Mfcttrf

In the spirit of the classic river-crossing puzzles:

Problem:

The word PLANS is on the west shore of a river, while the word PAINTER is on the east shore.
The farmer needs to take his word PLANS from the west side to the east side.
However, he can only cross the river with one "chunk" at a time,
and the words on both shores must be valid words at every intermediate step. 


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Solution:




 PLANS PAINTER
 | . |
 | . |
 | ER |
 | . |
 v . v
PLANERS PAINT
 | . |
 | . |
 | ERS |
 | . |
 v . v
 PLAN PAINTERS
 | . |
 | . |
 | TER |
 | . |
 v . v
PLANTER PAINS
 | . |
 | . |
 | LANT |
 | . |
 v . v
 PER PLANTAINS
 | . |
 | . |
 | TAIN |
 | . |
 v . v
PERTAIN PLANS

A "chunk" is a string of consecutive letters taken from anywhere within the word. It can also be inserted anywhere into the other word. It must consist of at least two letters (no single-letter chunks), but there is no length limit. The chunk does not need to be a valid word.

Notice that the farmer succeeded in moving his word PLANS from the west shore to the east shore, but the other word did not survive in its original form. There is no requirement to keep the other word in its original form.

Although the above example happens to show the movement of the chunks alternating between east-to-west and west-to-east, this is not a requirement. The farmer is permitted to ferry an empty boat from one shore to the other whenever he deems necessary.

Now you try it:

Problem:

The word RETESTED is on the west shore of a river, while the word INGRAIN is on the east shore.
The farmer needs to take his word RETESTED from the west side to the east side.
However, he can only cross the river with one "chunk" at a time,
and the words on both shores must be valid words at every intermediate step.

You can do it like this:

RETEST(ED) INGRAIN

RETEST (ING)RAINED

R(ET)ESTING RAINED

RESTING RE(TA)INED

RESTATING RE(IN)ED

REIN(STAT)ING REED

REINING RES(TA)TED

R(ET)AINING RESTED

RAINING RETESTED

On each line other than the last, parentheses indicate what is to be moved to the other side.

Same answer, but with some more observations:

RETESTED INGRAIN
RETEST INGRAINED
RETESTING RAINED
RESTING RETAINED
RESTATING REINED
REINSTATING REED
REINING RESTATED

Now we've swapped the positions of the verbs "rein(ing/ed)" and "restate(-ing/d)". We can continue all the way back because splitting the suffixes "-ing" and "-ed" wasn't necessary at all.

RETAINING RESTED
RAINING RETESTED (it was even shorter after that).