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) exp#(x, y) => exp#(2 * x, y) | x <= y /\ 0 < x /\ x < 100000
      (2) start# => exp#(1, y)

***** We apply the Graph Processor on P1.

There is only one SCC, so all DPs not inside the SCC can be removed:

  P2. (1) exp#(x, y) => exp#(2 * x, y) | x <= y /\ 0 < x /\ x < 100000

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

We use the following integer mapping:

  J(exp#) = 100000 - arg_1 - 1

We thus have:

  (1) x <= y /\ 0 < x /\ x < 100000 |= 100000 - x - 1 > 100000 - 2 * x - 1 (and 100000 - x - 1 >= 0)

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