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(Y), z) => ack#(Y, s(z))
      (2) ack#(s(U), s(V)) => ack#(s(U), V)
      (3) ack#(s(U), s(V)) => ack#(U, ack(s(U), V))

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

We use the following projection function:

  nu(ack#) = 1

We thus have:

  (1) s(Y) |>|  Y
  (2) s(U) |>=| s(U)
  (3) s(U) |>|  U

We may remove the strictly oriented DPs, which yields:

  P2. (1) ack#(s(U), s(V)) => ack#(s(U), V)

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

We use the following projection function:

  nu(ack#) = 2

We thus have:

  (1) s(V) |>| V

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