Minimal Fresh Substrings
PHP, 141 bytes



for($r=[];$i&lt;$l=strlen($a=$argn);$i++)for($t=1;$t;$t*=$t&lt;$l)in_array($s=substr($a,$i,$t),$r)|strpos($a,$s)&lt;$i?$t++:$r[]=$s.$t="";print_r($r);


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