The system is accessible function passing by a sort ordering that equates all sorts.

We start by computing the following initial DP problem:

  P1. (1) ack#(s(m), 0) => ack#(m, s(0))
      (2) ack#(s(m), s(n)) => ack#(s(m), n)
      (3) ack#(s(m), s(n)) => ack#(m, ack(s(m), n))

***** We apply the Subterm Criterion Processor on P1.

We use the following projection function:

  nu(ack#) = 1

We thus have:

  (1) s(m) |>|  m
  (2) s(m) |>=| s(m)
  (3) s(m) |>|  m

We may remove the strictly oriented DPs, which yields:

  P2. (1) ack#(s(m), s(n)) => ack#(s(m), n)

***** We apply the Subterm Criterion Processor on P2.

We use the following projection function:

  nu(ack#) = 2

We thus have:

  (1) s(n) |>| n

All DPs are strictly oriented, and may be removed.  Hence, this DP problem is finite.