Iterative loop for a given list

Question

Suppose I have the following list:

l={{"a"}, {"a", "h"}, {"a", "d", "k", "r", "v"}, {"a", "b", "c", 
  "k"}, {"a", "b", "c", "s", "u"}, {"a", "b", "f", "t"}, {"a", "b", 
  "e", "l", "n", "o"}, {"a", "b", "d", "n", "o"}, {"a", "b", "d", "e",
   "n", "o"}, {"a", "b", "d", "e", "m", "n", "o", "t"}, {"a", "b", 
  "e", "s"}, {"a", "b", "e", "m", "n", "s", "t"}, {"a", "b", "h", 
  "s"}, {"a", "b", "d", "e", "h", "s"}, {"a", "b", "e", "h", "m", "n",
   "s", "t"}, {"a", "b", "e", "t"}, {"a", "b", "e", "m", "n", 
  "t"}, {"a", "b", "i", "o", "r", "t"}, {"a", "b", "e"}, {"a", "b", 
  "e", "s"}}

In the following command I take each element in the list above, find the subsets of it of size 2 and sort them by frequency, I then make a new list and replace the most frequent pair by a name as follow:

Tally[Flatten[Map[Subsets[#, {2}] &, Select[l, Length[#1] >= 1 &]], 
   1]];
Pairs = Sort[%, #1[[2]] < #2[[2]] &] // Reverse
l1 = l //. {OrderlessPatternSequence[Pairs[[1, 1, 1]], 
     Pairs[[1, 1, 2]], p___]} :> {Pairs[[1, 1]] // Capitalize // 
     StringJoin, p}

I want to do the same 20 times, each time the operation Tally and Pairs shall produce a new list, so for example the next list would form as:

 Tally[Flatten[Map[Subsets[#, {2}] &, Select[l1, Length[#1] >= 1 &]], 
       1]];
    Pairs = Sort[%, #1[[2]] < #2[[2]] &] // Reverse
    l2 = l1 //. {OrderlessPatternSequence[Pairs[[1, 1, 1]], 
         Pairs[[1, 1, 2]], p___]} :> {Pairs[[1, 1]] // Capitalize // 
         StringJoin, p}

and so on. How one does this using do/for/function?

Answer 1

ClearAll[replace]
replace = With[{commonest = Commonest[Flatten[Map[Subsets[#, {2}] &, #], 1]][[1]] },
   # //. {OrderlessPatternSequence[##& @@ commonest , p___]} :> 
    {StringJoin[ToUpperCase[commonest]], p} ]&;

Nest[replace, l, 4]

{{"a"}, {"a", "h"}, {"a", "d", "k", "r", "v"}, {"AB", "c", "k"}, {"AB", "c", "s", "u"}, {"AB", "f", "t"}, {"ABEN", "l", "o"}, {"AB", "d", "n", "o"}, {"ABEN", "d", "o"}, {"ABENM", "d", "o", "t"}, {"ABE", "s"}, {"ABENM", "s", "t"}, {"AB", "h", "s"}, {"ABE", "d", "h", "s"}, {"ABENM", "h", "s", "t"}, {"ABE", "t"}, {"ABENM", "t"}, {"AB", "i", "o", "r", "t"}, {"ABE"}, {"ABE", "s"}}