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) log#(x, y) => logNat#(x >= 0 /\ y >= 2, x, y)
      (2) logNat#(true, x, y) => cond#(x <= y, x, y)
      (3) cond#(false, x, y) => log#(x, y * y)

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

We use the following theory arguments function:

  cond#   : [1, 2, 3]
  log#    : [1, 2]
  logNat# : [1, 2, 3]

This yields the following new DP problems:

  P2. (1) log#(x, y) => logNat#(x >= 0 /\ y >= 2, x, y)
      (2) logNat#(true, x, y) => cond#(x <= y, x, y) { x, y }
      (3) cond#(false, x, y) => log#(x, y * y) { x, y }

  P3. (1) logNat#(true, x, y) => cond#(x <= y, x, y)
      (2) cond#(false, x, y) => log#(x, y * y)

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

We use the following theory arguments function:

  cond#   : [1, 2, 3]
  log#    : [1, 2]
  logNat# : [1, 2, 3]

This yields the following new DP problems:

  P4. (1) log#(x, y) => logNat#(x >= 0 /\ y >= 2, x, y) { x, y }
      (2) logNat#(true, x, y) => cond#(x <= y, x, y) { x, y }
      (3) cond#(false, x, y) => log#(x, y * y) { x, y }

  P5. (1) log#(x, y) => logNat#(x >= 0 /\ y >= 2, x, y)

***** 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.