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) eval#(x, y, z) => eval#(x - 1, y - 1, z) | x >= 0 /\ z * z * z >= y
      (2) eval#(x, y, z) => eval#(x, y - 1, z + y) | x >= 0 /\ z * z * z >= y

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

We use the following integer mapping:

  J(eval#) = arg_1

We thus have:

  (1) x >= 0 /\ z * z * z >= y |= x >  x - 1 (and x >= 0)
  (2) x >= 0 /\ z * z * z >= y |= x >= x

We may remove the strictly oriented DPs, which yields:

  P2. (1) eval#(x, y, z) => eval#(x, y - 1, z + y) | x >= 0 /\ z * z * z >= y

***** No progress could be made on DP problem P2.