Termination w.r.t. Q proof of /tmp/tmp1xHxBI/Ex9_BLR02

Termination w.r.t. Q of the following Term Rewriting System could not be shown:

Q restricted rewrite system:
The TRS R consists of the following rules:

filter(cons(X, Y), 0, M) → cons(0, n__filter(activate(Y), M, M))
filter(cons(X, Y), s(N), M) → cons(X, n__filter(activate(Y), N, M))
sieve(cons(0, Y)) → cons(0, n__sieve(activate(Y)))
sieve(cons(s(N), Y)) → cons(s(N), n__sieve(n__filter(activate(Y), N, N)))
nats(N) → cons(N, n__nats(n__s(N)))
zprimes → sieve(nats(s(s(0))))
filter(X1, X2, X3) → n__filter(X1, X2, X3)
sieve(X) → n__sieve(X)
nats(X) → n__nats(X)
s(X) → n__s(X)
activate(n__filter(X1, X2, X3)) → filter(activate(X1), activate(X2), activate(X3))
activate(n__sieve(X)) → sieve(activate(X))
activate(n__nats(X)) → nats(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

Q restricted rewrite system:
The TRS R consists of the following rules:

filter(cons(X, Y), 0, M) → cons(0, n__filter(activate(Y), M, M))
filter(cons(X, Y), s(N), M) → cons(X, n__filter(activate(Y), N, M))
sieve(cons(0, Y)) → cons(0, n__sieve(activate(Y)))
sieve(cons(s(N), Y)) → cons(s(N), n__sieve(n__filter(activate(Y), N, N)))
nats(N) → cons(N, n__nats(n__s(N)))
zprimes → sieve(nats(s(s(0))))
filter(X1, X2, X3) → n__filter(X1, X2, X3)
sieve(X) → n__sieve(X)
nats(X) → n__nats(X)
s(X) → n__s(X)
activate(n__filter(X1, X2, X3)) → filter(activate(X1), activate(X2), activate(X3))
activate(n__sieve(X)) → sieve(activate(X))
activate(n__nats(X)) → nats(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X

Q is empty.

Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

ZPRIMES → S(0)
ACTIVATE(n__sieve(X)) → SIEVE(activate(X))
SIEVE(cons(0, Y)) → ACTIVATE(Y)
ZPRIMES → NATS(s(s(0)))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X3)
ACTIVATE(n__s(X)) → S(activate(X))
ACTIVATE(n__sieve(X)) → ACTIVATE(X)
ACTIVATE(n__filter(X1, X2, X3)) → FILTER(activate(X1), activate(X2), activate(X3))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X1)
SIEVE(cons(s(N), Y)) → ACTIVATE(Y)
ACTIVATE(n__s(X)) → ACTIVATE(X)
FILTER(cons(X, Y), 0, M) → ACTIVATE(Y)
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X2)
ZPRIMES → S(s(0))
ACTIVATE(n__nats(X)) → NATS(activate(X))
ZPRIMES → SIEVE(nats(s(s(0))))
ACTIVATE(n__nats(X)) → ACTIVATE(X)
FILTER(cons(X, Y), s(N), M) → ACTIVATE(Y)

The TRS R consists of the following rules:

filter(cons(X, Y), 0, M) → cons(0, n__filter(activate(Y), M, M))
filter(cons(X, Y), s(N), M) → cons(X, n__filter(activate(Y), N, M))
sieve(cons(0, Y)) → cons(0, n__sieve(activate(Y)))
sieve(cons(s(N), Y)) → cons(s(N), n__sieve(n__filter(activate(Y), N, N)))
nats(N) → cons(N, n__nats(n__s(N)))
zprimes → sieve(nats(s(s(0))))
filter(X1, X2, X3) → n__filter(X1, X2, X3)
sieve(X) → n__sieve(X)
nats(X) → n__nats(X)
s(X) → n__s(X)
activate(n__filter(X1, X2, X3)) → filter(activate(X1), activate(X2), activate(X3))
activate(n__sieve(X)) → sieve(activate(X))
activate(n__nats(X)) → nats(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

Q DP problem:
The TRS P consists of the following rules:

ZPRIMES → S(0)
ACTIVATE(n__sieve(X)) → SIEVE(activate(X))
SIEVE(cons(0, Y)) → ACTIVATE(Y)
ZPRIMES → NATS(s(s(0)))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X3)
ACTIVATE(n__s(X)) → S(activate(X))
ACTIVATE(n__sieve(X)) → ACTIVATE(X)
ACTIVATE(n__filter(X1, X2, X3)) → FILTER(activate(X1), activate(X2), activate(X3))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X1)
SIEVE(cons(s(N), Y)) → ACTIVATE(Y)
ACTIVATE(n__s(X)) → ACTIVATE(X)
FILTER(cons(X, Y), 0, M) → ACTIVATE(Y)
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X2)
ZPRIMES → S(s(0))
ACTIVATE(n__nats(X)) → NATS(activate(X))
ZPRIMES → SIEVE(nats(s(s(0))))
ACTIVATE(n__nats(X)) → ACTIVATE(X)
FILTER(cons(X, Y), s(N), M) → ACTIVATE(Y)

The TRS R consists of the following rules:

filter(cons(X, Y), 0, M) → cons(0, n__filter(activate(Y), M, M))
filter(cons(X, Y), s(N), M) → cons(X, n__filter(activate(Y), N, M))
sieve(cons(0, Y)) → cons(0, n__sieve(activate(Y)))
sieve(cons(s(N), Y)) → cons(s(N), n__sieve(n__filter(activate(Y), N, N)))
nats(N) → cons(N, n__nats(n__s(N)))
zprimes → sieve(nats(s(s(0))))
filter(X1, X2, X3) → n__filter(X1, X2, X3)
sieve(X) → n__sieve(X)
nats(X) → n__nats(X)
s(X) → n__s(X)
activate(n__filter(X1, X2, X3)) → filter(activate(X1), activate(X2), activate(X3))
activate(n__sieve(X)) → sieve(activate(X))
activate(n__nats(X)) → nats(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 6 less nodes.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

Q DP problem:
The TRS P consists of the following rules:

ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X2)
FILTER(cons(X, Y), 0, M) → ACTIVATE(Y)
ACTIVATE(n__sieve(X)) → SIEVE(activate(X))
SIEVE(cons(0, Y)) → ACTIVATE(Y)
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X3)
ACTIVATE(n__sieve(X)) → ACTIVATE(X)
FILTER(cons(X, Y), s(N), M) → ACTIVATE(Y)
ACTIVATE(n__nats(X)) → ACTIVATE(X)
ACTIVATE(n__filter(X1, X2, X3)) → FILTER(activate(X1), activate(X2), activate(X3))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X1)
SIEVE(cons(s(N), Y)) → ACTIVATE(Y)
ACTIVATE(n__s(X)) → ACTIVATE(X)

The TRS R consists of the following rules:

filter(cons(X, Y), 0, M) → cons(0, n__filter(activate(Y), M, M))
filter(cons(X, Y), s(N), M) → cons(X, n__filter(activate(Y), N, M))
sieve(cons(0, Y)) → cons(0, n__sieve(activate(Y)))
sieve(cons(s(N), Y)) → cons(s(N), n__sieve(n__filter(activate(Y), N, N)))
nats(N) → cons(N, n__nats(n__s(N)))
zprimes → sieve(nats(s(s(0))))
filter(X1, X2, X3) → n__filter(X1, X2, X3)
sieve(X) → n__sieve(X)
nats(X) → n__nats(X)
s(X) → n__s(X)
activate(n__filter(X1, X2, X3)) → filter(activate(X1), activate(X2), activate(X3))
activate(n__sieve(X)) → sieve(activate(X))
activate(n__nats(X)) → nats(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule ACTIVATE(n__filter(X1, X2, X3)) → FILTER(activate(X1), activate(X2), activate(X3)) at position [0] we obtained the following new rules:

ACTIVATE(n__filter(n__nats(x0), y1, y2)) → FILTER(nats(activate(x0)), activate(y1), activate(y2))
ACTIVATE(n__filter(x0, y1, y2)) → FILTER(x0, activate(y1), activate(y2))
ACTIVATE(n__filter(n__s(x0), y1, y2)) → FILTER(s(activate(x0)), activate(y1), activate(y2))
ACTIVATE(n__filter(n__filter(x0, x1, x2), y1, y2)) → FILTER(filter(activate(x0), activate(x1), activate(x2)), activate(y1), activate(y2))
ACTIVATE(n__filter(n__sieve(x0), y1, y2)) → FILTER(sieve(activate(x0)), activate(y1), activate(y2))

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ Narrowing

Q DP problem:
The TRS P consists of the following rules:

ACTIVATE(n__filter(n__nats(x0), y1, y2)) → FILTER(nats(activate(x0)), activate(y1), activate(y2))
ACTIVATE(n__sieve(X)) → SIEVE(activate(X))
ACTIVATE(n__filter(n__s(x0), y1, y2)) → FILTER(s(activate(x0)), activate(y1), activate(y2))
ACTIVATE(n__filter(x0, y1, y2)) → FILTER(x0, activate(y1), activate(y2))
SIEVE(cons(0, Y)) → ACTIVATE(Y)
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X3)
ACTIVATE(n__sieve(X)) → ACTIVATE(X)
ACTIVATE(n__filter(n__filter(x0, x1, x2), y1, y2)) → FILTER(filter(activate(x0), activate(x1), activate(x2)), activate(y1), activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X1)
SIEVE(cons(s(N), Y)) → ACTIVATE(Y)
ACTIVATE(n__s(X)) → ACTIVATE(X)
FILTER(cons(X, Y), 0, M) → ACTIVATE(Y)
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X2)
ACTIVATE(n__filter(n__sieve(x0), y1, y2)) → FILTER(sieve(activate(x0)), activate(y1), activate(y2))
ACTIVATE(n__nats(X)) → ACTIVATE(X)
FILTER(cons(X, Y), s(N), M) → ACTIVATE(Y)

The TRS R consists of the following rules:

filter(cons(X, Y), 0, M) → cons(0, n__filter(activate(Y), M, M))
filter(cons(X, Y), s(N), M) → cons(X, n__filter(activate(Y), N, M))
sieve(cons(0, Y)) → cons(0, n__sieve(activate(Y)))
sieve(cons(s(N), Y)) → cons(s(N), n__sieve(n__filter(activate(Y), N, N)))
nats(N) → cons(N, n__nats(n__s(N)))
zprimes → sieve(nats(s(s(0))))
filter(X1, X2, X3) → n__filter(X1, X2, X3)
sieve(X) → n__sieve(X)
nats(X) → n__nats(X)
s(X) → n__s(X)
activate(n__filter(X1, X2, X3)) → filter(activate(X1), activate(X2), activate(X3))
activate(n__sieve(X)) → sieve(activate(X))
activate(n__nats(X)) → nats(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule ACTIVATE(n__sieve(X)) → SIEVE(activate(X)) at position [0] we obtained the following new rules:

ACTIVATE(n__sieve(x0)) → SIEVE(x0)
ACTIVATE(n__sieve(n__sieve(x0))) → SIEVE(sieve(activate(x0)))
ACTIVATE(n__sieve(n__filter(x0, x1, x2))) → SIEVE(filter(activate(x0), activate(x1), activate(x2)))
ACTIVATE(n__sieve(n__s(x0))) → SIEVE(s(activate(x0)))
ACTIVATE(n__sieve(n__nats(x0))) → SIEVE(nats(activate(x0)))

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ Narrowing

                ↳ QDP

                  ↳ Narrowing

Q DP problem:
The TRS P consists of the following rules:

ACTIVATE(n__filter(n__nats(x0), y1, y2)) → FILTER(nats(activate(x0)), activate(y1), activate(y2))
ACTIVATE(n__sieve(n__filter(x0, x1, x2))) → SIEVE(filter(activate(x0), activate(x1), activate(x2)))
ACTIVATE(n__filter(x0, y1, y2)) → FILTER(x0, activate(y1), activate(y2))
ACTIVATE(n__filter(n__s(x0), y1, y2)) → FILTER(s(activate(x0)), activate(y1), activate(y2))
SIEVE(cons(0, Y)) → ACTIVATE(Y)
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X3)
ACTIVATE(n__sieve(x0)) → SIEVE(x0)
ACTIVATE(n__sieve(X)) → ACTIVATE(X)
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X1)
ACTIVATE(n__filter(n__filter(x0, x1, x2), y1, y2)) → FILTER(filter(activate(x0), activate(x1), activate(x2)), activate(y1), activate(y2))
SIEVE(cons(s(N), Y)) → ACTIVATE(Y)
ACTIVATE(n__s(X)) → ACTIVATE(X)
ACTIVATE(n__sieve(n__s(x0))) → SIEVE(s(activate(x0)))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X2)
FILTER(cons(X, Y), 0, M) → ACTIVATE(Y)
ACTIVATE(n__filter(n__sieve(x0), y1, y2)) → FILTER(sieve(activate(x0)), activate(y1), activate(y2))
ACTIVATE(n__sieve(n__sieve(x0))) → SIEVE(sieve(activate(x0)))
FILTER(cons(X, Y), s(N), M) → ACTIVATE(Y)
ACTIVATE(n__nats(X)) → ACTIVATE(X)
ACTIVATE(n__sieve(n__nats(x0))) → SIEVE(nats(activate(x0)))

The TRS R consists of the following rules:

filter(cons(X, Y), 0, M) → cons(0, n__filter(activate(Y), M, M))
filter(cons(X, Y), s(N), M) → cons(X, n__filter(activate(Y), N, M))
sieve(cons(0, Y)) → cons(0, n__sieve(activate(Y)))
sieve(cons(s(N), Y)) → cons(s(N), n__sieve(n__filter(activate(Y), N, N)))
nats(N) → cons(N, n__nats(n__s(N)))
zprimes → sieve(nats(s(s(0))))
filter(X1, X2, X3) → n__filter(X1, X2, X3)
sieve(X) → n__sieve(X)
nats(X) → n__nats(X)
s(X) → n__s(X)
activate(n__filter(X1, X2, X3)) → filter(activate(X1), activate(X2), activate(X3))
activate(n__sieve(X)) → sieve(activate(X))
activate(n__nats(X)) → nats(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule ACTIVATE(n__filter(n__nats(x0), y1, y2)) → FILTER(nats(activate(x0)), activate(y1), activate(y2)) at position [1] we obtained the following new rules:

ACTIVATE(n__filter(n__nats(y0), n__filter(x0, x1, x2), y2)) → FILTER(nats(activate(y0)), filter(activate(x0), activate(x1), activate(x2)), activate(y2))
ACTIVATE(n__filter(n__nats(y0), n__nats(x0), y2)) → FILTER(nats(activate(y0)), nats(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__nats(y0), n__s(x0), y2)) → FILTER(nats(activate(y0)), s(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__nats(y0), x0, y2)) → FILTER(nats(activate(y0)), x0, activate(y2))
ACTIVATE(n__filter(n__nats(y0), n__sieve(x0), y2)) → FILTER(nats(activate(y0)), sieve(activate(x0)), activate(y2))

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ Narrowing

                ↳ QDP

                  ↳ Narrowing

                    ↳ QDP

                      ↳ Narrowing

Q DP problem:
The TRS P consists of the following rules:

ACTIVATE(n__sieve(n__filter(x0, x1, x2))) → SIEVE(filter(activate(x0), activate(x1), activate(x2)))
ACTIVATE(n__filter(n__s(x0), y1, y2)) → FILTER(s(activate(x0)), activate(y1), activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X1)
ACTIVATE(n__s(X)) → ACTIVATE(X)
ACTIVATE(n__sieve(n__s(x0))) → SIEVE(s(activate(x0)))
FILTER(cons(X, Y), 0, M) → ACTIVATE(Y)
ACTIVATE(n__filter(n__nats(y0), n__filter(x0, x1, x2), y2)) → FILTER(nats(activate(y0)), filter(activate(x0), activate(x1), activate(x2)), activate(y2))
FILTER(cons(X, Y), s(N), M) → ACTIVATE(Y)
ACTIVATE(n__filter(x0, y1, y2)) → FILTER(x0, activate(y1), activate(y2))
SIEVE(cons(0, Y)) → ACTIVATE(Y)
ACTIVATE(n__filter(n__nats(y0), n__nats(x0), y2)) → FILTER(nats(activate(y0)), nats(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__nats(y0), n__s(x0), y2)) → FILTER(nats(activate(y0)), s(activate(x0)), activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X3)
ACTIVATE(n__filter(n__nats(y0), x0, y2)) → FILTER(nats(activate(y0)), x0, activate(y2))
ACTIVATE(n__sieve(x0)) → SIEVE(x0)
ACTIVATE(n__sieve(X)) → ACTIVATE(X)
ACTIVATE(n__filter(n__filter(x0, x1, x2), y1, y2)) → FILTER(filter(activate(x0), activate(x1), activate(x2)), activate(y1), activate(y2))
SIEVE(cons(s(N), Y)) → ACTIVATE(Y)
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X2)
ACTIVATE(n__filter(n__sieve(x0), y1, y2)) → FILTER(sieve(activate(x0)), activate(y1), activate(y2))
ACTIVATE(n__sieve(n__sieve(x0))) → SIEVE(sieve(activate(x0)))
ACTIVATE(n__filter(n__nats(y0), n__sieve(x0), y2)) → FILTER(nats(activate(y0)), sieve(activate(x0)), activate(y2))
ACTIVATE(n__nats(X)) → ACTIVATE(X)
ACTIVATE(n__sieve(n__nats(x0))) → SIEVE(nats(activate(x0)))

The TRS R consists of the following rules:

filter(cons(X, Y), 0, M) → cons(0, n__filter(activate(Y), M, M))
filter(cons(X, Y), s(N), M) → cons(X, n__filter(activate(Y), N, M))
sieve(cons(0, Y)) → cons(0, n__sieve(activate(Y)))
sieve(cons(s(N), Y)) → cons(s(N), n__sieve(n__filter(activate(Y), N, N)))
nats(N) → cons(N, n__nats(n__s(N)))
zprimes → sieve(nats(s(s(0))))
filter(X1, X2, X3) → n__filter(X1, X2, X3)
sieve(X) → n__sieve(X)
nats(X) → n__nats(X)
s(X) → n__s(X)
activate(n__filter(X1, X2, X3)) → filter(activate(X1), activate(X2), activate(X3))
activate(n__sieve(X)) → sieve(activate(X))
activate(n__nats(X)) → nats(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule ACTIVATE(n__filter(x0, y1, y2)) → FILTER(x0, activate(y1), activate(y2)) at position [1] we obtained the following new rules:

ACTIVATE(n__filter(y0, n__filter(x0, x1, x2), y2)) → FILTER(y0, filter(activate(x0), activate(x1), activate(x2)), activate(y2))
ACTIVATE(n__filter(y0, n__sieve(x0), y2)) → FILTER(y0, sieve(activate(x0)), activate(y2))
ACTIVATE(n__filter(y0, n__s(x0), y2)) → FILTER(y0, s(activate(x0)), activate(y2))
ACTIVATE(n__filter(y0, n__nats(x0), y2)) → FILTER(y0, nats(activate(x0)), activate(y2))
ACTIVATE(n__filter(y0, x0, y2)) → FILTER(y0, x0, activate(y2))

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ Narrowing

                ↳ QDP

                  ↳ Narrowing

                    ↳ QDP

                      ↳ Narrowing

                        ↳ QDP

                          ↳ Narrowing

Q DP problem:
The TRS P consists of the following rules:

ACTIVATE(n__filter(n__s(x0), y1, y2)) → FILTER(s(activate(x0)), activate(y1), activate(y2))
ACTIVATE(n__sieve(n__filter(x0, x1, x2))) → SIEVE(filter(activate(x0), activate(x1), activate(x2)))
ACTIVATE(n__filter(y0, n__sieve(x0), y2)) → FILTER(y0, sieve(activate(x0)), activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X1)
ACTIVATE(n__s(X)) → ACTIVATE(X)
ACTIVATE(n__sieve(n__s(x0))) → SIEVE(s(activate(x0)))
FILTER(cons(X, Y), 0, M) → ACTIVATE(Y)
ACTIVATE(n__filter(n__nats(y0), n__filter(x0, x1, x2), y2)) → FILTER(nats(activate(y0)), filter(activate(x0), activate(x1), activate(x2)), activate(y2))
ACTIVATE(n__filter(y0, n__filter(x0, x1, x2), y2)) → FILTER(y0, filter(activate(x0), activate(x1), activate(x2)), activate(y2))
FILTER(cons(X, Y), s(N), M) → ACTIVATE(Y)
ACTIVATE(n__filter(n__nats(y0), n__nats(x0), y2)) → FILTER(nats(activate(y0)), nats(activate(x0)), activate(y2))
SIEVE(cons(0, Y)) → ACTIVATE(Y)
ACTIVATE(n__filter(n__nats(y0), n__s(x0), y2)) → FILTER(nats(activate(y0)), s(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__nats(y0), x0, y2)) → FILTER(nats(activate(y0)), x0, activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X3)
ACTIVATE(n__sieve(X)) → ACTIVATE(X)
ACTIVATE(n__sieve(x0)) → SIEVE(x0)
ACTIVATE(n__filter(n__filter(x0, x1, x2), y1, y2)) → FILTER(filter(activate(x0), activate(x1), activate(x2)), activate(y1), activate(y2))
SIEVE(cons(s(N), Y)) → ACTIVATE(Y)
ACTIVATE(n__filter(y0, x0, y2)) → FILTER(y0, x0, activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X2)
ACTIVATE(n__filter(y0, n__s(x0), y2)) → FILTER(y0, s(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__sieve(x0), y1, y2)) → FILTER(sieve(activate(x0)), activate(y1), activate(y2))
ACTIVATE(n__filter(n__nats(y0), n__sieve(x0), y2)) → FILTER(nats(activate(y0)), sieve(activate(x0)), activate(y2))
ACTIVATE(n__sieve(n__sieve(x0))) → SIEVE(sieve(activate(x0)))
ACTIVATE(n__nats(X)) → ACTIVATE(X)
ACTIVATE(n__filter(y0, n__nats(x0), y2)) → FILTER(y0, nats(activate(x0)), activate(y2))
ACTIVATE(n__sieve(n__nats(x0))) → SIEVE(nats(activate(x0)))

The TRS R consists of the following rules:

filter(cons(X, Y), 0, M) → cons(0, n__filter(activate(Y), M, M))
filter(cons(X, Y), s(N), M) → cons(X, n__filter(activate(Y), N, M))
sieve(cons(0, Y)) → cons(0, n__sieve(activate(Y)))
sieve(cons(s(N), Y)) → cons(s(N), n__sieve(n__filter(activate(Y), N, N)))
nats(N) → cons(N, n__nats(n__s(N)))
zprimes → sieve(nats(s(s(0))))
filter(X1, X2, X3) → n__filter(X1, X2, X3)
sieve(X) → n__sieve(X)
nats(X) → n__nats(X)
s(X) → n__s(X)
activate(n__filter(X1, X2, X3)) → filter(activate(X1), activate(X2), activate(X3))
activate(n__sieve(X)) → sieve(activate(X))
activate(n__nats(X)) → nats(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule ACTIVATE(n__filter(n__s(x0), y1, y2)) → FILTER(s(activate(x0)), activate(y1), activate(y2)) at position [1] we obtained the following new rules:

ACTIVATE(n__filter(n__s(y0), n__s(x0), y2)) → FILTER(s(activate(y0)), s(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__s(y0), x0, y2)) → FILTER(s(activate(y0)), x0, activate(y2))
ACTIVATE(n__filter(n__s(y0), n__nats(x0), y2)) → FILTER(s(activate(y0)), nats(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__s(y0), n__filter(x0, x1, x2), y2)) → FILTER(s(activate(y0)), filter(activate(x0), activate(x1), activate(x2)), activate(y2))
ACTIVATE(n__filter(n__s(y0), n__sieve(x0), y2)) → FILTER(s(activate(y0)), sieve(activate(x0)), activate(y2))

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ Narrowing

                ↳ QDP

                  ↳ Narrowing

                    ↳ QDP

                      ↳ Narrowing

                        ↳ QDP

                          ↳ Narrowing

                            ↳ QDP

                              ↳ Narrowing

Q DP problem:
The TRS P consists of the following rules:

ACTIVATE(n__sieve(n__filter(x0, x1, x2))) → SIEVE(filter(activate(x0), activate(x1), activate(x2)))
ACTIVATE(n__filter(y0, n__sieve(x0), y2)) → FILTER(y0, sieve(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__s(y0), x0, y2)) → FILTER(s(activate(y0)), x0, activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X1)
ACTIVATE(n__s(X)) → ACTIVATE(X)
ACTIVATE(n__sieve(n__s(x0))) → SIEVE(s(activate(x0)))
FILTER(cons(X, Y), 0, M) → ACTIVATE(Y)
ACTIVATE(n__filter(n__nats(y0), n__filter(x0, x1, x2), y2)) → FILTER(nats(activate(y0)), filter(activate(x0), activate(x1), activate(x2)), activate(y2))
FILTER(cons(X, Y), s(N), M) → ACTIVATE(Y)
ACTIVATE(n__filter(y0, n__filter(x0, x1, x2), y2)) → FILTER(y0, filter(activate(x0), activate(x1), activate(x2)), activate(y2))
SIEVE(cons(0, Y)) → ACTIVATE(Y)
ACTIVATE(n__filter(n__nats(y0), n__nats(x0), y2)) → FILTER(nats(activate(y0)), nats(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__s(y0), n__nats(x0), y2)) → FILTER(s(activate(y0)), nats(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__nats(y0), n__s(x0), y2)) → FILTER(nats(activate(y0)), s(activate(x0)), activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X3)
ACTIVATE(n__filter(n__nats(y0), x0, y2)) → FILTER(nats(activate(y0)), x0, activate(y2))
ACTIVATE(n__sieve(x0)) → SIEVE(x0)
ACTIVATE(n__sieve(X)) → ACTIVATE(X)
ACTIVATE(n__filter(n__s(y0), n__s(x0), y2)) → FILTER(s(activate(y0)), s(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__filter(x0, x1, x2), y1, y2)) → FILTER(filter(activate(x0), activate(x1), activate(x2)), activate(y1), activate(y2))
SIEVE(cons(s(N), Y)) → ACTIVATE(Y)
ACTIVATE(n__filter(n__s(y0), n__sieve(x0), y2)) → FILTER(s(activate(y0)), sieve(activate(x0)), activate(y2))
ACTIVATE(n__filter(y0, x0, y2)) → FILTER(y0, x0, activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X2)
ACTIVATE(n__filter(y0, n__s(x0), y2)) → FILTER(y0, s(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__sieve(x0), y1, y2)) → FILTER(sieve(activate(x0)), activate(y1), activate(y2))
ACTIVATE(n__sieve(n__sieve(x0))) → SIEVE(sieve(activate(x0)))
ACTIVATE(n__filter(n__nats(y0), n__sieve(x0), y2)) → FILTER(nats(activate(y0)), sieve(activate(x0)), activate(y2))
ACTIVATE(n__nats(X)) → ACTIVATE(X)
ACTIVATE(n__filter(n__s(y0), n__filter(x0, x1, x2), y2)) → FILTER(s(activate(y0)), filter(activate(x0), activate(x1), activate(x2)), activate(y2))
ACTIVATE(n__filter(y0, n__nats(x0), y2)) → FILTER(y0, nats(activate(x0)), activate(y2))
ACTIVATE(n__sieve(n__nats(x0))) → SIEVE(nats(activate(x0)))

The TRS R consists of the following rules:

filter(cons(X, Y), 0, M) → cons(0, n__filter(activate(Y), M, M))
filter(cons(X, Y), s(N), M) → cons(X, n__filter(activate(Y), N, M))
sieve(cons(0, Y)) → cons(0, n__sieve(activate(Y)))
sieve(cons(s(N), Y)) → cons(s(N), n__sieve(n__filter(activate(Y), N, N)))
nats(N) → cons(N, n__nats(n__s(N)))
zprimes → sieve(nats(s(s(0))))
filter(X1, X2, X3) → n__filter(X1, X2, X3)
sieve(X) → n__sieve(X)
nats(X) → n__nats(X)
s(X) → n__s(X)
activate(n__filter(X1, X2, X3)) → filter(activate(X1), activate(X2), activate(X3))
activate(n__sieve(X)) → sieve(activate(X))
activate(n__nats(X)) → nats(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule ACTIVATE(n__filter(n__filter(x0, x1, x2), y1, y2)) → FILTER(filter(activate(x0), activate(x1), activate(x2)), activate(y1), activate(y2)) at position [1] we obtained the following new rules:

ACTIVATE(n__filter(n__filter(y0, y1, y2), x0, y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), x0, activate(y4))
ACTIVATE(n__filter(n__filter(y0, y1, y2), n__sieve(x0), y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), sieve(activate(x0)), activate(y4))
ACTIVATE(n__filter(n__filter(y0, y1, y2), n__filter(x0, x1, x2), y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), filter(activate(x0), activate(x1), activate(x2)), activate(y4))
ACTIVATE(n__filter(n__filter(y0, y1, y2), n__nats(x0), y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), nats(activate(x0)), activate(y4))
ACTIVATE(n__filter(n__filter(y0, y1, y2), n__s(x0), y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), s(activate(x0)), activate(y4))

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ Narrowing

                ↳ QDP

                  ↳ Narrowing

                    ↳ QDP

                      ↳ Narrowing

                        ↳ QDP

                          ↳ Narrowing

                            ↳ QDP

                              ↳ Narrowing

                                ↳ QDP

                                  ↳ Narrowing

Q DP problem:
The TRS P consists of the following rules:

ACTIVATE(n__filter(n__filter(y0, y1, y2), n__sieve(x0), y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), sieve(activate(x0)), activate(y4))
ACTIVATE(n__sieve(n__filter(x0, x1, x2))) → SIEVE(filter(activate(x0), activate(x1), activate(x2)))
ACTIVATE(n__filter(y0, n__sieve(x0), y2)) → FILTER(y0, sieve(activate(x0)), activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X1)
ACTIVATE(n__filter(n__s(y0), x0, y2)) → FILTER(s(activate(y0)), x0, activate(y2))
ACTIVATE(n__s(X)) → ACTIVATE(X)
ACTIVATE(n__sieve(n__s(x0))) → SIEVE(s(activate(x0)))
FILTER(cons(X, Y), 0, M) → ACTIVATE(Y)
ACTIVATE(n__filter(n__filter(y0, y1, y2), n__nats(x0), y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), nats(activate(x0)), activate(y4))
ACTIVATE(n__filter(n__nats(y0), n__filter(x0, x1, x2), y2)) → FILTER(nats(activate(y0)), filter(activate(x0), activate(x1), activate(x2)), activate(y2))
ACTIVATE(n__filter(y0, n__filter(x0, x1, x2), y2)) → FILTER(y0, filter(activate(x0), activate(x1), activate(x2)), activate(y2))
FILTER(cons(X, Y), s(N), M) → ACTIVATE(Y)
ACTIVATE(n__filter(n__filter(y0, y1, y2), x0, y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), x0, activate(y4))
ACTIVATE(n__filter(n__filter(y0, y1, y2), n__filter(x0, x1, x2), y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), filter(activate(x0), activate(x1), activate(x2)), activate(y4))
ACTIVATE(n__filter(n__nats(y0), n__nats(x0), y2)) → FILTER(nats(activate(y0)), nats(activate(x0)), activate(y2))
SIEVE(cons(0, Y)) → ACTIVATE(Y)
ACTIVATE(n__filter(n__nats(y0), n__s(x0), y2)) → FILTER(nats(activate(y0)), s(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__s(y0), n__nats(x0), y2)) → FILTER(s(activate(y0)), nats(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__nats(y0), x0, y2)) → FILTER(nats(activate(y0)), x0, activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X3)
ACTIVATE(n__sieve(X)) → ACTIVATE(X)
ACTIVATE(n__sieve(x0)) → SIEVE(x0)
ACTIVATE(n__filter(n__s(y0), n__s(x0), y2)) → FILTER(s(activate(y0)), s(activate(x0)), activate(y2))
SIEVE(cons(s(N), Y)) → ACTIVATE(Y)
ACTIVATE(n__filter(y0, x0, y2)) → FILTER(y0, x0, activate(y2))
ACTIVATE(n__filter(n__s(y0), n__sieve(x0), y2)) → FILTER(s(activate(y0)), sieve(activate(x0)), activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X2)
ACTIVATE(n__filter(y0, n__s(x0), y2)) → FILTER(y0, s(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__sieve(x0), y1, y2)) → FILTER(sieve(activate(x0)), activate(y1), activate(y2))
ACTIVATE(n__filter(n__nats(y0), n__sieve(x0), y2)) → FILTER(nats(activate(y0)), sieve(activate(x0)), activate(y2))
ACTIVATE(n__sieve(n__sieve(x0))) → SIEVE(sieve(activate(x0)))
ACTIVATE(n__nats(X)) → ACTIVATE(X)
ACTIVATE(n__filter(n__filter(y0, y1, y2), n__s(x0), y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), s(activate(x0)), activate(y4))
ACTIVATE(n__filter(y0, n__nats(x0), y2)) → FILTER(y0, nats(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__s(y0), n__filter(x0, x1, x2), y2)) → FILTER(s(activate(y0)), filter(activate(x0), activate(x1), activate(x2)), activate(y2))
ACTIVATE(n__sieve(n__nats(x0))) → SIEVE(nats(activate(x0)))

The TRS R consists of the following rules:

filter(cons(X, Y), 0, M) → cons(0, n__filter(activate(Y), M, M))
filter(cons(X, Y), s(N), M) → cons(X, n__filter(activate(Y), N, M))
sieve(cons(0, Y)) → cons(0, n__sieve(activate(Y)))
sieve(cons(s(N), Y)) → cons(s(N), n__sieve(n__filter(activate(Y), N, N)))
nats(N) → cons(N, n__nats(n__s(N)))
zprimes → sieve(nats(s(s(0))))
filter(X1, X2, X3) → n__filter(X1, X2, X3)
sieve(X) → n__sieve(X)
nats(X) → n__nats(X)
s(X) → n__s(X)
activate(n__filter(X1, X2, X3)) → filter(activate(X1), activate(X2), activate(X3))
activate(n__sieve(X)) → sieve(activate(X))
activate(n__nats(X)) → nats(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule ACTIVATE(n__filter(n__sieve(x0), y1, y2)) → FILTER(sieve(activate(x0)), activate(y1), activate(y2)) at position [1] we obtained the following new rules:

ACTIVATE(n__filter(n__sieve(y0), n__nats(x0), y2)) → FILTER(sieve(activate(y0)), nats(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__sieve(y0), n__filter(x0, x1, x2), y2)) → FILTER(sieve(activate(y0)), filter(activate(x0), activate(x1), activate(x2)), activate(y2))
ACTIVATE(n__filter(n__sieve(y0), x0, y2)) → FILTER(sieve(activate(y0)), x0, activate(y2))
ACTIVATE(n__filter(n__sieve(y0), n__sieve(x0), y2)) → FILTER(sieve(activate(y0)), sieve(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__sieve(y0), n__s(x0), y2)) → FILTER(sieve(activate(y0)), s(activate(x0)), activate(y2))

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ Narrowing

                ↳ QDP

                  ↳ Narrowing

                    ↳ QDP

                      ↳ Narrowing

                        ↳ QDP

                          ↳ Narrowing

                            ↳ QDP

                              ↳ Narrowing

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ SemLabProof

                                      ↳ SemLabProof2

Q DP problem:
The TRS P consists of the following rules:

ACTIVATE(n__filter(n__sieve(y0), n__filter(x0, x1, x2), y2)) → FILTER(sieve(activate(y0)), filter(activate(x0), activate(x1), activate(x2)), activate(y2))
ACTIVATE(n__filter(n__filter(y0, y1, y2), n__sieve(x0), y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), sieve(activate(x0)), activate(y4))
ACTIVATE(n__sieve(n__filter(x0, x1, x2))) → SIEVE(filter(activate(x0), activate(x1), activate(x2)))
ACTIVATE(n__filter(y0, n__sieve(x0), y2)) → FILTER(y0, sieve(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__s(y0), x0, y2)) → FILTER(s(activate(y0)), x0, activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X1)
ACTIVATE(n__s(X)) → ACTIVATE(X)
ACTIVATE(n__sieve(n__s(x0))) → SIEVE(s(activate(x0)))
FILTER(cons(X, Y), 0, M) → ACTIVATE(Y)
ACTIVATE(n__filter(n__nats(y0), n__filter(x0, x1, x2), y2)) → FILTER(nats(activate(y0)), filter(activate(x0), activate(x1), activate(x2)), activate(y2))
ACTIVATE(n__filter(n__filter(y0, y1, y2), n__nats(x0), y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), nats(activate(x0)), activate(y4))
FILTER(cons(X, Y), s(N), M) → ACTIVATE(Y)
ACTIVATE(n__filter(y0, n__filter(x0, x1, x2), y2)) → FILTER(y0, filter(activate(x0), activate(x1), activate(x2)), activate(y2))
ACTIVATE(n__filter(n__filter(y0, y1, y2), x0, y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), x0, activate(y4))
ACTIVATE(n__filter(n__filter(y0, y1, y2), n__filter(x0, x1, x2), y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), filter(activate(x0), activate(x1), activate(x2)), activate(y4))
SIEVE(cons(0, Y)) → ACTIVATE(Y)
ACTIVATE(n__filter(n__nats(y0), n__nats(x0), y2)) → FILTER(nats(activate(y0)), nats(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__s(y0), n__nats(x0), y2)) → FILTER(s(activate(y0)), nats(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__nats(y0), n__s(x0), y2)) → FILTER(nats(activate(y0)), s(activate(x0)), activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X3)
ACTIVATE(n__filter(n__nats(y0), x0, y2)) → FILTER(nats(activate(y0)), x0, activate(y2))
ACTIVATE(n__sieve(x0)) → SIEVE(x0)
ACTIVATE(n__sieve(X)) → ACTIVATE(X)
ACTIVATE(n__filter(n__s(y0), n__s(x0), y2)) → FILTER(s(activate(y0)), s(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__sieve(y0), n__sieve(x0), y2)) → FILTER(sieve(activate(y0)), sieve(activate(x0)), activate(y2))
SIEVE(cons(s(N), Y)) → ACTIVATE(Y)
ACTIVATE(n__filter(n__sieve(y0), n__s(x0), y2)) → FILTER(sieve(activate(y0)), s(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__s(y0), n__sieve(x0), y2)) → FILTER(s(activate(y0)), sieve(activate(x0)), activate(y2))
ACTIVATE(n__filter(y0, x0, y2)) → FILTER(y0, x0, activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X2)
ACTIVATE(n__filter(n__sieve(y0), x0, y2)) → FILTER(sieve(activate(y0)), x0, activate(y2))
ACTIVATE(n__filter(y0, n__s(x0), y2)) → FILTER(y0, s(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__sieve(y0), n__nats(x0), y2)) → FILTER(sieve(activate(y0)), nats(activate(x0)), activate(y2))
ACTIVATE(n__sieve(n__sieve(x0))) → SIEVE(sieve(activate(x0)))
ACTIVATE(n__filter(n__nats(y0), n__sieve(x0), y2)) → FILTER(nats(activate(y0)), sieve(activate(x0)), activate(y2))
ACTIVATE(n__nats(X)) → ACTIVATE(X)
ACTIVATE(n__filter(n__s(y0), n__filter(x0, x1, x2), y2)) → FILTER(s(activate(y0)), filter(activate(x0), activate(x1), activate(x2)), activate(y2))
ACTIVATE(n__filter(y0, n__nats(x0), y2)) → FILTER(y0, nats(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__filter(y0, y1, y2), n__s(x0), y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), s(activate(x0)), activate(y4))
ACTIVATE(n__sieve(n__nats(x0))) → SIEVE(nats(activate(x0)))

The TRS R consists of the following rules:

filter(cons(X, Y), 0, M) → cons(0, n__filter(activate(Y), M, M))
filter(cons(X, Y), s(N), M) → cons(X, n__filter(activate(Y), N, M))
sieve(cons(0, Y)) → cons(0, n__sieve(activate(Y)))
sieve(cons(s(N), Y)) → cons(s(N), n__sieve(n__filter(activate(Y), N, N)))
nats(N) → cons(N, n__nats(n__s(N)))
zprimes → sieve(nats(s(s(0))))
filter(X1, X2, X3) → n__filter(X1, X2, X3)
sieve(X) → n__sieve(X)
nats(X) → n__nats(X)
s(X) → n__s(X)
activate(n__filter(X1, X2, X3)) → filter(activate(X1), activate(X2), activate(X3))
activate(n__sieve(X)) → sieve(activate(X))
activate(n__nats(X)) → nats(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We found the following model for the rules of the TRS R. Interpretation over the domain with elements from 0 to 1.SIEVE: 0
FILTER: 0
filter: 0
activate: x₀
n__s: 1
n__filter: 0
0: 0
cons: 0
nats: 0
n__nats: 0
s: 1
n__sieve: 0
ACTIVATE: 0
sieve: 0
zprimes: 0
By semantic labelling [33] we obtain the following labelled TRS:Q DP problem:
The TRS P consists of the following rules:

