# First define the mapping by defining the strings T0 and T1:
# 00 / 1101 A284116 This is the "Post Tag System"
T0:="00"; T1:="1101";
# 00 / 1011 A291067 These three are from the Watanabe paper
T0:="00"; T1:="1011";
# 00 / 1110 A291068
T0:="00"; T1:="1110";
# 00 / 0111 A291069
T0:="00"; T1:="0111";

with(StringTools):
read(format):

# the mapping:
f1:=proc(w) local L, ws, w2; global T0,T1;
ws:=convert(w, string);
if ws="-1" then return("-1"); fi;
if ws[1]="0" then w2:=Join([ws, T0], ""); else w2:=Join([ws, T1], "");  fi;
L:=length(w2); if L <= 3 then return("-1"); fi;
w2[4..L]; end;

# Compute the trajectory of s1 as a set
tr:=proc(s1) local ss,n,M,traj; global f1,T0,T1;
ss:=convert(s1,string);
M:=1000; traj:={};
for n from 1 to M do
traj := traj union {ss};
ss:=f1(ss);
od:
#lprint(nops(traj),traj);
nops(traj);
end:

# Compute max length of any trajectory for strings of length <= 7
# rec holds records for length n, best holds an example of an optimal string
lprint("Results for the case T0, T1 =", T0, T1);
S:=["0","1","00","10","000","100","0000","0001","1000","1001","00000","00010","10000","10010","000000","000100","100000","100100","0000000","0000001","0001000","0001001","1000000","1000001","1001000","1001001"];
rec:=Array(1..7,0); best:=Array(1..7,0);
for i in S do L:=length(i);
ll:=tr(i); if ll > rec[L] then rec[L]:=ll; best[L]:=i; fi;
od:
rec; best;