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#(l, u) => eval#((l + u) / 2 + 1, u) | l >= 0 /\ u >= 0 /\ l < u
      (2) eval#(l, u) => eval#(l, (l + u) / 2) | l >= 0 /\ u >= 0 /\ l < u

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

We use the following integer mapping:

  J(eval#) = arg_2

We thus have:

  (1) l >= 0 /\ u >= 0 /\ l < u |= u >= u
  (2) l >= 0 /\ u >= 0 /\ l < u |= u >  (l + u) / 2 (and u >= 0)

We may remove the strictly oriented DPs, which yields:

  P2. (1) eval#(l, u) => eval#((l + u) / 2 + 1, u) | l >= 0 /\ u >= 0 /\ l < u

***** We apply the Integer Function Processor on P2.

We use the following integer mapping:

  J(eval#) = arg_2 - arg_1 - 1

We thus have:

  (1) l >= 0 /\ u >= 0 /\ l < u |= u - l - 1 > u - ((l + u) / 2 + 1) - 1 (and u - l - 1 >= 0)

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