ACTIVATE.0(n__nats.0(X)) → ACTIVATE.0(X)
ACTIVATE.0(n__sieve.0(n__nats.1(x0))) → SIEVE.0(nats.1(activate.1(x0)))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__sieve.1(x0), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__sieve.0(x0), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(y0, n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.1-0-1(y0, filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), x0, y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__nats.0(y0), n__s.0(x0), y2)) → FILTER.0-1-0(nats.0(activate.0(y0)), s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__nats.1(x0), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(y0, n__s.0(x0), y2)) → FILTER.0-1-0(y0, s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__nats.1(y0), n__s.0(x0), y2)) → FILTER.0-1-0(nats.1(activate.1(y0)), s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__nats.0(y0), n__s.1(x0), y2)) → FILTER.0-1-0(nats.0(activate.0(y0)), s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__sieve.1(y0), n__s.0(x0), y2)) → FILTER.0-1-0(sieve.1(activate.1(y0)), s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__sieve.0(y0), n__s.1(x0), y2)) → FILTER.0-1-0(sieve.0(activate.0(y0)), s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), x0, y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-1(y0, n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.1-0-1(y0, filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-0(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
FILTER.0-1-1(cons.1-0(X, Y), s.0(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__nats.1(X)) → ACTIVATE.1(X)
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__sieve.0(x0), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__sieve.0(n__sieve.0(x0))) → SIEVE.0(sieve.0(activate.0(x0)))
ACTIVATE.0(n__filter.1-0-0(y0, n__nats.1(x0), y2)) → FILTER.1-0-0(y0, nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__sieve.1(y0), n__s.1(x0), y2)) → FILTER.0-1-0(sieve.1(activate.1(y0)), s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__nats.1(y0), x0, y2)) → FILTER.0-1-0(nats.1(activate.1(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(X1, X2, X3)) → ACTIVATE.1(X2)
ACTIVATE.0(n__filter.1-0-1(y0, n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.1-0-1(y0, filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), x0, y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.1-1-1(y0, n__s.1(x0), y2)) → FILTER.1-1-1(y0, s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__nats.1(x0), y2)) → FILTER.0-0-0(y0, nats.1(activate.1(x0)), activate.0(y2))
FILTER.0-1-0(cons.0-1(X, Y), s.1(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-1-1(n__sieve.1(y0), n__s.0(x0), y2)) → FILTER.0-1-1(sieve.1(activate.1(y0)), s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__sieve.0(y0), n__s.1(x0), y2)) → FILTER.0-1-1(sieve.0(activate.0(y0)), s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(y0, x0, y2)) → FILTER.1-0-0(y0, x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(X1, X2, X3)) → ACTIVATE.0(X3)
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-0(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__nats.1(x0), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__nats.0(x0), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(y0, n__s.1(x0), y2)) → FILTER.0-1-1(y0, s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__nats.0(y0), n__s.0(x0), y2)) → FILTER.0-1-1(nats.0(activate.0(y0)), s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), x0, y2)) → FILTER.1-0-0(s.1(activate.1(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-1(X1, X2, X3)) → ACTIVATE.1(X3)
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-0(y0, n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.1-0-0(y0, filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
FILTER.0-1-1(cons.0-1(X, Y), s.0(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__nats.0(x0), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), x0, y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-0(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.1-1-0(y0, n__s.1(x0), y2)) → FILTER.1-1-0(y0, s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
FILTER.0-0-0(cons.0-0(X, Y), 0., M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(y0, n__sieve.0(x0), y2)) → FILTER.1-0-0(y0, sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__sieve.0(n__filter.1-0-1(x0, x1, x2))) → SIEVE.0(filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)))
ACTIVATE.0(n__filter.1-1-1(X1, X2, X3)) → ACTIVATE.1(X1)
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(X1, X2, X3)) → ACTIVATE.0(X2)
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__sieve.1(y0), x0, y2)) → FILTER.0-1-1(sieve.1(activate.1(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), x0, y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__nats.1(x0), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), x0, y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-0(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
FILTER.0-1-1(cons.0-1(X, Y), s.1(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-1-0(n__s.0(y0), n__s.0(x0), y2)) → FILTER.1-1-0(s.0(activate.0(y0)), s.0(activate.0(x0)), activate.0(y2))
FILTER.0-1-0(cons.1-0(X, Y), s.1(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__sieve.0(n__filter.1-1-1(x0, x1, x2))) → SIEVE.0(filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__nats.1(x0), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__nats.0(x0), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__nats.1(x0), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__nats.0(x0), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(X1, X2, X3)) → ACTIVATE.0(X2)
ACTIVATE.0(n__filter.0-1-1(X1, X2, X3)) → ACTIVATE.0(X1)
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-1-1(n__s.0(y0), n__s.0(x0), y2)) → FILTER.1-1-1(s.0(activate.0(y0)), s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(y0, n__sieve.1(x0), y2)) → FILTER.1-0-0(y0, sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__sieve.0(y0), n__s.0(x0), y2)) → FILTER.0-1-0(sieve.0(activate.0(y0)), s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-1(y0, n__sieve.0(x0), y2)) → FILTER.1-0-1(y0, sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.1(n__s.1(X)) → ACTIVATE.1(X)
SIEVE.0(cons.0-0(0., Y)) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-1-0(y0, x0, y2)) → FILTER.1-1-0(y0, x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__sieve.0(y0), n__s.0(x0), y2)) → FILTER.0-1-1(sieve.0(activate.0(y0)), s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-1(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(X1, X2, X3)) → ACTIVATE.1(X3)
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__nats.0(x0), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), nats.0(activate.0(x0)), activate.0(y2))
FILTER.0-1-0(cons.1-0(X, Y), s.0(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__sieve.1(x0), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__nats.1(y0), n__s.1(x0), y2)) → FILTER.0-1-0(nats.1(activate.1(y0)), s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.1-1-0(n__s.1(y0), x0, y2)) → FILTER.1-1-0(s.1(activate.1(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__sieve.0(x0)) → SIEVE.0(x0)
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(y0, x0, y2)) → FILTER.0-1-1(y0, x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-1-0(X1, X2, X3)) → ACTIVATE.1(X2)
ACTIVATE.0(n__filter.1-1-1(y0, n__s.0(x0), y2)) → FILTER.1-1-1(y0, s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.0(y4))
FILTER.0-0-1(cons.0-0(X, Y), 0., M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
FILTER.0-1-1(cons.0-0(X, Y), s.1(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__sieve.1(n__s.1(x0))) → SIEVE.1(s.1(activate.1(x0)))
ACTIVATE.0(n__filter.0-1-0(n__sieve.1(y0), x0, y2)) → FILTER.0-1-0(sieve.1(activate.1(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__sieve.0(n__filter.1-0-0(x0, x1, x2))) → SIEVE.0(filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__sieve.0(x0), y2)) → FILTER.0-0-1(y0, sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(X1, X2, X3)) → ACTIVATE.0(X1)
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-1(y0, n__nats.1(x0), y2)) → FILTER.1-0-1(y0, nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__nats.1(x0), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(y0, n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.1-0-0(y0, filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-1-1(n__s.0(y0), x0, y2)) → FILTER.1-1-1(s.0(activate.0(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__nats.0(x0), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), nats.0(activate.0(x0)), activate.1(y2))
FILTER.0-1-0(cons.1-1(X, Y), s.0(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(y0, n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.1-0-1(y0, filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__sieve.0(n__filter.0-1-1(x0, x1, x2))) → SIEVE.0(filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-1(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), x0, y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), x0, activate.1(y4))
FILTER.0-0-1(cons.1-1(X, Y), 0., M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(y0, n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.1-0-0(y0, filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(X1, X2, X3)) → ACTIVATE.1(X1)
FILTER.0-0-1(cons.0-1(X, Y), 0., M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-0(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), x0, activate.1(y4))
FILTER.0-0-0(cons.0-1(X, Y), 0., M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-1-0(X1, X2, X3)) → ACTIVATE.1(X1)
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__nats.1(x0), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__sieve.1(x0), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(y0, n__s.1(x0), y2)) → FILTER.0-1-0(y0, s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__sieve.1(x0)) → SIEVE.1(x0)
ACTIVATE.0(n__filter.1-0-0(y0, n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.1-0-0(y0, filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(y0, n__nats.1(x0), y2)) → FILTER.0-0-1(y0, nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-0(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), x0, activate.1(y4))
FILTER.0-1-0(cons.0-1(X, Y), s.0(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-0-1(y0, n__nats.0(x0), y2)) → FILTER.1-0-1(y0, nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__sieve.0(x0), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__sieve.0(n__sieve.1(x0))) → SIEVE.0(sieve.1(activate.1(x0)))
FILTER.0-1-1(cons.0-0(X, Y), s.0(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-1(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), x0, y2)) → FILTER.1-0-0(s.0(activate.0(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__sieve.0(x0), y2)) → FILTER.0-0-0(y0, sieve.0(activate.0(x0)), activate.0(y2))
FILTER.0-0-1(cons.1-0(X, Y), 0., M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-1-0(X1, X2, X3)) → ACTIVATE.0(X1)
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__nats.1(x0), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__nats.0(x0), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__sieve.1(x0), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(y0, n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.1-0-0(y0, filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-1(y0, n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.1-0-1(y0, filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
FILTER.0-1-1(cons.1-1(X, Y), s.1(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-1-0(X1, X2, X3)) → ACTIVATE.0(X3)
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__sieve.0(x0), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__sieve.1(x0), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), sieve.1(activate.1(x0)), activate.1(y2))
FILTER.0-1-1(cons.1-1(X, Y), s.0(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__sieve.0(n__nats.0(x0))) → SIEVE.0(nats.0(activate.0(x0)))
SIEVE.0(cons.1-0(s.1(N), Y)) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-1(X1, X2, X3)) → ACTIVATE.0(X1)
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__nats.1(x0), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__sieve.1(x0), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.1(n__s.0(X)) → ACTIVATE.0(X)
ACTIVATE.0(n__filter.0-1-1(n__sieve.0(y0), x0, y2)) → FILTER.0-1-1(sieve.0(activate.0(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__nats.0(x0), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__nats.1(x0), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__sieve.0(x0), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__sieve.1(x0), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.1-1-0(n__s.1(y0), n__s.1(x0), y2)) → FILTER.1-1-0(s.1(activate.1(y0)), s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__sieve.1(n__s.0(x0))) → SIEVE.1(s.0(activate.0(x0)))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-1-1(n__s.1(y0), x0, y2)) → FILTER.1-1-1(s.1(activate.1(y0)), x0, activate.1(y2))
FILTER.0-1-0(cons.0-0(X, Y), s.1(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__nats.0(y0), x0, y2)) → FILTER.0-1-0(nats.0(activate.0(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.0(y4))
SIEVE.0(cons.1-1(s.1(N), Y)) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-0-0(y0, n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.1-0-0(y0, filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-0(y0, n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.1-0-0(y0, filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(y0, n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.1-0-1(y0, filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-1-1(X1, X2, X3)) → ACTIVATE.1(X2)
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__nats.0(x0), y2)) → FILTER.0-0-0(y0, nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-1(y0, n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.1-0-1(y0, filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__sieve.0(x0), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__nats.0(x0), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__nats.1(x0), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__sieve.0(x0), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__sieve.1(x0), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
FILTER.0-0-0(cons.1-0(X, Y), 0., M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.1-1-1(n__s.1(y0), n__s.0(x0), y2)) → FILTER.1-1-1(s.1(activate.1(y0)), s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-1-1(n__s.0(y0), n__s.1(x0), y2)) → FILTER.1-1-1(s.0(activate.0(y0)), s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-0(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__nats.0(x0), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__sieve.0(x0), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__nats.1(x0), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__sieve.1(X)) → ACTIVATE.1(X)
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
FILTER.0-1-0(cons.0-0(X, Y), s.0(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__sieve.0(n__filter.0-0-1(x0, x1, x2))) → SIEVE.0(filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)))
ACTIVATE.0(n__filter.1-0-1(y0, n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.1-0-1(y0, filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
FILTER.0-1-1(cons.1-0(X, Y), s.1(N), M) → ACTIVATE.0(Y)
SIEVE.0(cons.1-1(s.0(N), Y)) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-0-1(y0, n__sieve.1(x0), y2)) → FILTER.1-0-1(y0, sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(X1, X2, X3)) → ACTIVATE.0(X2)
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(X1, X2, X3)) → ACTIVATE.0(X3)
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.1-1-1(n__s.1(y0), n__s.1(x0), y2)) → FILTER.1-1-1(s.1(activate.1(y0)), s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__sieve.0(x0), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(y0, n__nats.0(x0), y2)) → FILTER.1-0-0(y0, nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__sieve.1(x0), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__nats.0(x0), y2)) → FILTER.0-0-1(y0, nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(y0, n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.1-0-0(y0, filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__sieve.0(n__filter.0-0-0(x0, x1, x2))) → SIEVE.0(filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)))
ACTIVATE.0(n__sieve.0(X)) → ACTIVATE.0(X)
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-1-0(y0, n__s.0(x0), y2)) → FILTER.1-1-0(y0, s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-1(X1, X2, X3)) → ACTIVATE.1(X1)
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(y0, x0, y2)) → FILTER.0-1-0(y0, x0, activate.0(y2))
SIEVE.0(cons.0-1(0., Y)) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__nats.1(y0), x0, y2)) → FILTER.0-1-1(nats.1(activate.1(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
FILTER.0-0-0(cons.1-1(X, Y), 0., M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__sieve.0(x0), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__sieve.1(x0), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-1(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), x0, activate.0(y4))
SIEVE.0(cons.1-0(s.0(N), Y)) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-1-1(n__nats.0(y0), x0, y2)) → FILTER.0-1-1(nats.0(activate.0(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(X1, X2, X3)) → ACTIVATE.0(X3)
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-1(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.1-1-1(y0, x0, y2)) → FILTER.1-1-1(y0, x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__sieve.1(x0), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__sieve.1(x0), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__sieve.0(x0), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-1-0(n__s.0(y0), x0, y2)) → FILTER.1-1-0(s.0(activate.0(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__sieve.1(y0), n__s.1(x0), y2)) → FILTER.0-1-1(sieve.1(activate.1(y0)), s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(y0, n__s.0(x0), y2)) → FILTER.0-1-1(y0, s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(y0, n__sieve.1(x0), y2)) → FILTER.0-0-0(y0, sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__nats.1(y0), n__s.1(x0), y2)) → FILTER.0-1-1(nats.1(activate.1(y0)), s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), x0, activate.0(y4))
FILTER.0-1-0(cons.1-1(X, Y), s.1(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-1-0(n__s.1(y0), n__s.0(x0), y2)) → FILTER.1-1-0(s.1(activate.1(y0)), s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-1-0(n__s.0(y0), n__s.1(x0), y2)) → FILTER.1-1-0(s.0(activate.0(y0)), s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(y0, x0, y2)) → FILTER.0-0-1(y0, x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__nats.0(x0), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__sieve.1(x0), y2)) → FILTER.0-0-1(y0, sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-0(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-1(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), x0, y2)) → FILTER.1-0-1(s.0(activate.0(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), x0, y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(y0, x0, y2)) → FILTER.1-0-1(y0, x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(X1, X2, X3)) → ACTIVATE.1(X3)
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(X1, X2, X3)) → ACTIVATE.0(X2)
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-1(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.1-1-1(X1, X2, X3)) → ACTIVATE.1(X3)
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-1(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(y0, x0, y2)) → FILTER.0-0-0(y0, x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-0(n__sieve.0(y0), x0, y2)) → FILTER.0-1-0(sieve.0(activate.0(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__sieve.0(n__filter.0-1-0(x0, x1, x2))) → SIEVE.0(filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__nats.1(y0), n__s.0(x0), y2)) → FILTER.0-1-1(nats.1(activate.1(y0)), s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__nats.0(y0), n__s.1(x0), y2)) → FILTER.0-1-1(nats.0(activate.0(y0)), s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), x0, y2)) → FILTER.1-0-1(s.1(activate.1(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__sieve.0(n__filter.1-1-0(x0, x1, x2))) → SIEVE.0(filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(X1, X2, X3)) → ACTIVATE.1(X2)
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__nats.0(x0), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__sieve.0(x0), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), sieve.0(activate.0(x0)), activate.1(y2))

The TRS R consists of the following rules:

filter.0-0-0(X1, X2, X3) → n__filter.0-0-0(X1, X2, X3)
filter.0-1-1(cons.0-1(X, Y), s.1(N), M) → cons.0-0(X, n__filter.1-1-1(activate.1(Y), N, M))
filter.0-0-0(cons.1-0(X, Y), 0., M) → cons.0-0(0., n__filter.0-0-0(activate.0(Y), M, M))
sieve.0(cons.0-1(0., Y)) → cons.0-0(0., n__sieve.1(activate.1(Y)))
filter.0-0-1(cons.1-1(X, Y), 0., M) → cons.0-0(0., n__filter.1-1-1(activate.1(Y), M, M))
nats.1(X) → n__nats.1(X)
filter.1-1-1(X1, X2, X3) → n__filter.1-1-1(X1, X2, X3)
filter.0-1-0(cons.0-0(X, Y), s.1(N), M) → cons.0-0(X, n__filter.0-1-0(activate.0(Y), N, M))
filter.0-1-0(cons.1-0(X, Y), s.0(N), M) → cons.1-0(X, n__filter.0-0-0(activate.0(Y), N, M))
s.1(X) → n__s.1(X)
activate.0(n__filter.0-1-1(X1, X2, X3)) → filter.0-1-1(activate.0(X1), activate.1(X2), activate.1(X3))
activate.0(n__filter.1-0-1(X1, X2, X3)) → filter.1-0-1(activate.1(X1), activate.0(X2), activate.1(X3))
nats.1(N) → cons.1-0(N, n__nats.1(n__s.1(N)))
filter.1-0-1(X1, X2, X3) → n__filter.1-0-1(X1, X2, X3)
activate.0(n__filter.1-1-0(X1, X2, X3)) → filter.1-1-0(activate.1(X1), activate.1(X2), activate.0(X3))
filter.0-1-1(cons.0-0(X, Y), s.1(N), M) → cons.0-0(X, n__filter.0-1-1(activate.0(Y), N, M))
activate.0(X) → X
filter.0-1-1(cons.0-0(X, Y), s.0(N), M) → cons.0-0(X, n__filter.0-0-1(activate.0(Y), N, M))
filter.0-1-0(cons.1-0(X, Y), s.1(N), M) → cons.1-0(X, n__filter.0-1-0(activate.0(Y), N, M))
filter.1-0-0(X1, X2, X3) → n__filter.1-0-0(X1, X2, X3)
activate.0(n__filter.0-0-0(X1, X2, X3)) → filter.0-0-0(activate.0(X1), activate.0(X2), activate.0(X3))
activate.1(n__s.1(X)) → s.1(activate.1(X))
activate.1(n__s.0(X)) → s.0(activate.0(X))
activate.1(X) → X
filter.0-0-0(cons.0-1(X, Y), 0., M) → cons.0-0(0., n__filter.1-0-0(activate.1(Y), M, M))
filter.0-1-0(cons.0-1(X, Y), s.1(N), M) → cons.0-0(X, n__filter.1-1-0(activate.1(Y), N, M))
sieve.0(X) → n__sieve.0(X)
nats.0(N) → cons.0-0(N, n__nats.1(n__s.0(N)))
filter.0-0-1(cons.1-0(X, Y), 0., M) → cons.0-0(0., n__filter.0-1-1(activate.0(Y), M, M))
activate.0(n__nats.0(X)) → nats.0(activate.0(X))
filter.0-1-0(cons.0-0(X, Y), s.0(N), M) → cons.0-0(X, n__filter.0-0-0(activate.0(Y), N, M))
activate.0(n__nats.1(X)) → nats.1(activate.1(X))
filter.0-1-1(cons.1-0(X, Y), s.0(N), M) → cons.1-0(X, n__filter.0-0-1(activate.0(Y), N, M))
s.0(X) → n__s.0(X)
filter.0-1-1(cons.1-1(X, Y), s.1(N), M) → cons.1-0(X, n__filter.1-1-1(activate.1(Y), N, M))
zprimes. → sieve.0(nats.1(s.1(s.0(0.))))
filter.0-1-0(cons.0-1(X, Y), s.0(N), M) → cons.0-0(X, n__filter.1-0-0(activate.1(Y), N, M))
sieve.0(cons.1-1(s.1(N), Y)) → cons.1-0(s.1(N), n__sieve.0(n__filter.1-1-1(activate.1(Y), N, N)))
filter.0-0-0(cons.1-1(X, Y), 0., M) → cons.0-0(0., n__filter.1-0-0(activate.1(Y), M, M))
filter.0-0-1(cons.0-1(X, Y), 0., M) → cons.0-0(0., n__filter.1-1-1(activate.1(Y), M, M))
activate.0(n__filter.1-0-0(X1, X2, X3)) → filter.1-0-0(activate.1(X1), activate.0(X2), activate.0(X3))
sieve.1(X) → n__sieve.1(X)
activate.0(n__sieve.0(X)) → sieve.0(activate.0(X))
filter.0-1-1(cons.0-1(X, Y), s.0(N), M) → cons.0-0(X, n__filter.1-0-1(activate.1(Y), N, M))
filter.1-1-0(X1, X2, X3) → n__filter.1-1-0(X1, X2, X3)
activate.0(n__sieve.1(X)) → sieve.1(activate.1(X))
filter.0-0-1(X1, X2, X3) → n__filter.0-0-1(X1, X2, X3)
filter.0-0-1(cons.0-0(X, Y), 0., M) → cons.0-0(0., n__filter.0-1-1(activate.0(Y), M, M))
activate.0(n__filter.0-1-0(X1, X2, X3)) → filter.0-1-0(activate.0(X1), activate.1(X2), activate.0(X3))
filter.0-1-1(X1, X2, X3) → n__filter.0-1-1(X1, X2, X3)
activate.0(n__filter.0-0-1(X1, X2, X3)) → filter.0-0-1(activate.0(X1), activate.0(X2), activate.1(X3))
filter.0-1-0(cons.1-1(X, Y), s.1(N), M) → cons.1-0(X, n__filter.1-1-0(activate.1(Y), N, M))
nats.0(X) → n__nats.0(X)
filter.0-1-0(X1, X2, X3) → n__filter.0-1-0(X1, X2, X3)
sieve.0(cons.1-0(s.0(N), Y)) → cons.1-0(s.0(N), n__sieve.0(n__filter.0-0-0(activate.0(Y), N, N)))
activate.0(n__filter.1-1-1(X1, X2, X3)) → filter.1-1-1(activate.1(X1), activate.1(X2), activate.1(X3))
sieve.0(cons.0-0(0., Y)) → cons.0-0(0., n__sieve.0(activate.0(Y)))
filter.0-1-0(cons.1-1(X, Y), s.0(N), M) → cons.1-0(X, n__filter.1-0-0(activate.1(Y), N, M))
sieve.0(cons.1-1(s.0(N), Y)) → cons.1-0(s.0(N), n__sieve.0(n__filter.1-0-0(activate.1(Y), N, N)))
filter.0-0-0(cons.0-0(X, Y), 0., M) → cons.0-0(0., n__filter.0-0-0(activate.0(Y), M, M))
filter.0-1-1(cons.1-0(X, Y), s.1(N), M) → cons.1-0(X, n__filter.0-1-1(activate.0(Y), N, M))
filter.0-1-1(cons.1-1(X, Y), s.0(N), M) → cons.1-0(X, n__filter.1-0-1(activate.1(Y), N, M))
sieve.0(cons.1-0(s.1(N), Y)) → cons.1-0(s.1(N), n__sieve.0(n__filter.0-1-1(activate.0(Y), N, N)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ Narrowing

                ↳ QDP

                  ↳ Narrowing

                    ↳ QDP

                      ↳ Narrowing

                        ↳ QDP

                          ↳ Narrowing

                            ↳ QDP

                              ↳ Narrowing

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ SemLabProof

                                        ↳ QDP

                                          ↳ DependencyGraphProof

                                      ↳ SemLabProof2

Q DP problem:
The TRS P consists of the following rules:

ACTIVATE.0(n__nats.0(X)) → ACTIVATE.0(X)
ACTIVATE.0(n__sieve.0(n__nats.1(x0))) → SIEVE.0(nats.1(activate.1(x0)))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__sieve.1(x0), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__sieve.0(x0), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(y0, n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.1-0-1(y0, filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), x0, y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__nats.0(y0), n__s.0(x0), y2)) → FILTER.0-1-0(nats.0(activate.0(y0)), s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__nats.1(x0), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(y0, n__s.0(x0), y2)) → FILTER.0-1-0(y0, s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__nats.1(y0), n__s.0(x0), y2)) → FILTER.0-1-0(nats.1(activate.1(y0)), s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__nats.0(y0), n__s.1(x0), y2)) → FILTER.0-1-0(nats.0(activate.0(y0)), s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__sieve.1(y0), n__s.0(x0), y2)) → FILTER.0-1-0(sieve.1(activate.1(y0)), s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__sieve.0(y0), n__s.1(x0), y2)) → FILTER.0-1-0(sieve.0(activate.0(y0)), s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), x0, y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-1(y0, n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.1-0-1(y0, filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-0(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
FILTER.0-1-1(cons.1-0(X, Y), s.0(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__nats.1(X)) → ACTIVATE.1(X)
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__sieve.0(x0), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__sieve.0(n__sieve.0(x0))) → SIEVE.0(sieve.0(activate.0(x0)))
ACTIVATE.0(n__filter.1-0-0(y0, n__nats.1(x0), y2)) → FILTER.1-0-0(y0, nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__sieve.1(y0), n__s.1(x0), y2)) → FILTER.0-1-0(sieve.1(activate.1(y0)), s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__nats.1(y0), x0, y2)) → FILTER.0-1-0(nats.1(activate.1(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(X1, X2, X3)) → ACTIVATE.1(X2)
ACTIVATE.0(n__filter.1-0-1(y0, n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.1-0-1(y0, filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), x0, y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.1-1-1(y0, n__s.1(x0), y2)) → FILTER.1-1-1(y0, s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__nats.1(x0), y2)) → FILTER.0-0-0(y0, nats.1(activate.1(x0)), activate.0(y2))
FILTER.0-1-0(cons.0-1(X, Y), s.1(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-1-1(n__sieve.1(y0), n__s.0(x0), y2)) → FILTER.0-1-1(sieve.1(activate.1(y0)), s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__sieve.0(y0), n__s.1(x0), y2)) → FILTER.0-1-1(sieve.0(activate.0(y0)), s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(y0, x0, y2)) → FILTER.1-0-0(y0, x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(X1, X2, X3)) → ACTIVATE.0(X3)
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-0(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__nats.1(x0), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__nats.0(x0), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(y0, n__s.1(x0), y2)) → FILTER.0-1-1(y0, s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__nats.0(y0), n__s.0(x0), y2)) → FILTER.0-1-1(nats.0(activate.0(y0)), s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), x0, y2)) → FILTER.1-0-0(s.1(activate.1(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-1(X1, X2, X3)) → ACTIVATE.1(X3)
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-0(y0, n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.1-0-0(y0, filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
FILTER.0-1-1(cons.0-1(X, Y), s.0(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__nats.0(x0), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), x0, y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-0(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.1-1-0(y0, n__s.1(x0), y2)) → FILTER.1-1-0(y0, s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
FILTER.0-0-0(cons.0-0(X, Y), 0., M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(y0, n__sieve.0(x0), y2)) → FILTER.1-0-0(y0, sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__sieve.0(n__filter.1-0-1(x0, x1, x2))) → SIEVE.0(filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)))
ACTIVATE.0(n__filter.1-1-1(X1, X2, X3)) → ACTIVATE.1(X1)
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(X1, X2, X3)) → ACTIVATE.0(X2)
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__sieve.1(y0), x0, y2)) → FILTER.0-1-1(sieve.1(activate.1(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), x0, y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__nats.1(x0), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), x0, y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-0(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
FILTER.0-1-1(cons.0-1(X, Y), s.1(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-1-0(n__s.0(y0), n__s.0(x0), y2)) → FILTER.1-1-0(s.0(activate.0(y0)), s.0(activate.0(x0)), activate.0(y2))
FILTER.0-1-0(cons.1-0(X, Y), s.1(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__sieve.0(n__filter.1-1-1(x0, x1, x2))) → SIEVE.0(filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__nats.1(x0), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__nats.0(x0), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__nats.1(x0), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__nats.0(x0), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(X1, X2, X3)) → ACTIVATE.0(X2)
ACTIVATE.0(n__filter.0-1-1(X1, X2, X3)) → ACTIVATE.0(X1)
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-1-1(n__s.0(y0), n__s.0(x0), y2)) → FILTER.1-1-1(s.0(activate.0(y0)), s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(y0, n__sieve.1(x0), y2)) → FILTER.1-0-0(y0, sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__sieve.0(y0), n__s.0(x0), y2)) → FILTER.0-1-0(sieve.0(activate.0(y0)), s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-1(y0, n__sieve.0(x0), y2)) → FILTER.1-0-1(y0, sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.1(n__s.1(X)) → ACTIVATE.1(X)
SIEVE.0(cons.0-0(0., Y)) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-1-0(y0, x0, y2)) → FILTER.1-1-0(y0, x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__sieve.0(y0), n__s.0(x0), y2)) → FILTER.0-1-1(sieve.0(activate.0(y0)), s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-1(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(X1, X2, X3)) → ACTIVATE.1(X3)
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__nats.0(x0), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), nats.0(activate.0(x0)), activate.0(y2))
FILTER.0-1-0(cons.1-0(X, Y), s.0(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__sieve.1(x0), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__nats.1(y0), n__s.1(x0), y2)) → FILTER.0-1-0(nats.1(activate.1(y0)), s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.1-1-0(n__s.1(y0), x0, y2)) → FILTER.1-1-0(s.1(activate.1(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__sieve.0(x0)) → SIEVE.0(x0)
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(y0, x0, y2)) → FILTER.0-1-1(y0, x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-1-0(X1, X2, X3)) → ACTIVATE.1(X2)
ACTIVATE.0(n__filter.1-1-1(y0, n__s.0(x0), y2)) → FILTER.1-1-1(y0, s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.0(y4))
FILTER.0-0-1(cons.0-0(X, Y), 0., M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
FILTER.0-1-1(cons.0-0(X, Y), s.1(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__sieve.1(n__s.1(x0))) → SIEVE.1(s.1(activate.1(x0)))
ACTIVATE.0(n__filter.0-1-0(n__sieve.1(y0), x0, y2)) → FILTER.0-1-0(sieve.1(activate.1(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__sieve.0(n__filter.1-0-0(x0, x1, x2))) → SIEVE.0(filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__sieve.0(x0), y2)) → FILTER.0-0-1(y0, sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(X1, X2, X3)) → ACTIVATE.0(X1)
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-1(y0, n__nats.1(x0), y2)) → FILTER.1-0-1(y0, nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__nats.1(x0), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(y0, n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.1-0-0(y0, filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-1-1(n__s.0(y0), x0, y2)) → FILTER.1-1-1(s.0(activate.0(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__nats.0(x0), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), nats.0(activate.0(x0)), activate.1(y2))
FILTER.0-1-0(cons.1-1(X, Y), s.0(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(y0, n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.1-0-1(y0, filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__sieve.0(n__filter.0-1-1(x0, x1, x2))) → SIEVE.0(filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-1(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), x0, y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), x0, activate.1(y4))
FILTER.0-0-1(cons.1-1(X, Y), 0., M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(y0, n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.1-0-0(y0, filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(X1, X2, X3)) → ACTIVATE.1(X1)
FILTER.0-0-1(cons.0-1(X, Y), 0., M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-0(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), x0, activate.1(y4))
FILTER.0-0-0(cons.0-1(X, Y), 0., M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-1-0(X1, X2, X3)) → ACTIVATE.1(X1)
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__nats.1(x0), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__sieve.1(x0), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(y0, n__s.1(x0), y2)) → FILTER.0-1-0(y0, s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__sieve.1(x0)) → SIEVE.1(x0)
ACTIVATE.0(n__filter.1-0-0(y0, n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.1-0-0(y0, filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(y0, n__nats.1(x0), y2)) → FILTER.0-0-1(y0, nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-0(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), x0, activate.1(y4))
FILTER.0-1-0(cons.0-1(X, Y), s.0(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-0-1(y0, n__nats.0(x0), y2)) → FILTER.1-0-1(y0, nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__sieve.0(x0), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__sieve.0(n__sieve.1(x0))) → SIEVE.0(sieve.1(activate.1(x0)))
FILTER.0-1-1(cons.0-0(X, Y), s.0(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-1(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), x0, y2)) → FILTER.1-0-0(s.0(activate.0(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__sieve.0(x0), y2)) → FILTER.0-0-0(y0, sieve.0(activate.0(x0)), activate.0(y2))
FILTER.0-0-1(cons.1-0(X, Y), 0., M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-1-0(X1, X2, X3)) → ACTIVATE.0(X1)
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__nats.1(x0), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__nats.0(x0), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__sieve.1(x0), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(y0, n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.1-0-0(y0, filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-1(y0, n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.1-0-1(y0, filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
FILTER.0-1-1(cons.1-1(X, Y), s.1(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-1-0(X1, X2, X3)) → ACTIVATE.0(X3)
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__sieve.0(x0), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__sieve.1(x0), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), sieve.1(activate.1(x0)), activate.1(y2))
FILTER.0-1-1(cons.1-1(X, Y), s.0(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__sieve.0(n__nats.0(x0))) → SIEVE.0(nats.0(activate.0(x0)))
SIEVE.0(cons.1-0(s.1(N), Y)) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-1(X1, X2, X3)) → ACTIVATE.0(X1)
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__nats.1(x0), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__sieve.1(x0), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.1(n__s.0(X)) → ACTIVATE.0(X)
ACTIVATE.0(n__filter.0-1-1(n__sieve.0(y0), x0, y2)) → FILTER.0-1-1(sieve.0(activate.0(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__nats.0(x0), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__nats.1(x0), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__sieve.0(x0), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__sieve.1(x0), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.1-1-0(n__s.1(y0), n__s.1(x0), y2)) → FILTER.1-1-0(s.1(activate.1(y0)), s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__sieve.1(n__s.0(x0))) → SIEVE.1(s.0(activate.0(x0)))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-1-1(n__s.1(y0), x0, y2)) → FILTER.1-1-1(s.1(activate.1(y0)), x0, activate.1(y2))
FILTER.0-1-0(cons.0-0(X, Y), s.1(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__nats.0(y0), x0, y2)) → FILTER.0-1-0(nats.0(activate.0(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.0(y4))
SIEVE.0(cons.1-1(s.1(N), Y)) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-0-0(y0, n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.1-0-0(y0, filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-0(y0, n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.1-0-0(y0, filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(y0, n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.1-0-1(y0, filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-1-1(X1, X2, X3)) → ACTIVATE.1(X2)
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__nats.0(x0), y2)) → FILTER.0-0-0(y0, nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-1(y0, n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.1-0-1(y0, filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__sieve.0(x0), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__nats.0(x0), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__nats.1(x0), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__sieve.0(x0), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__sieve.1(x0), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
FILTER.0-0-0(cons.1-0(X, Y), 0., M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.1-1-1(n__s.1(y0), n__s.0(x0), y2)) → FILTER.1-1-1(s.1(activate.1(y0)), s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-1-1(n__s.0(y0), n__s.1(x0), y2)) → FILTER.1-1-1(s.0(activate.0(y0)), s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-0(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__nats.0(x0), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__sieve.0(x0), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__nats.1(x0), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__sieve.1(X)) → ACTIVATE.1(X)
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
FILTER.0-1-0(cons.0-0(X, Y), s.0(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__sieve.0(n__filter.0-0-1(x0, x1, x2))) → SIEVE.0(filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)))
ACTIVATE.0(n__filter.1-0-1(y0, n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.1-0-1(y0, filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
FILTER.0-1-1(cons.1-0(X, Y), s.1(N), M) → ACTIVATE.0(Y)
SIEVE.0(cons.1-1(s.0(N), Y)) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-0-1(y0, n__sieve.1(x0), y2)) → FILTER.1-0-1(y0, sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(X1, X2, X3)) → ACTIVATE.0(X2)
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(X1, X2, X3)) → ACTIVATE.0(X3)
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.1-1-1(n__s.1(y0), n__s.1(x0), y2)) → FILTER.1-1-1(s.1(activate.1(y0)), s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__sieve.0(x0), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(y0, n__nats.0(x0), y2)) → FILTER.1-0-0(y0, nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__sieve.1(x0), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__nats.0(x0), y2)) → FILTER.0-0-1(y0, nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(y0, n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.1-0-0(y0, filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__sieve.0(n__filter.0-0-0(x0, x1, x2))) → SIEVE.0(filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)))
ACTIVATE.0(n__sieve.0(X)) → ACTIVATE.0(X)
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-1-0(y0, n__s.0(x0), y2)) → FILTER.1-1-0(y0, s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-1(X1, X2, X3)) → ACTIVATE.1(X1)
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(y0, x0, y2)) → FILTER.0-1-0(y0, x0, activate.0(y2))
SIEVE.0(cons.0-1(0., Y)) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__nats.1(y0), x0, y2)) → FILTER.0-1-1(nats.1(activate.1(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
FILTER.0-0-0(cons.1-1(X, Y), 0., M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__sieve.0(x0), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__sieve.1(x0), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-1(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), x0, activate.0(y4))
SIEVE.0(cons.1-0(s.0(N), Y)) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-1-1(n__nats.0(y0), x0, y2)) → FILTER.0-1-1(nats.0(activate.0(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(X1, X2, X3)) → ACTIVATE.0(X3)
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-1(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.1-1-1(y0, x0, y2)) → FILTER.1-1-1(y0, x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__sieve.1(x0), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__sieve.1(x0), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__sieve.0(x0), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-1-0(n__s.0(y0), x0, y2)) → FILTER.1-1-0(s.0(activate.0(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__sieve.1(y0), n__s.1(x0), y2)) → FILTER.0-1-1(sieve.1(activate.1(y0)), s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.1-0-1(s.1(activate.1(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(y0, n__s.0(x0), y2)) → FILTER.0-1-1(y0, s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(y0, n__sieve.1(x0), y2)) → FILTER.0-0-0(y0, sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__nats.1(y0), n__s.1(x0), y2)) → FILTER.0-1-1(nats.1(activate.1(y0)), s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), x0, activate.0(y4))
FILTER.0-1-0(cons.1-1(X, Y), s.1(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-1-0(n__s.1(y0), n__s.0(x0), y2)) → FILTER.1-1-0(s.1(activate.1(y0)), s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.1-1-0(n__s.0(y0), n__s.1(x0), y2)) → FILTER.1-1-0(s.0(activate.0(y0)), s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(y0, x0, y2)) → FILTER.0-0-1(y0, x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(n__s.0(y0), n__nats.0(x0), y2)) → FILTER.1-0-0(s.0(activate.0(y0)), nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__sieve.1(x0), y2)) → FILTER.0-0-1(y0, sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-0(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-1(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), x0, y2)) → FILTER.1-0-1(s.0(activate.0(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), x0, y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(y0, x0, y2)) → FILTER.1-0-1(y0, x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(X1, X2, X3)) → ACTIVATE.1(X3)
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(X1, X2, X3)) → ACTIVATE.0(X2)
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-1(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.1-1-1(X1, X2, X3)) → ACTIVATE.1(X3)
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-1(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(y0, x0, y2)) → FILTER.0-0-0(y0, x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-0(n__sieve.0(y0), x0, y2)) → FILTER.0-1-0(sieve.0(activate.0(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__sieve.0(n__filter.0-1-0(x0, x1, x2))) → SIEVE.0(filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(n__s.1(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.1-0-0(s.1(activate.1(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__nats.1(y0), n__s.0(x0), y2)) → FILTER.0-1-1(nats.1(activate.1(y0)), s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__nats.0(y0), n__s.1(x0), y2)) → FILTER.0-1-1(nats.0(activate.0(y0)), s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-1(n__s.1(y0), x0, y2)) → FILTER.1-0-1(s.1(activate.1(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-1(n__s.0(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.1-0-1(s.0(activate.0(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__sieve.0(n__filter.1-1-0(x0, x1, x2))) → SIEVE.0(filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(X1, X2, X3)) → ACTIVATE.1(X2)
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__nats.0(x0), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__sieve.0(x0), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), sieve.0(activate.0(x0)), activate.1(y2))

