title: Regular Expression Simplification Issue
body: <p>I'm trying to understand the equivalence between regular expressions α and β defined below, but I'm losing my mind over conflicting information.<br>
  <br></p>
  
  <pre><code>a+b:   a or b
  ab:    concatenation of a and b
  $:     empty string
  </code></pre>
  
  <p>α = <strong>(1*+0)+(1*+0)</strong>(0+1)*($+0+1)</p>
  
  <p>β = <strong>(1*+0)</strong>(0+1)*($+0+1)</p>
  
  <p><a href="https://ivanzuzak.info/noam/webapps/regex_simplifier/" rel="nofollow noreferrer">https://ivanzuzak.info/noam/webapps/regex_simplifier/</a> says, that <strong>α</strong> is equivalent to <strong>β</strong>.</p>
  
  <p>My school however teaches that concatenation has stronger binding than union, meaning that:</p>
  
  <p>11*+0 <strong>=/=</strong> 1(1*+0)</p>
  
  <p>Which would mean that my <strong>α</strong> looks like this with parentheses:</p>
  
  <p><strong>α =</strong> (1*+0) + <strong>( (1*+0)(0+1)*($+0+1) )</strong></p>
  
  <p>and that</p>
  
  <p><strong>α =/=</strong> <strong>( (1*+0) + (1*+0) )</strong> (0+1)*($+0+1)</p>
  
  <p><br></p>
  
  <p>I hope it's clear what my problem is, I'd appreciate any kind of help. Thanks.</p>