// Deletes the elements S[n]...S[k] from the string
Delete := procedure(~S,n,k)
   if k ne #S then 
   	S := Substring(S,1,n-1)*Substring(S,k+1,#S); //Note, Substring function deals with overflow caused by #s
   else
	S := Substring(S,1,n-1);
   end if;
end procedure;


// Capitol letters represent inverses
// pq := a, qr := b, rp := c, qp := A, rq := B, pr := C
PQRtoABC := procedure(~S)
    ABC := "";	
    for k in [1..(#S-1) by 2] do
        if S[k] eq "p" then
	    if S[k+1] eq "q" then
    		ABC := ABC*"a";
	    else
		ABC := ABC*"C";
	    end if;
	elif S[k] eq "q" then
	    if S[k+1] eq "r" then
		ABC := ABC*"b";
	    else
		ABC := ABC*"A";
  	    end if;
	else
	    if S[k+1] eq "p" then
		ABC := ABC*"c";
	    else 
		ABC := ABC*"B";
	    end if;
	end if; 		
    end for;
    if #S mod 2 eq 1 then
	ABC := ABC*S[#S];
    end if;
    S := ABC;
end procedure;


//Destructively changes an ABCabc(pqr) string to a pqr string
ABCtoPQR := procedure(~S)
    PQR := "";
    for k in [1..#S] do
	if S[k] eq "a" then
	    PQR := PQR*"pq";
	elif S[k] eq "b" then
	    PQR := PQR*"qr";
 	elif S[k] eq "c" then
	    PQR := PQR*"rp";
   	elif S[k] eq "A" then
	    PQR := PQR*"qp";
	elif S[k] eq "B" then
	    PQR := PQR*"rq";
	elif S[k] eq "C" then	
	    PQR := PQR*"pr";
	else
	    PQR := PQR*S[k];
	end if;
    end for;
    S := PQR;
end procedure;


// removes l, m, and n powers of a, b, and c, respectively
Cycling := procedure(~S,l,m,n)
   location := Position(S,"a"^l);
   while location ne 0 do
  	Delete(~S,location,location+l-1);
	location:= Position(S,"a"^l);
   end while;
   location:= Position(S,"A"^l);
   while location ne 0 do
  	Delete(~S,location,location+l-1);
	location:= Position(S,"A"^l);
   end while;
   location:= Position(S,"b"^m);
   while location ne 0 do
  	Delete(~S,location,location+m-1);
	location:= Position(S,"b"^m);
   end while;
   location:= Position(S,"B"^m);
   while location ne 0 do
  	Delete(~S,location,location+m-1);
	location:= Position(S,"B"^m);
   end while;
   location:= Position(S,"c"^n);
   while location ne 0 do
  	Delete(~S,location,location+n-1);
	location:= Position(S,"c"^n);
   end while;
   location:= Position(S,"C"^n);
   while location ne 0 do
  	Delete(~S,location,location+n-1);
	location:= Position(S,"C"^n);
   end while;
end procedure;

Samplify := procedure(~S,l,m,n)
   Size := -1;
   while Size ne #S do 
       Size := #S;
       k := 1;
       while k lt #S do
	   if S[k] eq S[k+1] then
	       Delete(~S,k,k+1);
	   else
   	       k := k + 1;
           end if;
       end while;
       PQRtoABC(~S);
       Cycling(~S,l,m,n);   
       ABCtoPQR(~S);
   end while;
end procedure;

Samp := function(S,l,m,n);
    Samplify(~S,l,m,n);
    return S;
end function;


//Destructively simplifies a string
Simplify := procedure(~S,l,m,n)
   Size := -1;
   while Size ne #S do 
       Size := #S;
       k := 1;
       while k lt #S do
	   if S[k] eq S[k+1] then
	       Delete(~S,k,k+1);
	   else
   	       k := k + 1;
           end if;
       end while;
   end while;
   Size := -1;
   while Size ne #S do 
       Size := #S;
       PQRtoABC(~S);
       Cycling(~S,l,m,n);   
       ABCtoPQR(~S);
   end while;
   Size := -1;
   while Size ne #S do 
       Size := #S;
       k := 1;
       while k lt #S do
	   if S[k] eq S[k+1] then
	       Delete(~S,k,k+1);
	   else
   	       k := k + 1;
           end if;
       end while;
       PQRtoABC(~S);
       Cycling(~S,l,m,n);   
       ABCtoPQR(~S);
   end while;
   if #S mod 2 eq 1 then
	P := Samp(Samp(S*"p",l,m,n)*"p",l,m,n);
	Q := Samp(Samp(S*"q",l,m,n)*"q",l,m,n);
	R := Samp(Samp(S*"r",l,m,n)*"r",l,m,n);
	S := P;
	if #S gt #Q then
	    S := Q;
	end if;
	if #S gt #R then
    	    S := R;
        end if;
   end if;
end procedure;


// Version of simplify that doesnt' require a variable reference and doesn't change the value of the variable
SimpLite := function(S,l,m,n)
    Simplify(~S,l,m,n);
    return S;
end function;

SimpMax := function(S,l,m,n)
    Simplify(~S,l,m,n);
    Size := 0;
    while Size ne #S do	
    	Size := #S;
	result := S;
	for k in [1..(#S-1)] do
	    for j in [k..(#S-1)] do
	     tmp := SimpLite(Substring(S,1,k),2,3,7)*SimpLite(Substring(S,k+1,j),2,3,7)*SimpLite(Substring(S,j+1,#S),2,3,7);
	     if #tmp lt #result then
		result := tmp;
	     end if;
	    end for;
	end for;
	S := result;
    end while;
    return S;
end function;