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) f#(x) => cond1#(x > 1, x)
      (2) cond1#(true, x) => cond2#(x % 2 = 0, x)
      (3) cond2#(true, x) => f#(x / 2)
      (4) cond2#(false, x) => f#(3 * x + 1)

***** We apply the Theory Arguments Processor on P1.

We use the following theory arguments function:

  cond1# : [1, 2]
  cond2# : [1, 2]
  f#     : [1]

This yields the following new DP problems:

  P2. (1) f#(x) => cond1#(x > 1, x)
      (2) cond1#(true, x) => cond2#(x % 2 = 0, x) { x }
      (3) cond2#(true, x) => f#(x / 2) { x }
      (4) cond2#(false, x) => f#(3 * x + 1) { x }

  P3. (1) cond1#(true, x) => cond2#(x % 2 = 0, x)
      (2) cond2#(true, x) => f#(x / 2)
      (3) cond2#(false, x) => f#(3 * x + 1)

***** We apply the Theory Arguments Processor on P2.

We use the following theory arguments function:

  cond1# : [1, 2]
  cond2# : [1, 2]
  f#     : [1]

This yields the following new DP problems:

  P4. (1) f#(x) => cond1#(x > 1, x) { x }
      (2) cond1#(true, x) => cond2#(x % 2 = 0, x) { x }
      (3) cond2#(true, x) => f#(x / 2) { x }
      (4) cond2#(false, x) => f#(3 * x + 1) { x }

  P5. (1) f#(x) => cond1#(x > 1, x)

***** We apply the Graph Processor on P3.

As there are no SCCs, this DP problem is removed.

***** No progress could be made on DP problem P4.