MyWormSeq:=proc(N) local L, s, t, i, n, maxlist, maxsteps:
maxsteps:=0:
L:=[seq(seq([NuM([s[1], op(t[1..s[1]-1]), s[2], op(t[s[1]..nops(t)])])], s in [seq(seq([i,j], j=0..N-1-i), i=0..N-1)]), t in Comps(N, N-2))]:
for s in L do
   if s[1] <> FAIL and s[2] > maxsteps then
      maxlist:=s[1]:
      maxsteps:=s[2]:
   fi:
od:
maxlist, maxsteps:
end:

#number of total moves
NuTM:=proc(L) local Orb,L1:
L1:=L:
Orb:=[L]:
while L1<>FAIL and  not IsOld(Orb)[1] do
   L1:=V1(L1):
   Orb:=[op(Orb),L1]:
od:
if L1=FAIL then
   RETURN(FAIL,nops(Orb)-1):
else
   RETURN(Orb,nops(Orb)-1):
fi:
end:

WorstWorm:=proc(N) local L, s, t, i, n, maxlist, maxsteps:
maxsteps:=0:
L:=[seq(seq([NuTM([s[1], op(t[1..s[1]-1]), s[2], op(t[s[1]..nops(t)])])], s in [seq(seq([i,j], j=0..N-1-i), i=0..N-1)]), t in Comps(N, N-2))]:
for s in L do
   if s[1] <> FAIL and s[2] > maxsteps then
      maxlist:=s[1]:
      maxsteps:=s[2]:
   fi:
od:
maxlist, maxsteps:
end:

LegalWorms:=proc(N) local L, s, t, i, n, c:
c:=0:
L:=[seq(seq([NuM([s[1], op(t[1..s[1]-1]), s[2], op(t[s[1]..nops(t)])])], s in [seq(seq([i,j], j=0..N-1-i), i=0..N-1)]), t in Comps(N, N-2))]:
for s in L do
   if s[1] <> FAIL then
      c:=c+1:
   fi:
od:
c:
end:

AllCycles:=proc(N) local L, S, s, t, i, n:
S:={}:
L:=[seq(seq([NuM([s[1], op(t[1..s[1]-1]), s[2], op(t[s[1]..nops(t)])])], s in [seq(seq([i,j], j=0..N-1-i), i=0..N-1)]), t in Comps(N, N-2))]:
for s in L do
   if s[1] <> FAIL then
      S:=S union {s[1][1]}:
   fi:
od:
S:
end:

EquivCycles:=proc(N) local L, S, s, t, i, n:
S:={}:
L:=[seq(seq([NuM([s[1], op(t[1..s[1]-1]), s[2], op(t[s[1]..nops(t)])])], s in [seq(seq([i,j], j=0..N-1-i), i=0..N-1)]), t in Comps(N, N-2))]:
for s in L do
   if s[1] <> FAIL then
      S:=S union {convert(s[1], set)}:
   fi:
od:
S:
end:

#Inputs x and {[x, y], ...}, returns [x, y], else returns FAIL.
FindPair:=proc(x, S) local s:
for s in S do
   if s[1] = x then
      return(s):
   fi:
od:
return(FAIL):
end:

AllCycleFreqs:=proc(N) local L, S, s, T, i, n:
S:={}:
L:=[seq(seq([NuM([s[1], op(t[1..s[1]-1]), s[2], op(t[s[1]..nops(t)])])], s in [seq(seq([i,j], j=0..N-1-i), i=0..N-1)]), t in Comps(N, N-2))]:
for s in L do
   if s[1] <> FAIL then
      T:=FindPair(s[1][1], S):
      if T = FAIL then
         S:=S union {[s[1][1], 1]}:
      else
         S:=S minus {T} union {[T[1], T[2]+1]}:
      fi
   fi:
od:
S:
end:

EquivCycleFreqs:=proc(N) local L, S, s, T, i, n:
S:={}:
L:=[seq(seq([NuM([s[1], op(t[1..s[1]-1]), s[2], op(t[s[1]..nops(t)])])], s in [seq(seq([i,j], j=0..N-1-i), i=0..N-1)]), t in Comps(N, N-2))]:
for s in L do
   if s[1] <> FAIL then
      T:=FindPair(convert(s[1], set), S):
      if T = FAIL then
         S:=S union {[convert(s[1], set), 1]}:
      else
         S:=S minus {T} union {[T[1], T[2]+1]}:
      fi
   fi:
od:
S:
end:

# modified procedures from class

#V1(L):Inputs a sequence of non-neg. integers
#and performs one step n Eric Angelini's
#(see A151986)'s glass worms game 
V1:=proc(L) local i,k:
k:=L[1]:
 if nops(L)<k+1 then
   RETURN(FAIL):
 else
    
   if k=0 then
       RETURN([op(2..nops(L),L),0]):
    else
     RETURN([op(2..k,L),L[k+1]+k,op(k+2..nops(L),L), 0]):
    fi:
 fi:  
           
   
end:

#IsOld(L): inputs a list and outputs
#true if the last entry already showed up before
#followed by the cycle. For example
#IsOld([3,5,1,2,1]); reuturs true,[1,2,1] .
IsOld:=proc(L) local i,la:
la:=L[nops(L)]:

if not member(la, {op(1..nops(L)-1,L)}) then
  RETURN(false, FAIL):
fi:

for i from 1 to nops(L)-1 while L[i]<>la do od:

true,[op(i..nops(L),L)]:

end:




#NuM(L): inputs a sequence of non-neg. integers and
#outputs either the CYCLE,#MovesToGetThere
#or FAIL,#MovesToGetThere
NuM:=proc(L) local Orb,L1:

L1:=L:
Orb:=[L]:

while L1<>FAIL and  not IsOld(Orb)[1] do

L1:=V1(L1):
Orb:=[op(Orb),L1]:

od:

if L1=FAIL then
  RETURN(FAIL,nops(Orb)-1):
else
  RETURN(IsOld(Orb)[2],nops(Orb)-1):
fi:

end:

Comps:=proc(n,k) local L,S,b,S1,s1:
option remember:

if k=0 then
   RETURN({[]}):
fi:

S:={}:

for b from 0 to n-1 do
S1:=Comps(n,k-1):
S:= S union {seq([op(s1),b], s1 in S1)}:
od:

S:

end: