>You can not apply a rule based on the 2^power to find
>the maximum reduced string with a default number of substitutions.
>
>Reduce_Successive fail on string 456718+1
>
>

>CLEAR
>? 2^20,LEN(Reduce_Successive(SPACE(456718+1)))
>
>FUNCTION Reduce_Successive
>LPARAMETERS lcString
>
>	lcString = STRTRAN( lcString, [                ], [ ] )
>	lcString = STRTRAN( lcString, [                ], [ ] )
>	lcString = STRTRAN( lcString, [        ], [ ] )
>	lcString = STRTRAN( lcString, [        ], [ ] )
>	lcString = STRTRAN( lcString, [    ], [ ] )
>	lcString = STRTRAN( lcString, [    ], [ ] )
>	lcString = STRTRAN( lcString, [  ], [ ] )
>	lcString = STRTRAN( lcString, [  ], [ ] )
>
>RETURN m.lcString
>

I ran two brute-force tests:

- one with the top two lines of the Reduce_Successive function commented out (nominally "good" for up to 2^12, or 4,096 spaces)

- the full function, as shown above (nominally "good" for up to 2^20, or 1,048,576 spaces)

As you point out, the function as shown above has failures. The first failure was at 456,719 spaces. In that test, there were 295,929 failures (out of 1,048,576 tests).

However, in both tests the length of the result string for the failures is always exactly 2. There are no failures with longer result strings. So, it's simple to modify Reduce_Successive() to work properly in all cases by adding one extra STRTRAN() call:

FUNCTION Reduce_Successive
LPARAMETERS lcString

	m.lcString = STRTRAN( m.lcString, [                ], [ ] )
	m.lcString = STRTRAN( m.lcString, [                ], [ ] )
	m.lcString = STRTRAN( m.lcString, [        ], [ ] )
	m.lcString = STRTRAN( m.lcString, [        ], [ ] )
	m.lcString = STRTRAN( m.lcString, [    ], [ ] )
	m.lcString = STRTRAN( m.lcString, [    ], [ ] )
	m.lcString = STRTRAN( m.lcString, [  ], [ ] )
	m.lcString = STRTRAN( m.lcString, [  ], [ ] )
	m.lcString = STRTRAN( m.lcString, [  ], [ ] )  && This line added 2009.07.27

RETURN m.lcString

So, it's possible to reduce series of spaces (or any other characters) down to 1 with a fixed number of STRTRAN() calls:

- up to and including 4,096 spaces with 7 STRTRAN() calls
- up to and including 1,048,576 spaces with 9 STRTRAN() calls