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

  Signature: f :: Int -> Int -> o

  Rules: f(x, y) -> f(x, y + 1) | x > y

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, f, c), where:

  P1. (1) f#(x, y) => f#(x, y + 1) | x > y

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

We use the following integer mapping:

  J(f#) = arg_1 - arg_2

We thus have:

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

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

Processor output: { }.