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) sumto#(x, y) => sumto#(x + 1, y) | y >= x
      (2) sumto#(x, y) => if#(sumto(x + 1, y), x, y) | y >= x

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

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

  P2. (1) sumto#(x, y) => sumto#(x + 1, y) | y >= x

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

We use the following integer mapping:

  J(sumto#) = arg_2 - arg_1

We thus have:

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

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