```PiecewiseExpand``` doesn't work as expected with a recursive function

Question

In an effort to examine this question on Math.SE, I defined the following functions

c[n_, x_] := (a[n - 1, x] + b[n - 1, x])/4 + x/2;
a[n_, x_] := 
  Return[If[n == 0, 0, t = c[n, x]; If[t > x, a[n - 1, x], t]]];
b[n_, x_] := 
  Return[If[n == 0, 1, t = c[n, x]; If[t > x, t, b[n - 1, x]]]];

These functions work as expected and return the correct output. However, when I call PiecewiseExpand[a[2, x]] I get the output of

1/4 (1 + 2 x) if x >= 1/22
0 else

This is clearly wrong - a[2, 0.3] = 0.25 while $\frac{1+2\cdot0.3}{4} = 0.4$. For some reason, PiecewiseExpand is not working properly here. Why is this happening, and how can I fix this problem?

Edit: At the suggestion of Nasser, I changed the functions to

c[n_, x_] := (a[n - 1, x] + b[n - 1, x])/4 + x/2;
a[n_, x_] := 
  If[n == 0, 0, t = c[n, x]; If[t > x, a[n - 1, x], t, "idk"], "idk1"];
b[n_, x_] := 
  If[n == 0, 1, t = c[n, x]; If[t > x, t, b[n - 1, x], "idk"], "idk1"];

Now with PiecewiseExpand[a[1, x], {0 < x < 1}], the output is idk.