The next 4 lines conform to the <a href=http://en.wikipedia.org/wiki/Primitive_recursive_function><i>general recursive</i></a> pattern.
S is the primitive successor function: S(x) = x+1
<pre>A(x, 1, 1) = S(x)
A(x, S(y), 1) = S(A(x, y, 1))
A(x, 1, S(z)) = x
A(x, S(y), S(z)) = A(x, A(x, y, S(z)), z)</pre>
For instance A(x, y, 1) = x+y; A(x, y, 2) = x*y; A(x, y, 3) = x<sup>y</sup>.
<br>Note that:
<pre>A(x, 1, 2) = x 
A(x, S(y), 2) = S(x, A(x, y, 2), 1)
A(x, 1, 3) = x 
A(x, S(y), 3) = S(x, A(x, y, 3), 2)</pre>
For positive integer arguments A always terminates but
A(x, x, x) grows faster than any primitive recursive function and may be easier to understand than the simpler Ackerman’s function.
<p>In Scheme:
<pre>(define (S x) (+ x 1))
(define (A x y z) (if (= 1 z) (if (= 1 y) (S x) (S (A x (- y 1) 1)))
  (if (= 1 y) x (A x (A x (- y 1) z) (- z 1)))))</pre>
Beware that execution time is proportional to value of A.