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

  Signature: cd :: Bool -> Int -> o

  Rules: cd(true, x) -> cd(x > 0, x - 1) | x = x

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) cd#(true, x) => cd#(x > 0, x - 1) | x = x

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

We obtain 0 usable rules (out of 1 rules in the input problem).

Processor output: { D2 = (P1, {}, i, c) }.

***** No progress could be made on DP problem D2 = (P1, {}, i, c).