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) f#(x, y, z) => f#(x, y + 1, z) | x > y + z
      (2) f#(x, y, z) => f#(x, y, z + 1) | x > y + z

***** We apply the Integer Function Processor on P1.

We use the following integer mapping:

  J(f#) = arg_1 - (arg_2 + arg_3) - 1

We thus have:

  (1) x > y + z |= x - (y + z) - 1 > x - (y + 1 + z) - 1   (and x - (y + z) - 1 >= 0)
  (2) x > y + z |= x - (y + z) - 1 > x - (y + (z + 1)) - 1 (and x - (y + z) - 1 >= 0)

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