how to evaluate/simplify a term contain if-then-else's?

Hello,

I have the following function

exactf_tau_arithprog(k,n) :=
 if n < k then 0
 elseif k=1 then n
 elseif k=2 then n-1
 elseif n <= 2*k-1 and evenp(k) then
   if n = 2*k-1 then 2 else 1
 elseif n <= 2*k and oddp(k) then
   if n = 2*k then 2 else 1
 else unknown$

which yields

exactf_tau_arithprog(1,n);
 if n < 1 then 0 elseif 1 = 1 then n elseif 1 = 2 then n-1 elseif n <= 1 and evenp(1)
           then (if n = 1 then 2 else 1) elseif n <= 2 and oddp(1) then (if n = 2 then 2 else 1)
           else unknown
   
however this should yield "if n < 1 then 0 else n" --- how to achieve this?
I've tried ev in variations, and simp, but no results.

Thanks for your help.

Oliver