Simple Circular Words
Perl 6, 46 bytes

{!/[(.).*]**4&lt;?{[+^] $0 Xeq[...] ~&lt;&lt;$0[^2]}&gt;/}

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A regex solution that finds if there are four characters in the string such that the two later characters are in different sections of the circle, as defined by the first two characters.
Explanation
{                                           }   # Anonymous code block returning
 !/                                        /    # If the input does not match
   [(.).*]**4                                     # Any 4 characters
             &lt;?{                          }       # Where
                           [...]                    # The range from
                                 ~&lt;&lt;$0[^2]          # The first character to the second
                        Xeq                         # Contains which of  
                     $0                             # The four characters
                [+^]                                # Reduce the list of booleans by xor
                 # Effectively, if only one of the 3rd or 4th character is in that range