Find a substring that contains increased 1s

I have a string only made by 0 and 1, and I need to find a sub string that starts with one 1, and ends with another cascade of 1s, each match of 1 the consecutive 1 increases by one.

For example, 0101101011101 would catch 1011010111.

I tried

(?:(1(?(1)\1)).*?)+

but it doesn't work.

input	groups	output
`01`	`0[(1)]`	`1`
`1001111`	`[(1)00(11)]11`	`10011`
`010011111`	`0[(1)00(11)(111)]`	`10011111`
`0100111110001110`	`0[(1)00(11)(111)]0001110`	`10011111`
`0100111011001110`	`0[(1)00(11)101100(111)]0`	`10011101100111`
`0100111110011110`	`0[(1)00(11)(111)00(1111)]0`	`10011111001111`

Solution

You might also use (with credits to JvdV)

^0*\K(?:[01]*?((?(1)\1)1))+

^ Start of string
0* Match optional zeroes
\K Clean the current match buffer
(?: Non capture group to repeat as a whole
- [01]*? Match optional 0 or 1 as least as possible
- ( Capture group 1
  - (?(1)\1)1 If clause, if where is group 1, match what we already have and add a 1
- ) Close group 1
)+ Close non capture group and repeat 1+ times

Regex demo | Php demo

$strings = [
    "01",
    "1001111",
    "010011111",
    "0100111110001110",
    "0100111011001110",
    "0100111110011110",
    "0100111111111111110001110",
    "0100111011001110",
    "1011010111",
    "0100111011001110",
];

$pattern = '/^0*\K(?:[01]*?((?(1)\1)1))+/m';

foreach ($strings as $s) {
    if (preg_match($pattern, $s, $match)) {
        echo "$s --> " . $match[0] . PHP_EOL;
    }
}

Output

01 --> 1
1001111 --> 10011
010011111 --> 10011111
0100111110001110 --> 10011111
0100111011001110 --> 10011101100111
0100111110011110 --> 10011111001111
0100111111111111110001110 --> 10011111111111111
0100111011001110 --> 10011101100111
1011010111 --> 1011010111
0100111011001110 --> 10011101100111