What is wrong with this recursive Windows CMD script? It won't do Ackermann properly

Question

I'm trying to get to calculate the Ackermann function. A description of what I'm trying to achieve is at http://rosettacode.org/wiki/Ackermann_function.

Using the test script, Test 0 4 gives me 5 which is correct. However Test 1 4 gives 5 not 6, and Test 2 4 gives 5 instead of 11.

Where am I going wrong?

::echo off
set depth=0
:ack
if %1==0 goto m0
if %2==0 goto n0

:else
set /a n=%2-1
set /a depth+=1
call :ack %1 %n%
set t=%errorlevel%
set /a depth-=1
set /a m=%1-1
set /a depth+=1
call :ack %m% %t%
set t=%errorlevel%
set /a depth-=1
if %depth%==0 ( exit %t% ) else ( exit /b %t% )

:m0
set/a n=%2+1
if %depth%==0 ( exit %n% ) else ( exit /b %n% )

:n0
set /a m=%1-1
set /a depth+=1
call :ack %m% %2
set t=%errorlevel%
set /a depth-=1
if %depth%==0 ( exit %t% ) else ( exit /b %t% )

I use this script to test it

@echo off
cmd/c ackermann.cmd %1 %2
echo Ackermann of %1 %2 is %errorlevel%

A sample output, for Test 1 1, gives:

>test 1 1
>set depth=0
>if 1 == 0 goto m0
>if 1 == 0 goto n0
>set /a n=1-1
>set /a depth+=1
>call :ack 1 0
>if 1 == 0 goto m0
>if 0 == 0 goto n0
>set /a m=1-1
>set /a depth+=1
>call :ack 0 0
>if 0 == 0 goto m0
>set/a n=0+1
>if 2 == 0 (exit 1  )  else (exit /b 1  )
>set t=1
>set /a depth-=1
>if 1 == 0 (exit 1  )  else (exit /b 1  )
>set t=1
>set /a depth-=1
>set /a m=1-1
>set /a depth+=1
>call :ack 0 1
>if 0 == 0 goto m0
>set/a n=1+1
>if 1 == 0 (exit 2  )  else (exit /b 2  )
>set t=2
>set /a depth-=1
>if 0 == 0 (exit 2  )  else (exit /b 2  )
Ackermann of 1 1 is 2

Answer 1

What is the scope of your variables m and n?

You set values within one call to :ack, and then recursively call again, setting values. Do you overwrite them? In Stack-based languages such as C and Java, local variables are fine, each level of recursion gets new variables. What happens in cmd?

Answer 2

Change line 27 above from

call :ack %m% %2 

to

call :ack %m% 1