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)  le#(s(U), s(V)) => le#(U, V)
      (2)  minus#(X1, s(Y1)) => minus#(X1, Y1)
      (3)  minus#(X1, s(Y1)) => pred#(minus(X1, Y1))
      (4)  gcd#(s(W1), s(P1)) => le#(P1, W1)
      (5)  gcd#(s(W1), s(P1)) => if_gcd#(le(P1, W1), s(W1), s(P1))
      (6)  if_gcd#(true, s(X2), s(Y2)) => minus#(X2, Y2)
      (7)  if_gcd#(true, s(X2), s(Y2)) => gcd#(minus(X2, Y2), s(Y2))
      (8)  if_gcd#(false, s(U2), s(V2)) => minus#(V2, U2)
      (9)  if_gcd#(false, s(U2), s(V2)) => gcd#(minus(V2, U2), s(U2))
      (10) map#(J2, cons(X3, Y3)) => map#(J2, Y3)
      (11) filter#(H3, cons(W3, P3)) => filter2#(H3(W3), H3, W3, P3)
      (12) filter2#(true, F4, Y4, U4) => filter#(F4, U4)
      (13) filter2#(false, H4, W4, P4) => filter#(H4, P4)

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

Considering the 5 SCCs, this DP problem is split into the following new problems.

  P2. (1) le#(s(U), s(V)) => le#(U, V)

  P3. (1) minus#(X1, s(Y1)) => minus#(X1, Y1)

  P4. (1) gcd#(s(W1), s(P1)) => if_gcd#(le(P1, W1), s(W1), s(P1))
      (2) if_gcd#(true, s(X2), s(Y2)) => gcd#(minus(X2, Y2), s(Y2))
      (3) if_gcd#(false, s(U2), s(V2)) => gcd#(minus(V2, U2), s(U2))

  P5. (1) map#(J2, cons(X3, Y3)) => map#(J2, Y3)

  P6. (1) filter#(H3, cons(W3, P3)) => filter2#(H3(W3), H3, W3, P3)
      (2) filter2#(true, F4, Y4, U4) => filter#(F4, U4)
      (3) filter2#(false, H4, W4, P4) => filter#(H4, P4)

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

We use the following projection function:

  nu(le#) = 1

We thus have:

  (1) s(U) |>| U

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

***** We apply the Subterm Criterion Processor on P3.

We use the following projection function:

  nu(minus#) = 2

We thus have:

  (1) s(Y1) |>| Y1

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

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