We consider universal computability of the LCTRS with only rule scheme Calc:

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

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

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 UNION R_?, f, c), where:

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

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

We use the following integer mapping:

  J(eval#) = arg_1 - (arg_2 + 1)

We thus have:

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

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

Processor output: { }.