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) sqrt#(x) => f#(x, 0, 1, 1)
      (2) f#(x, z, u, w) => f#(x, z + 1, u + 2, w + u + 2) | x >= w /\ u >= 0

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

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

  P2. (1) f#(x, z, u, w) => f#(x, z + 1, u + 2, w + u + 2) | x >= w /\ u >= 0

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

We use the following integer mapping:

  J(f#) = arg_1 - arg_4

We thus have:

  (1) x >= w /\ u >= 0 |= x - w > x - (w + u + 2) (and x - w >= 0)

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