Help:=proc():  print(`W(a,b), Wt(HorizA,VertA,w), BPb(HorizA,VertA,a,b)`):end:

W:=proc(a,b) local S1,S2,i:
option remember:

if a=0 then
 RETURN({ [seq([0,i],i=0..b) ]}):
elif b=0 then
RETURN({ [seq([i,0],i=0..a) ]}):
fi:

S1:=W(a,b-1):
S2:=W(a-1,b):

 {seq([op(S1[i]),[a,b]],i=1..nops(S1)),
seq([op(S2[i]),[a,b]],i=1..nops(S2))}:



end:


#BPb(HorizA,VertA,a,b): The best path from [0,0] to [a,b]
#given the Attraction Lists HorizA, VertA
BPb:=proc(HorizA,VertA,a,b)
end:

#Wt(HorizA,VertB,w): Given the Horiz. and Vertical attraction
#tables (given as lists of lists, 
#where HorizA[i][j] is
#the number of attractions between [i-1,j-1] to [i-1,j]
#where VertA[i][j] is
#the number of attractions between [i-1,j-1] to [i,j-1]
Wt:=proc(HorizA,VertA,w) local c,i,w1,pt1,pt2:

if w=[[0,0]] then
 RETURN(0):
fi:

w1:=[op(1..nops(w)-1,w)]:
c:=Wt(HorizA,VertA,w1):


pt1:=w[nops(w)-1]:
pt2:=w[nops(w)]:

if pt1[2]=pt2[2] then
 RETURN(c+ HorizA[pt1[1]+1][pt1[2]+1]):
elif pt1[1]=pt2[1] then
RETURN(c+ VertA[pt1[1]+1][pt1[2]+1]):
else
   print(`Something is wrong`):
   RETURN(FAIL):
fi:
end: