We consider termination of the LCTRS with only rule scheme Calc:

  Signature: eval :: Int -> Int -> Int -> o

  Rules: eval(x, y, z) -> eval(x - 1, y - 1, z) | x > z /\ y > z

The system is accessible function passing by a sort ordering that equates all sorts.

We start by computing the initial DP problem D1 = (P1, R, i, c), where:

  P1. (1) eval#(x, y, z) => eval#(x - 1, y - 1, z) | x > z /\ y > z

***** We apply the Integer Function Processor on D1 = (P1, R, i, c).

We use the following integer mapping:

  J(eval#) = arg_2 - arg_3 - 1

We thus have:

  (1) x > z /\ y > z |= y - z - 1 > y - 1 - z - 1 (and y - z - 1 >= 0)

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

Processor output: { }.