Скрипт поика разреза на одинаковые части.

cat.js

"use strict";

let res = `
1111110
1111100
1111111
1111111
1111111
0111111
0111111
0011110
`.trim().split('\n').map(row => row.split('').map(e => e === '1' ? 0 : -1));

let fields = 0;
res.forEach(row => row.forEach(e => fields += e === 0));
if ((fields % 2) !== 0) return false;


let order = [];
for (let i = 0; i < fields / 2; i++) order.push(1);
for (let i = 0; i < fields / 2; i++) order.push(0);

let plan;



/////////////////////////////////////////////////////////////////////////////////////



do {
	bindOrder();

	if (!checkArialsСontinuity()) continue;

	if (checkArials(...getArials())) writePlan();

} while (nextOrder());



//////////////////////////////////////////////////////////////////////////////////////



function nextOrder () {
	if (order[fields - 1] === 0)
		for (let i = fields - 2; i >= 0 ; i--)
			if (order[i] === 1 && order[i + 1] === 0) {
				order[i] = 0;
				order[i + 1] = 1;

				return true;
			}

	let counter = 0;
	for (let i = fields - 1; i > 0; i--)
		if (order[i] === 1) counter++;
		else if (order[i - 1] === 1) {
			counter++;
			order[i - 1] = 0;

			for (var j = 0; j < counter; j++)
				order[i + j] = 1;

			for (; i + j < fields; j++)
				order[i + j] = 0;

			return true;
		}

	return false;
}

function bindOrder () {
	let i = 0;
	plan = res.map(row => row.map(e => e === -1 ? -1 : order[i++]));
}

function checkArialsСontinuity () {

	return checkArialСontinuityByFlag(0) && checkArialСontinuityByFlag(1);

	function checkArialСontinuityByFlag (flag) {
		let plan1 = plan.map(row => row.map(e => e));

		let isInfected = false;
		for (let i = 0; i < plan1.length; i++) {
			if (isInfected) break;
			for (let j = 0; j < plan1[i].length; j++) {
				if (plan1[i][j] === flag) {
					plan1[i][j] = 2;
					isInfected = true;
					break;
				}
			}
		}

		isInfected = true;
		while (isInfected) {
			isInfected = false;

			for (let i = 0; i < plan1.length; i++)
				for (let j = 0; j < plan1[i].length; j++) {
					if (plan1[i][j] !== 2) continue;

					if (i > 0 && plan1[i - 1][j] === flag) { plan1[i - 1][j] = 2; isInfected = true; }
					if (i < (plan1.length - 1) && plan1[i + 1][j] === flag) { plan1[i + 1][j] = 2; isInfected = true; }
					if (j > 0 && plan1[i][j - 1] === flag) { plan1[i][j - 1] = 2; isInfected = true; }
					if (j < (plan1[i].length - 1) && plan1[i][j + 1] === flag) { plan1[i][j + 1] = 2; isInfected = true; }
				}
		}

		for (let i = 0; i < plan1.length; i++)
			for (let j = 0; j < plan1[i].length; j++)
				if (plan1[i][j] === flag) return false;

		return true;		
	}
}

function getArials () {
	return [getArialByFlag(0), getArialByFlag(1)];

	function getArialByFlag (flag) {
		let plan1 = plan.filter(row => row.some(e => e === flag));
		let plan2 = [];

		for (let j = 0; j < plan1[0].length; j++) {
			let row = [];
			for (let i = 0; i < plan1.length; i++)
				row.push(plan1[i][j]);
			plan2.push(row);
		}

		plan2 = plan2.filter(row => row.some(e => e === flag));

		return plan2;
	}
}

function checkArials (arial0, arial1) {
	arial0 = righter(arial0);
	arial1 = righter(arial1);

	if (arial0.length !== arial1.length || arial0[0].length !== arial1[0].length) return false;

	if (check()) return true;

	arial0 = arial0.map(row => row.reverse());
	if (check()) return true;

	arial0 = arial0.reverse();
	if (check()) return true;

	arial0 = arial0.map(row => row.reverse());
	if (check()) return true;

	if (arial0.length !== arial1[0].length) return false;

	let plan1 = [];
	for (let j = 0; j < arial0[0].length; j++) {
		let row = [];
		for (let i = 0; i < arial0.length; i++)
			row.push(arial0[i][j]);
		plan1.push(row);
	}

	arial0 = plan1;
	if (check()) return true;

	arial0 = arial0.map(row => row.reverse());
	if (check()) return true;

	arial0 = arial0.reverse();
	if (check()) return true;

	arial0 = arial0.map(row => row.reverse());
	if (check()) return true;

	return false;

	function righter (arial) {
		if (arial.length > arial[0].length) {
			let plan1 = [];
			for (let j = 0; j < arial[0].length; j++) {
				let row = [];
				for (let i = 0; i < arial.length; i++)
					row.push(arial[i][j]);
				plan1.push(row);
			}
			return plan1;
		}
		return arial;
	}

	function check () {
		for (let i = 0; i < arial0.length; i++) {
			for (let j = 0; j < arial0[0].length; j++) {
				if (arial0[i][j] === 0 && arial1[i][j] !== 1) return false;
			}
		}

		for (let i = 0; i < plan.length; i++)
			for (let j = 0; j < plan[0].length; j++) {
				if (plan[i][j] === -1) continue;
				if (plan[i][j] === 0) return false;

				return true
			}

		return true;
	}
}

function writePlan () {
	console.log(plan.map(row => row.map(e => e === -1 ? 0 : (e === 0 ? 1 : 2))).map(row => row.join('')).join('\n'), '\n');
}