Sort a concatenated sequence
JavaScript ES6, 127 135

(a,b)=&gt;eval("for(n=r=[],v=13,o=a+n+b;v--;a=b,b=t)o+=t=b+a;for(d of o+'0'.repeat(99))(n+=d)&gt;+v&amp;&amp;(r.push(v=n),n='');+v?r:[...o]")


Test



F=(a,b)=&gt;eval("for(n=r=[],v=13,o=a+n+b;v--;a=b,b=t)o+=t=b+a;for(d of o+'0'.repeat(99))(n+=d)&gt;+v&amp;&amp;(r.push(v=n),n='');+v?r:[...o]")

// less golfed

U=(a,b)=&gt;{
  for(n=r=[], o=a+n+b, v=13; v--; a=b, b=t)
    o+= t= b+a;
  for(d of o+'0'.repeat(99))
    if ((n+=d) &gt; +v)
      r.push(v=n), n='';
  return +v ? r : [...o]
}

function test(){
  var i = I.value.match(/\d+/g)
  O.textContent = i.length &gt; 1 ? F(+i[0],+i[1]) : ''
}
test()
A,B : &lt;input id=I value='0 1' oninput='test()'&gt;
&lt;pre id=O&gt;&lt;/pre&gt;