What is an R-complete Word™?

Question

If a word conforms to a special rule, I call it an R-complete Word™.

Use the examples below to find the rule.

$$ % set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{0.0}} \def\Title{\textbf{ R-complete }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Words}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2019.05.15}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{TAX} & \text{TRIBUTE}\\\hline \text{NEEDLE} & \text{PIN}\\\hline \text{SUN} & \text{MOON}\\\hline \text{BEST} & \text{WORST}\\\hline \text{PUZZLE} & \text{RIDDLE}\\\hline \text{COFFEE} & \text{TEA}\\\hline \text{SCIENCE} & \text{PHILOSOPHY}\\\hline \text{COLUMN} & \text{ROW}\\\hline \text{CARTOONS*} & \text{SERIES}\\\hline \text{HEAVEN} & \text{HELL}\\\hline \text{TRUCK} & \text{LORRY}\\\hline \end{array}$$ * This is a Double R-complete Word™

CSV Version:

R-complete Words™,Not R-complete Words™
TAX,TRIBUTE
NEEDLE,PIN
SUN,MOON
BEST,WORST
PUZZLE,RIDDLE
COFFEE,TEA
SCIENCE,PHILOSOPHY
COLUMN,ROW
CARTOONS,SERIES
HEAVEN,HELL
TRUCK,LORRY

What is the rule?
There are many more R-complete Words™

Hints: A hint will be given every 50 views for the first three hints. After that, 1 hint every 100 views or 15 votes.

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Hint #1 (50 views):

- It is also called 3R word because it is based on a 3-component score (Bonus: "Truck" is R-Complete and "Lorry" is not)

Hint #2 (100 views):

The R-score is defined as $$R = (R_1, R_2, R_3)$$ and a word is R-complete if $$ \min(R) > 0 $$

Hint #3 (150 views):

- Here is a hint in the form of mini-puzzle
- Bonus: Answering @rand-althor question, Yes, an anagram of the word will keep its property, it's still a 3-complete word.

Hint #4 (250 views):

More examples:
- R-Complete, Not R-Complete
- Ant, Bee
- Bull, Cow
- Camera, Picture
- Double, Triple

Answer 1

I think an R-complete word is one which:

Uses letters from all 3 rows on a standard QWERTY keyboard.

In each of the counter-examples above:

There is at least one row of the keyboard which is not used.

If we:

Label letters from each row as (T)op, (M)iddle or (B)ottom and count up how many of each are used in a word then you can produce the 3-part 'R-score', R(T,M,B) like so:

TAX = TMB = R(1,1,1)
NEEDLE = BTTMMT = R(3,2,1)
SUN = MTB = R(1,1,1)
BEST = BTMT = R(2,1,1)
PUZZLE = TTBBMT = R(3,1,2)
COFFEE = BTMMTT = R(3,2,1)
SCIENCE = MBTTBBT = R(3,1,3)
COLUMN = BTMTBB = R(2,1,3)
CARTOONS = BMTTTTBM = R(4,2,2)
HEAVEN = MTMBTB = R(2,2,2)
TRUCK = TTTBM = R(3,1,1)

As per the second hint, you can see that:

The minimum value in brackets in each of these is 1 or more.

In contrast, for the counterexamples:

TRIBUTE, PIN and MOON have no letters from the middle row,
WORST, RIDDLE, TEA, PHILOSOPHY, SERIES, HELL and LORRY have no letters from the bottom row,
ROW has no letters from the middle or bottom rows.

Hence, each of these will contain a '0' somewhere in their R(T,M,B) triplet, making min(R)=0 and ensuring these words are not 'R-complete'.

The 'R' in R-complete most probably stands for:

ROWS