val zero = Sym.fromString "0";
val one  = Sym.fromString "1";

fun diff (nil : str) = 0
  | diff (b :: bs)   =
      if Sym.equal(b, zero)
      then ~1 + diff bs
      else 1 + diff bs;

fun equal n =
      Set.filter
      (fn x => diff x = 0)
      (StrSet.power(StrSet.fromString "0, 1", n));

fun upto 0 = equal 0
  | upto n = StrSet.union(equal n, upto(n - 1));

fun locSimp n = Reg.locallySimplify(SOME n, Reg.obviousSubset);

fun assess reg =
      (Reg.size reg, Reg.numConcats reg,
       Reg.numSyms reg, Reg.standardized reg);