Help:=proc() :print(`Rev(pi,i,j) , StupidS(pi), StupidS1(pi) `):
end:

#Rev(pi,i,j): the permutation obtained
#by reversing pi[i], ..., pi[j] and
#keeping the rest the same
Rev:=proc(pi,i,j)  local k:
[op(1..i-1,pi),
seq(pi[j-k],k=0..j-i),
op(j+1..nops(pi),pi)]

end:

#StupidS1(pi): the pair [i,j] needed to restore
#the first item not in its place to its place
StupidS1:=proc(pi) local i,j:


for i from 1 to nops(pi) while pi[i]=i do od:

if i=nops(pi)+1 then
 RETURN(FAIL):
fi:

for j from i+1 to nops(pi)  while pi[j]<>i do od:
[i,j]:

end:

#StupidS(pi): inputs a permutation pi
#and outputs a list of reversals [i,j]
#that restores it to the identity

StupidS:=proc(pi) local i,n,pi1,L,id1,pair1:
n:=nops(pi):
pi1:=pi:
L:=[]:
id1:=[seq(i,i=1..n)]:

while pi1<>id1 do
pair1:=StupidS1(pi1):
L:=[op(L),pair1]:
pi1:=Rev(pi1,op(pair1)):

od:
L:

end: