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#(F, Y, U) => g#(Y, U, F, Y)
      (2) g#(s(Y), s(U), F, V) => g#(Y, U, F, V)
      (3) g#(0, 0, F, V) => h#(V)
      (4) g#(0, 0, F, V) => f#(F, s(V), F(h(V)))
      (5) h#(s(Y)) => h#(Y)
      (6) i#(a(Y)) => i#(Y)

***** We apply the Graph Processor on P1.

Considering the 3 SCCs, this DP problem is split into the following new problems.

  P2. (1) h#(s(Y)) => h#(Y)

  P3. (1) f#(F, Y, U) => g#(Y, U, F, Y)
      (2) g#(s(Y), s(U), F, V) => g#(Y, U, F, V)
      (3) g#(0, 0, F, V) => f#(F, s(V), F(h(V)))

  P4. (1) i#(a(Y)) => i#(Y)

***** We apply the Subterm Criterion Processor on P2.

We use the following projection function:

  nu(h#) = 1

We thus have:

  (1) s(Y) |>| Y

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

***** No progress could be made on DP problem P3.