Does the fishy road have an end?
Non-compliant >&lt;> answer

You wanted >&lt;>, I give you >&lt;> !

I believe the only sane way to do this in >&lt;> is by copying the input in the codespace and letting the interpreter decide by itself if the input leads somewhere. Since >&lt;> doesn't implement threading anymore, that leaves us with a big problem : if the input has a loop, we'll get stuck into it.

These considerations taken into account, I decided to make a solution compatible with >&lt;> online interpreter so that it would be possible to assert if the interpreter is stuck in the input or just taking ages to do everything. I also had to add trailing lines to the code so the online interpreter shows the added code and doesn't crash when trying to write to it.

Oh and since I'm clearly disqualified by now, I didn't bother with golfing the code.

Without further ado, the code in all its glory :

50i:0(?v   :"^"=?v:"v"=?v:"&gt;"=?v:"&lt;"=?v:"/"=?v:"\"=?v:"|"=?v:"-"=?va=?v1+10.
&gt;.!603f&lt;         v"."~                                     &lt;      &lt;   &gt;~1+010.
&gt;.!01+1p}:$}:}v! &lt;      &lt;      &lt;      &lt;      &lt;      &lt;
  ;oooo"true" &lt;&lt;
              ^


To use it, copy it in the online interpreter, add enough trailing lines to handle your input, submit the code, give it the input as ;-separated lines and enjoy the ride.

A few tests :


  With

+--------------------+
|&gt;\/  this way &gt;\/&gt;  | this one ends here
| v^            \/   |
| v^   ^.^           |
| \/\         &gt;v     |
| /\/         ^&lt;     |
+--------------------+` 

  
  Final codespace :

50i:0(?v   :"^"=?v:"v"=?v:"&gt;"=?v:"&lt;"=?v:"/"=?v:"\"=?v:"|"=?v:"-"=?va=?v1+10.
&gt;.!603f&lt;         v"."~                                     &lt;      &lt;   &gt;~1+010.
&gt;.!01+1p}:$}:}v! &lt;      &lt;      &lt;      &lt;      &lt;      &lt;
  ;oooo"true" &lt;&lt;
            ^
 ....................
.&gt;\/           &gt;\/&gt;  .                   
. v^            \/   .
. v^   ^ ^           .
. \/\         &gt;v     .
. /\/         ^&lt;     .
 ....................

  
  Outputs "true" and stops.





  With

+--------+
|&gt;&gt;\ This|
|\\   is |
|  \\ a  |
| \ /trap| 
+--------+

  
  Final codespace :

50i:0(?v   :"^"=?v:"v"=?v:"&gt;"=?v:"&lt;"=?v:"/"=?v:"\"=?v:"|"=?v:"-"=?va=?v1+10.
&gt;.!603f&lt;         v"."~                                     &lt;      &lt;   &gt;~1+010.
&gt;.!01+1p}:$}:}v! &lt;      &lt;      &lt;      &lt;      &lt;      &lt;
  ;oooo"true" &lt;&lt;
            ^
 ........ 
.&gt;&gt;\     .
.\\      .
.  \\    .
. \ /    .
 ........

  
  Loops forever.