The TRS R consists of the following rules:

filter.0-0-0(X1, X2, X3) → n__filter.0-0-0(X1, X2, X3)
filter.0-1-1(cons.0-1(X, Y), s.1(N), M) → cons.0-0(X, n__filter.1-1-1(activate.1(Y), N, M))
filter.0-0-0(cons.1-0(X, Y), 0., M) → cons.0-0(0., n__filter.0-0-0(activate.0(Y), M, M))
sieve.0(cons.0-1(0., Y)) → cons.0-0(0., n__sieve.1(activate.1(Y)))
filter.0-0-1(cons.1-1(X, Y), 0., M) → cons.0-0(0., n__filter.1-1-1(activate.1(Y), M, M))
nats.1(X) → n__nats.1(X)
filter.1-1-1(X1, X2, X3) → n__filter.1-1-1(X1, X2, X3)
filter.0-1-0(cons.0-0(X, Y), s.1(N), M) → cons.0-0(X, n__filter.0-1-0(activate.0(Y), N, M))
filter.0-1-0(cons.1-0(X, Y), s.0(N), M) → cons.1-0(X, n__filter.0-0-0(activate.0(Y), N, M))
s.1(X) → n__s.1(X)
activate.0(n__filter.0-1-1(X1, X2, X3)) → filter.0-1-1(activate.0(X1), activate.1(X2), activate.1(X3))
activate.0(n__filter.1-0-1(X1, X2, X3)) → filter.1-0-1(activate.1(X1), activate.0(X2), activate.1(X3))
nats.1(N) → cons.1-0(N, n__nats.1(n__s.1(N)))
filter.1-0-1(X1, X2, X3) → n__filter.1-0-1(X1, X2, X3)
activate.0(n__filter.1-1-0(X1, X2, X3)) → filter.1-1-0(activate.1(X1), activate.1(X2), activate.0(X3))
filter.0-1-1(cons.0-0(X, Y), s.1(N), M) → cons.0-0(X, n__filter.0-1-1(activate.0(Y), N, M))
activate.0(X) → X
filter.0-1-1(cons.0-0(X, Y), s.0(N), M) → cons.0-0(X, n__filter.0-0-1(activate.0(Y), N, M))
filter.0-1-0(cons.1-0(X, Y), s.1(N), M) → cons.1-0(X, n__filter.0-1-0(activate.0(Y), N, M))
filter.1-0-0(X1, X2, X3) → n__filter.1-0-0(X1, X2, X3)
activate.0(n__filter.0-0-0(X1, X2, X3)) → filter.0-0-0(activate.0(X1), activate.0(X2), activate.0(X3))
activate.1(n__s.1(X)) → s.1(activate.1(X))
activate.1(n__s.0(X)) → s.0(activate.0(X))
activate.1(X) → X
filter.0-0-0(cons.0-1(X, Y), 0., M) → cons.0-0(0., n__filter.1-0-0(activate.1(Y), M, M))
filter.0-1-0(cons.0-1(X, Y), s.1(N), M) → cons.0-0(X, n__filter.1-1-0(activate.1(Y), N, M))
sieve.0(X) → n__sieve.0(X)
nats.0(N) → cons.0-0(N, n__nats.1(n__s.0(N)))
filter.0-0-1(cons.1-0(X, Y), 0., M) → cons.0-0(0., n__filter.0-1-1(activate.0(Y), M, M))
activate.0(n__nats.0(X)) → nats.0(activate.0(X))
filter.0-1-0(cons.0-0(X, Y), s.0(N), M) → cons.0-0(X, n__filter.0-0-0(activate.0(Y), N, M))
activate.0(n__nats.1(X)) → nats.1(activate.1(X))
filter.0-1-1(cons.1-0(X, Y), s.0(N), M) → cons.1-0(X, n__filter.0-0-1(activate.0(Y), N, M))
s.0(X) → n__s.0(X)
filter.0-1-1(cons.1-1(X, Y), s.1(N), M) → cons.1-0(X, n__filter.1-1-1(activate.1(Y), N, M))
zprimes. → sieve.0(nats.1(s.1(s.0(0.))))
filter.0-1-0(cons.0-1(X, Y), s.0(N), M) → cons.0-0(X, n__filter.1-0-0(activate.1(Y), N, M))
sieve.0(cons.1-1(s.1(N), Y)) → cons.1-0(s.1(N), n__sieve.0(n__filter.1-1-1(activate.1(Y), N, N)))
filter.0-0-0(cons.1-1(X, Y), 0., M) → cons.0-0(0., n__filter.1-0-0(activate.1(Y), M, M))
filter.0-0-1(cons.0-1(X, Y), 0., M) → cons.0-0(0., n__filter.1-1-1(activate.1(Y), M, M))
activate.0(n__filter.1-0-0(X1, X2, X3)) → filter.1-0-0(activate.1(X1), activate.0(X2), activate.0(X3))
sieve.1(X) → n__sieve.1(X)
activate.0(n__sieve.0(X)) → sieve.0(activate.0(X))
filter.0-1-1(cons.0-1(X, Y), s.0(N), M) → cons.0-0(X, n__filter.1-0-1(activate.1(Y), N, M))
filter.1-1-0(X1, X2, X3) → n__filter.1-1-0(X1, X2, X3)
activate.0(n__sieve.1(X)) → sieve.1(activate.1(X))
filter.0-0-1(X1, X2, X3) → n__filter.0-0-1(X1, X2, X3)
filter.0-0-1(cons.0-0(X, Y), 0., M) → cons.0-0(0., n__filter.0-1-1(activate.0(Y), M, M))
activate.0(n__filter.0-1-0(X1, X2, X3)) → filter.0-1-0(activate.0(X1), activate.1(X2), activate.0(X3))
filter.0-1-1(X1, X2, X3) → n__filter.0-1-1(X1, X2, X3)
activate.0(n__filter.0-0-1(X1, X2, X3)) → filter.0-0-1(activate.0(X1), activate.0(X2), activate.1(X3))
filter.0-1-0(cons.1-1(X, Y), s.1(N), M) → cons.1-0(X, n__filter.1-1-0(activate.1(Y), N, M))
nats.0(X) → n__nats.0(X)
filter.0-1-0(X1, X2, X3) → n__filter.0-1-0(X1, X2, X3)
sieve.0(cons.1-0(s.0(N), Y)) → cons.1-0(s.0(N), n__sieve.0(n__filter.0-0-0(activate.0(Y), N, N)))
activate.0(n__filter.1-1-1(X1, X2, X3)) → filter.1-1-1(activate.1(X1), activate.1(X2), activate.1(X3))
sieve.0(cons.0-0(0., Y)) → cons.0-0(0., n__sieve.0(activate.0(Y)))
filter.0-1-0(cons.1-1(X, Y), s.0(N), M) → cons.1-0(X, n__filter.1-0-0(activate.1(Y), N, M))
sieve.0(cons.1-1(s.0(N), Y)) → cons.1-0(s.0(N), n__sieve.0(n__filter.1-0-0(activate.1(Y), N, N)))
filter.0-0-0(cons.0-0(X, Y), 0., M) → cons.0-0(0., n__filter.0-0-0(activate.0(Y), M, M))
filter.0-1-1(cons.1-0(X, Y), s.1(N), M) → cons.1-0(X, n__filter.0-1-1(activate.0(Y), N, M))
filter.0-1-1(cons.1-1(X, Y), s.0(N), M) → cons.1-0(X, n__filter.1-0-1(activate.1(Y), N, M))
sieve.0(cons.1-0(s.1(N), Y)) → cons.1-0(s.1(N), n__sieve.0(n__filter.0-1-1(activate.0(Y), N, N)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 99 less nodes.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ Narrowing

                ↳ QDP

                  ↳ Narrowing

                    ↳ QDP

                      ↳ Narrowing

                        ↳ QDP

                          ↳ Narrowing

                            ↳ QDP

                              ↳ Narrowing

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ SemLabProof

                                        ↳ QDP

                                          ↳ DependencyGraphProof

                                            ↳ QDP

                                      ↳ SemLabProof2

Q DP problem:
The TRS P consists of the following rules:

