Word Changer Reachability Word changer is a game where you are trying to turn one word into another via single-character edits, with each step being its own word. For this challenge, edits may be replacements, insertions, or deletions. For example, WINNER &rarr; LOSER can be done with this route (there may be others):

WINNER
DINNER
DINER
DINE
LINE
LONE
LOSE
LOSER


Phrased another way, you must be able to reach one word from the other going only through other words at a Levenshtein distance of 1 each time.

Coding

You will be given a word list and two words and you must output a valid route from one word to the other if a route exists or a distinct constant value or consistent behavior if no route exists.


You may assume that the input words are both in the word list
The word list can be taken in via any convenient flat format.


Lists, sets, tries, space-separated strings, and line-separated files are all valid (for instance), but a pre-computed graph of Levenshtein adjacency is not.

The output route should include both input words, but which starts and ends doesn't matter.
If no route is found, you can output a specific constant, a falsy value, empty list, throw an exception, exit with a nonzero code, or any other behavior that happens in finite time.
The route does not need to be optimal and there is no requirement of which route should be taken
Computational complexity does not matter, however your program must be provably guaranteed to terminate in a finite amount of time. (even if it would run beyond the heat death of the universe)
You may assume all words are entirely composed of letters in the same case


Example Test Cases


CAT &rarr; DOG; [CAT, DOG, COG, COT, FROG, GROG, BOG]


CAT, COT, COG, DOG

BATH &rarr; SHOWER; [BATH, SHOWER, HATH, HAT, BAT, SAT, SAW, SOW, SHOW, HOW]


No Route Found

BREAK &rarr; FIX; [BREAK, FIX, BEAK, BREAD, READ, BEAD, RED, BED, BAD, BID, FAD, FAX]


BREAK, BREAD, BEAD, BAD, FAD, FAX, FIX

BUILD &rarr; DESTROY; [BUILD, DESTROY, BUILT, GUILT, GUILD, GILD, GILL, BILL, DILL, FILL, DESTRUCT, STRUCTURE, CONSTRUCT]


No Route Found

CARD &rarr; BOARD; [CARD, BOARD, BARD]


CARD, BARD, BOARD

DEMON &rarr; ANGEL; [DEMON, ANGEL]


No Route Found

LAST &rarr; PAST; [LAST, PAST, BLAST, CAST, BLACK, GHOST, POST, BOAST]


LAST, PAST

INSERT &rarr; DELETE; This word list


INSERT, INVERT, INVENT, INBENT, UNBENT, UNBEND, UNBIND, UNKIND, UNKING, INKING, IRKING, DIRKING, DARKING, DARLING, ARLING, AILING, SIRING, SERING, SERINE, NERINE, NERITE, CERITE, CERATE, DERATE, DELATE, DELETE
05AB1E, 23 21 20 bytes

Prints a list of valid routes.
Saved 2 bytes thanks to Kevin Cruijssen.

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Try it online!