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) => eval#(x - 1) | x > 0 /\ not (x = 0) /\ x % 2 > 0
      (2) eval#(x) => eval#(x / 2) | x > 0 /\ not (x = 0) /\ x % 2 = 0

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

We use the following integer mapping:

  J(eval#) = arg_1

We thus have:

  (1) x > 0 /\ not (x = 0) /\ x % 2 > 0 |= x > x - 1 (and x >= 0)
  (2) x > 0 /\ not (x = 0) /\ x % 2 = 0 |= x > x / 2 (and x >= 0)

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