '14:20', '14:00', '15:00', true],

    //                   [AAAAAAAAAAAAAAAAAAA]
    // [BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB]
    ['14:40', '15:00', '14:00', '15:00', true],

    // [AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA]
    // [BBBBBBBBBBBBBBBBBBBBB]
    ['14:00', '15:00', '14:00', '14:20', true],

    // [AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA]
    //                 [BBBBBBBBBBBBBBBBBBBBB]
    ['14:00', '15:00', '14:40', '15:00', true],

    //        [AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA]
    // [BBBBBBBBBBBBBBBBBBBBBBBBBBBBBB]
    ['14:20', '15:20', '14:00', '15:00', true],

    // [AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA]
    //        [BBBBBBBBBBBBBBBBBBBBBBBBBBBBBB]
    ['14:00', '15:00', '14:20', '15:20', true],

    // [AAAAAAAAAAAAAAAAAA]
    //                    [BBBBBBBBBBBBBBBBBB]
    ['13:00', '14:00', '14:00', '15:00', false],

    //                    [AAAAAAAAAAAAAAAAAA]
    // [BBBBBBBBBBBBBBBBBB]
    ['15:00', '16:00', '14:00', '15:00', false],

    // [AAAAAAAAAAAAAAA]
    //                        [BBBBBBBBBBBBBBB]
    ['13:00', '14:00', '15:00', '16:00', false],


    //                        [AAAAAAAAAAAAAAA]
    // [BBBBBBBBBBBBBBB]
    ['15:00', '16:00', '13:00', '14:00', false],

];

foreach ($scenarios as $scenario) {
    list($a1, $a2, $b1, $b2, $expectedResult) = $scenario;

    $result = $a1 < $b2 && $a2 > $b1;

    echo "$a1 < $b2 && $a2 > $b1 === ",
         $result ? 'true' : 'false',
         " (expected result was ",
         $expectedResult ? 'true' : 'false',
         ")",
         PHP_EOL;
}

PS: assumes that lower and upper bounds are exclusive. If you wish to include that, change the < and > operators to <= and =>. Refer to http://stackoverflow.com/a/325964/1102265.