function bracketsAreValid(brackets)
{
    var repl = brackets.replace(/\(\)/g, "");
    if (repl === "")
        return true;
    if (brackets === repl)
        return false;
    return bracketsAreValid(repl);
}

function reverse(brackets, start, end)
{
    var sub = brackets.substring(start, end + 1);
    sub = sub.replace(/\(/g, "-");
    sub = sub.replace(/\)/g, "(");
    sub = sub.replace(/-/g, ")");
    return brackets.substring(0, start) +  sub + brackets.substring(end + 1, brackets.length);
}

function canBeReversed(brackets)
{
    if (bracketsAreValid(brackets))
        return true;

    for (var start = 0; start < brackets.length - 1; start++)
        for (var end = start; end < brackets.length; end++)
            if (bracketsAreValid(reverse(brackets, start, end)))
                return true;

    return false;
}


// TEST
var test1 = "())(";
var test2 = "()))";
var test3 = ")))(";
var test4 = "()";
var test5 = "()()";

console.log(test1 + " => " + canBeReversed(test1));
console.log(test2 + " => " + canBeReversed(test2));
console.log(test3 + " => " + canBeReversed(test3));
console.log(test4 + " => " + canBeReversed(test4));
console.log(test5 + " => " + canBeReversed(test5));