Removing blankspace before string - linux

Question

I would like to count the occurence of strings from certain file using pipelines, without awk and sed command.
my_file content:
ls -al
bash
cat datoteka.txt
cat d.txt | sort | less
/bin/bash
terminal command that I use:
cat $my_file | cut -d ' ' -f 1 | tr '|' '\n' | xargs -r -L1 basename | sort | uniq -c | xargs -r -L1 sh -c 'echo $1 $0'
desired output:
bash 2
cat 2
less 1
ls 1
sort 1
In my case, I get:
bash 2
cat 2
ls 1
_sort 1 (not counted )
_less 1 (not counted )
Sort and less comand are not counted because of the whitespace (I marked with _ ) infront of those two strings. How shall I improve my code, to remove this blank space before "sort" and "less"? Thanks in advance!
Update: Here is a second and longer example of an input file:
nl /etc/passwd
seq 1 10 | tr "\n" ","
seq 1 10 | tr -d 13579 | tr -s "\n "
seq 1 100 | split -d -a 2 -l10 - blabla-
uname -a | cut -d" " -f1,3
cut -d: -f1 /etc/passwd > fst
cut -d: -f3 /etc/passwd > scnd
ps -e | column
echo -n ABC | wc -m -c
cmp -s dat1.txt dat1.txt ; echo $?
diff dat1 dat2
ps -e | grep firefox
echo dat1 dat2 dat3 | tr " " "\n" | xargs -I {} -p ln -s {}

Answer 1

The problem with the code in the question, as you were aware, was with the cut statement. This replaces cut with a shell while loop that also includes the basename command:
$ tr '|' '\n' <my_file | while read cmd other; do basename "$cmd"; done | sort | uniq -c | xargs -r -L1 sh -c 'echo $1 $0'
bash 2
cat 2
less 1
ls 1
sort 1
Alternate Sorting
The above sorts the results alphabetically by the name of the command. If instead we want to sort in descending numerical order of number of occurrences, then:
tr '|' '\n' <file2 | while read cmd other; do basename "$cmd"; done | sort | uniq -c | xargs -r -L1 sh -c 'echo $1 $0' | sort -snrk2
Applying this command to the second input example in the question:
$ tr '|' '\n' <file2 | while read cmd other; do basename "$cmd"; done | sort | uniq -c | xargs -r -L1 sh -c 'echo $1 $0' | sort -snrk2
tr 4
cut 3
seq 3
echo 2
ps 2
cmp 1
column 1
diff 1
grep 1
nl 1
split 1
uname 1
wc 1
xargs 1

Answer 2

while IFS='|' read -ra commands; do
for cmd in "${commands[#]}"; do
set -- $cmd # unquoted to discard irrelevant whitespace
basename $1
done
done < myfile |
sort |
uniq -c |
while read num cmd; do
echo "$cmd $num"
done
bash 2
cat 2
less 1
ls 1
sort 1