Nope. If you want to know if string2 is in string1, you need string1 on the left side and string2 on the right side of the binding operator. 
$  perl -E 'my $str1 = qq(one two three); my $str2 = qq(two); if ($str
+2 =~ m/$str1/) { say "foo";}'


$  perl -E 'my $str1 = qq(one two three); my $str2 = qq(two); if ($str
+1 =~ m/$str2/) { say "foo";}'
foo

[download]
Your test is wrong for the following reason: if you want to try to put string1 on the right side, then it is string1 that should be a quotemetaed regex or have the pipes escaped: 
$ perl -E 'my $str1 = qr(\|L\|D\|);  my $str2 = qq(\|L\|); if ($str2 =
+~ m/$str1/) { say "foo";}'

$ perl -E 'my $str1 = qq(\|L\|D\|);  my $str2 = qr(\|L\|); if ($str1 =
+~ m/$str2/) { say "foo";}'
foo

$ perl -E 'my $str1 = qq(|L|D|);  my $str2 = qq(|L|); if ($str1 =~ m/\
+Q$str2/) { say "foo";}'
foo

[download]

In reply to Re^3: Stupid question about strings... by Laurent_R
in thread Stupid question about strings... by kepler

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.