ACTIVATE.0(n__sieve.0(n__nats.1(x0))) → SIEVE.0(nats.1(activate.1(x0)))
ACTIVATE.0(n__nats.0(X)) → ACTIVATE.0(X)
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), x0, y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__nats.0(y0), n__s.0(x0), y2)) → FILTER.0-1-0(nats.0(activate.0(y0)), s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__nats.1(x0), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(y0, n__s.0(x0), y2)) → FILTER.0-1-0(y0, s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__nats.1(y0), n__s.0(x0), y2)) → FILTER.0-1-0(nats.1(activate.1(y0)), s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__nats.0(y0), n__s.1(x0), y2)) → FILTER.0-1-0(nats.0(activate.0(y0)), s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__sieve.1(y0), n__s.0(x0), y2)) → FILTER.0-1-0(sieve.1(activate.1(y0)), s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__sieve.0(y0), n__s.1(x0), y2)) → FILTER.0-1-0(sieve.0(activate.0(y0)), s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), x0, y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-0(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.1(y4))
FILTER.0-1-1(cons.1-0(X, Y), s.0(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__nats.1(X)) → ACTIVATE.1(X)
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__sieve.0(n__sieve.0(x0))) → SIEVE.0(sieve.0(activate.0(x0)))
ACTIVATE.0(n__filter.0-1-0(n__sieve.1(y0), n__s.1(x0), y2)) → FILTER.0-1-0(sieve.1(activate.1(y0)), s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__nats.1(y0), x0, y2)) → FILTER.0-1-0(nats.1(activate.1(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(X1, X2, X3)) → ACTIVATE.1(X2)
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), x0, y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(y0, n__nats.1(x0), y2)) → FILTER.0-0-0(y0, nats.1(activate.1(x0)), activate.0(y2))
FILTER.0-1-0(cons.0-1(X, Y), s.1(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-1-1(n__sieve.1(y0), n__s.0(x0), y2)) → FILTER.0-1-1(sieve.1(activate.1(y0)), s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__sieve.0(y0), n__s.1(x0), y2)) → FILTER.0-1-1(sieve.0(activate.0(y0)), s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(X1, X2, X3)) → ACTIVATE.0(X3)
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-0(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__nats.1(x0), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__nats.0(x0), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(y0, n__s.1(x0), y2)) → FILTER.0-1-1(y0, s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__nats.0(y0), n__s.0(x0), y2)) → FILTER.0-1-1(nats.0(activate.0(y0)), s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-1(X1, X2, X3)) → ACTIVATE.1(X3)
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), s.1(activate.1(x0)), activate.0(y4))
FILTER.0-1-1(cons.0-1(X, Y), s.0(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), x0, y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-0(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
FILTER.0-0-0(cons.0-0(X, Y), 0., M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__sieve.0(n__filter.1-0-1(x0, x1, x2))) → SIEVE.0(filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)))
ACTIVATE.0(n__filter.1-1-1(X1, X2, X3)) → ACTIVATE.1(X1)
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(X1, X2, X3)) → ACTIVATE.0(X2)
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__sieve.1(y0), x0, y2)) → FILTER.0-1-1(sieve.1(activate.1(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), x0, y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), x0, y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-0(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
FILTER.0-1-1(cons.0-1(X, Y), s.1(N), M) → ACTIVATE.1(Y)
FILTER.0-1-0(cons.1-0(X, Y), s.1(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__sieve.0(n__filter.1-1-1(x0, x1, x2))) → SIEVE.0(filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__nats.1(x0), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__nats.0(x0), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(X1, X2, X3)) → ACTIVATE.0(X2)
ACTIVATE.0(n__filter.0-1-1(X1, X2, X3)) → ACTIVATE.0(X1)
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__sieve.0(y0), n__s.0(x0), y2)) → FILTER.0-1-0(sieve.0(activate.0(y0)), s.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.1(n__s.1(X)) → ACTIVATE.1(X)
SIEVE.0(cons.0-0(0., Y)) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__sieve.0(y0), n__s.0(x0), y2)) → FILTER.0-1-1(sieve.0(activate.0(y0)), s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-1(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(X1, X2, X3)) → ACTIVATE.1(X3)
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__nats.0(x0), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), nats.0(activate.0(x0)), activate.0(y2))
FILTER.0-1-0(cons.1-0(X, Y), s.0(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__sieve.1(x0), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__nats.1(y0), n__s.1(x0), y2)) → FILTER.0-1-0(nats.1(activate.1(y0)), s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__sieve.0(x0)) → SIEVE.0(x0)
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(y0, x0, y2)) → FILTER.0-1-1(y0, x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-1-0(X1, X2, X3)) → ACTIVATE.1(X2)
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.0(y4))
FILTER.0-0-1(cons.0-0(X, Y), 0., M) → ACTIVATE.0(Y)
FILTER.0-1-1(cons.0-0(X, Y), s.1(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__sieve.1(y0), x0, y2)) → FILTER.0-1-0(sieve.1(activate.1(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__sieve.0(n__filter.1-0-0(x0, x1, x2))) → SIEVE.0(filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__sieve.0(x0), y2)) → FILTER.0-0-1(y0, sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(X1, X2, X3)) → ACTIVATE.0(X1)
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__nats.1(x0), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__nats.0(x0), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), nats.0(activate.0(x0)), activate.1(y2))
FILTER.0-1-0(cons.1-1(X, Y), s.0(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__sieve.0(n__filter.0-1-1(x0, x1, x2))) → SIEVE.0(filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-1(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), x0, y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), x0, activate.1(y4))
FILTER.0-0-1(cons.1-1(X, Y), 0., M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(X1, X2, X3)) → ACTIVATE.1(X1)
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), x0, activate.1(y4))
FILTER.0-0-1(cons.0-1(X, Y), 0., M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-0(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), x0, activate.1(y4))
FILTER.0-0-0(cons.0-1(X, Y), 0., M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-1-0(X1, X2, X3)) → ACTIVATE.1(X1)
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__nats.1(x0), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__sieve.1(x0), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(y0, n__s.1(x0), y2)) → FILTER.0-1-0(y0, s.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-0(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__nats.1(x0), y2)) → FILTER.0-0-1(y0, nats.1(activate.1(x0)), activate.1(y2))
FILTER.0-1-0(cons.0-1(X, Y), s.0(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__sieve.0(x0), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__sieve.0(n__sieve.1(x0))) → SIEVE.0(sieve.1(activate.1(x0)))
FILTER.0-1-1(cons.0-0(X, Y), s.0(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-1(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(y0, n__sieve.0(x0), y2)) → FILTER.0-0-0(y0, sieve.0(activate.0(x0)), activate.0(y2))
FILTER.0-0-1(cons.1-0(X, Y), 0., M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-1-0(X1, X2, X3)) → ACTIVATE.0(X1)
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__sieve.1(x0), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), sieve.1(activate.1(x0)), activate.0(y2))
FILTER.0-1-1(cons.1-1(X, Y), s.1(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.1-1-0(X1, X2, X3)) → ACTIVATE.0(X3)
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__sieve.0(x0), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__sieve.1(x0), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), sieve.1(activate.1(x0)), activate.1(y2))
FILTER.0-1-1(cons.1-1(X, Y), s.0(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__sieve.0(n__nats.0(x0))) → SIEVE.0(nats.0(activate.0(x0)))
SIEVE.0(cons.1-0(s.1(N), Y)) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-1(X1, X2, X3)) → ACTIVATE.0(X1)
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__nats.1(x0), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__sieve.1(x0), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.1(n__s.0(X)) → ACTIVATE.0(X)
ACTIVATE.0(n__filter.0-1-1(n__sieve.0(y0), x0, y2)) → FILTER.0-1-1(sieve.0(activate.0(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__nats.0(x0), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__nats.1(x0), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), nats.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__sieve.0(x0), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__sieve.1(x0), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), s.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
FILTER.0-1-0(cons.0-0(X, Y), s.1(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__nats.0(y0), x0, y2)) → FILTER.0-1-0(nats.0(activate.0(y0)), x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.0(y4))
SIEVE.0(cons.1-1(s.1(N), Y)) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-0-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-1-1(X1, X2, X3)) → ACTIVATE.1(X2)
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(y0, n__nats.0(x0), y2)) → FILTER.0-0-0(y0, nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__nats.0(x0), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__nats.1(x0), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), nats.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__sieve.0(x0), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__sieve.1(x0), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
FILTER.0-0-0(cons.1-0(X, Y), 0., M) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-0(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__nats.0(x0), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), nats.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__sieve.0(x0), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), x0, y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), x0, activate.1(y4))
ACTIVATE.0(n__sieve.1(X)) → ACTIVATE.1(X)
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
FILTER.0-1-0(cons.0-0(X, Y), s.0(N), M) → ACTIVATE.0(Y)
ACTIVATE.0(n__sieve.0(n__filter.0-0-1(x0, x1, x2))) → SIEVE.0(filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)))
FILTER.0-1-1(cons.1-0(X, Y), s.1(N), M) → ACTIVATE.0(Y)
SIEVE.0(cons.1-1(s.0(N), Y)) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-1(X1, X2, X3)) → ACTIVATE.0(X2)
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-0-0(X1, X2, X3)) → ACTIVATE.0(X3)
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-1(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-0(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__sieve.0(x0), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), sieve.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), s.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__nats.0(x0), y2)) → FILTER.0-0-1(y0, nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.0-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__sieve.0(n__filter.0-0-0(x0, x1, x2))) → SIEVE.0(filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)))
ACTIVATE.0(n__sieve.0(X)) → ACTIVATE.0(X)
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.1-0-1(X1, X2, X3)) → ACTIVATE.1(X1)
ACTIVATE.0(n__filter.0-0-0(n__nats.0(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.0(activate.0(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__nats.0(x0), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), nats.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-0(y0, x0, y2)) → FILTER.0-1-0(y0, x0, activate.0(y2))
SIEVE.0(cons.0-1(0., Y)) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__nats.1(y0), x0, y2)) → FILTER.0-1-1(nats.1(activate.1(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
FILTER.0-0-0(cons.1-1(X, Y), 0., M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__sieve.1(y0), n__sieve.0(x0), y2)) → FILTER.0-0-0(sieve.1(activate.1(y0)), sieve.0(activate.0(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__sieve.0(y0), n__sieve.1(x0), y2)) → FILTER.0-0-0(sieve.0(activate.0(y0)), sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-1-1(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__nats.0(y0), x0, y2)) → FILTER.0-1-1(nats.0(activate.0(y0)), x0, activate.1(y2))
SIEVE.0(cons.1-0(s.0(N), Y)) → ACTIVATE.0(Y)
ACTIVATE.0(n__filter.0-1-0(X1, X2, X3)) → ACTIVATE.0(X3)
ACTIVATE.0(n__filter.0-0-0(y0, n__filter.1-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(y0, filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__filter.1-1-1(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__sieve.1(y0), n__s.1(x0), y2)) → FILTER.0-1-1(sieve.1(activate.1(y0)), s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(y0, n__s.0(x0), y2)) → FILTER.0-1-1(y0, s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(y0, n__sieve.1(x0), y2)) → FILTER.0-0-0(y0, sieve.1(activate.1(x0)), activate.0(y2))
ACTIVATE.0(n__filter.0-1-1(n__nats.1(y0), n__s.1(x0), y2)) → FILTER.0-1-1(nats.1(activate.1(y0)), s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-1(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), x0, activate.0(y4))
FILTER.0-1-0(cons.1-1(X, Y), s.1(N), M) → ACTIVATE.1(Y)
ACTIVATE.0(n__filter.0-0-1(y0, x0, y2)) → FILTER.0-0-1(y0, x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.0-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__sieve.1(x0), y2)) → FILTER.0-0-1(y0, sieve.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.0-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-0-1(y0, y1, y2), n__s.1(x0), y4)) → FILTER.0-1-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), s.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.1-0-0(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(n__filter.0-1-1(y0, y1, y2), x0, y4)) → FILTER.0-1-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), x0, activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), x0, y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), x0, activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-1(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(X1, X2, X3)) → ACTIVATE.1(X3)
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.1-0-0(X1, X2, X3)) → ACTIVATE.0(X2)
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-0-1(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.1-1-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-0(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y4))
ACTIVATE.0(n__filter.1-1-1(X1, X2, X3)) → ACTIVATE.1(X3)
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-1(y0, y1, y2), x0, y4)) → FILTER.0-1-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(y0, n__filter.1-1-0(x0, x1, x2), y2)) → FILTER.0-0-1(y0, filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-1-0(y0, y1, y2), x0, y4)) → FILTER.0-0-0(filter.1-1-0(activate.1(y0), activate.1(y1), activate.0(y2)), x0, activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(y0, x0, y2)) → FILTER.0-0-0(y0, x0, activate.0(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__filter.1-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), filter.1-1-1(activate.1(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-1-1(y0, y1, y2), n__filter.1-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__filter.0-1-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-1-1(y0, y1, y2), n__filter.0-0-1(x0, x1, x2), y4)) → FILTER.0-0-1(filter.1-1-1(activate.1(y0), activate.1(y1), activate.1(y2)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-0(n__sieve.0(y0), x0, y2)) → FILTER.0-1-0(sieve.0(activate.0(y0)), x0, activate.0(y2))
ACTIVATE.0(n__sieve.0(n__filter.0-1-0(x0, x1, x2))) → SIEVE.0(filter.0-1-0(activate.0(x0), activate.1(x1), activate.0(x2)))
ACTIVATE.0(n__filter.0-0-0(n__nats.1(y0), n__filter.0-1-1(x0, x1, x2), y2)) → FILTER.0-0-0(nats.1(activate.1(y0)), filter.0-1-1(activate.0(x0), activate.1(x1), activate.1(x2)), activate.0(y2))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-1-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-0(filter.0-1-1(activate.0(y0), activate.1(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__nats.1(y0), n__filter.0-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(nats.1(activate.1(y0)), filter.0-0-1(activate.0(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__filter.0-0-1(y0, y1, y2), n__nats.1(x0), y4)) → FILTER.0-0-1(filter.0-0-1(activate.0(y0), activate.0(y1), activate.1(y2)), nats.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-1-1(n__nats.1(y0), n__s.0(x0), y2)) → FILTER.0-1-1(nats.1(activate.1(y0)), s.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-1(n__nats.0(y0), n__s.1(x0), y2)) → FILTER.0-1-1(nats.0(activate.0(y0)), s.1(activate.1(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-1-0(n__filter.0-1-0(y0, y1, y2), n__s.0(x0), y4)) → FILTER.0-1-0(filter.0-1-0(activate.0(y0), activate.1(y1), activate.0(y2)), s.0(activate.0(x0)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-1(n__sieve.1(y0), n__filter.1-0-0(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.1(activate.1(y0)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__filter.1-0-1(x0, x1, x2), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), filter.1-0-1(activate.1(x0), activate.0(x1), activate.1(x2)), activate.1(y2))
ACTIVATE.0(n__sieve.0(n__filter.1-1-0(x0, x1, x2))) → SIEVE.0(filter.1-1-0(activate.1(x0), activate.1(x1), activate.0(x2)))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-0(y0, y1, y2), n__sieve.1(x0), y4)) → FILTER.0-0-1(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), sieve.1(activate.1(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-1(n__filter.1-0-1(y0, y1, y2), n__sieve.0(x0), y4)) → FILTER.0-0-1(filter.1-0-1(activate.1(y0), activate.0(y1), activate.1(y2)), sieve.0(activate.0(x0)), activate.1(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.0-0-0(y0, y1, y2), n__filter.1-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.0-0-0(activate.0(y0), activate.0(y1), activate.0(y2)), filter.1-0-0(activate.1(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-0-0(n__filter.1-0-0(y0, y1, y2), n__filter.0-0-0(x0, x1, x2), y4)) → FILTER.0-0-0(filter.1-0-0(activate.1(y0), activate.0(y1), activate.0(y2)), filter.0-0-0(activate.0(x0), activate.0(x1), activate.0(x2)), activate.0(y4))
ACTIVATE.0(n__filter.0-1-1(X1, X2, X3)) → ACTIVATE.1(X2)
ACTIVATE.0(n__filter.0-0-1(n__sieve.0(y0), n__nats.0(x0), y2)) → FILTER.0-0-1(sieve.0(activate.0(y0)), nats.0(activate.0(x0)), activate.1(y2))
ACTIVATE.0(n__filter.0-0-1(n__nats.0(y0), n__sieve.0(x0), y2)) → FILTER.0-0-1(nats.0(activate.0(y0)), sieve.0(activate.0(x0)), activate.1(y2))

The TRS R consists of the following rules:

filter.0-0-0(X1, X2, X3) → n__filter.0-0-0(X1, X2, X3)
filter.0-1-1(cons.0-1(X, Y), s.1(N), M) → cons.0-0(X, n__filter.1-1-1(activate.1(Y), N, M))
filter.0-0-0(cons.1-0(X, Y), 0., M) → cons.0-0(0., n__filter.0-0-0(activate.0(Y), M, M))
sieve.0(cons.0-1(0., Y)) → cons.0-0(0., n__sieve.1(activate.1(Y)))
filter.0-0-1(cons.1-1(X, Y), 0., M) → cons.0-0(0., n__filter.1-1-1(activate.1(Y), M, M))
nats.1(X) → n__nats.1(X)
filter.1-1-1(X1, X2, X3) → n__filter.1-1-1(X1, X2, X3)
filter.0-1-0(cons.0-0(X, Y), s.1(N), M) → cons.0-0(X, n__filter.0-1-0(activate.0(Y), N, M))
filter.0-1-0(cons.1-0(X, Y), s.0(N), M) → cons.1-0(X, n__filter.0-0-0(activate.0(Y), N, M))
s.1(X) → n__s.1(X)
activate.0(n__filter.0-1-1(X1, X2, X3)) → filter.0-1-1(activate.0(X1), activate.1(X2), activate.1(X3))
activate.0(n__filter.1-0-1(X1, X2, X3)) → filter.1-0-1(activate.1(X1), activate.0(X2), activate.1(X3))
nats.1(N) → cons.1-0(N, n__nats.1(n__s.1(N)))
filter.1-0-1(X1, X2, X3) → n__filter.1-0-1(X1, X2, X3)
activate.0(n__filter.1-1-0(X1, X2, X3)) → filter.1-1-0(activate.1(X1), activate.1(X2), activate.0(X3))
filter.0-1-1(cons.0-0(X, Y), s.1(N), M) → cons.0-0(X, n__filter.0-1-1(activate.0(Y), N, M))
activate.0(X) → X
filter.0-1-1(cons.0-0(X, Y), s.0(N), M) → cons.0-0(X, n__filter.0-0-1(activate.0(Y), N, M))
filter.0-1-0(cons.1-0(X, Y), s.1(N), M) → cons.1-0(X, n__filter.0-1-0(activate.0(Y), N, M))
filter.1-0-0(X1, X2, X3) → n__filter.1-0-0(X1, X2, X3)
activate.0(n__filter.0-0-0(X1, X2, X3)) → filter.0-0-0(activate.0(X1), activate.0(X2), activate.0(X3))
activate.1(n__s.1(X)) → s.1(activate.1(X))
activate.1(n__s.0(X)) → s.0(activate.0(X))
activate.1(X) → X
filter.0-0-0(cons.0-1(X, Y), 0., M) → cons.0-0(0., n__filter.1-0-0(activate.1(Y), M, M))
filter.0-1-0(cons.0-1(X, Y), s.1(N), M) → cons.0-0(X, n__filter.1-1-0(activate.1(Y), N, M))
sieve.0(X) → n__sieve.0(X)
nats.0(N) → cons.0-0(N, n__nats.1(n__s.0(N)))
filter.0-0-1(cons.1-0(X, Y), 0., M) → cons.0-0(0., n__filter.0-1-1(activate.0(Y), M, M))
activate.0(n__nats.0(X)) → nats.0(activate.0(X))
filter.0-1-0(cons.0-0(X, Y), s.0(N), M) → cons.0-0(X, n__filter.0-0-0(activate.0(Y), N, M))
activate.0(n__nats.1(X)) → nats.1(activate.1(X))
filter.0-1-1(cons.1-0(X, Y), s.0(N), M) → cons.1-0(X, n__filter.0-0-1(activate.0(Y), N, M))
s.0(X) → n__s.0(X)
filter.0-1-1(cons.1-1(X, Y), s.1(N), M) → cons.1-0(X, n__filter.1-1-1(activate.1(Y), N, M))
zprimes. → sieve.0(nats.1(s.1(s.0(0.))))
filter.0-1-0(cons.0-1(X, Y), s.0(N), M) → cons.0-0(X, n__filter.1-0-0(activate.1(Y), N, M))
sieve.0(cons.1-1(s.1(N), Y)) → cons.1-0(s.1(N), n__sieve.0(n__filter.1-1-1(activate.1(Y), N, N)))
filter.0-0-0(cons.1-1(X, Y), 0., M) → cons.0-0(0., n__filter.1-0-0(activate.1(Y), M, M))
filter.0-0-1(cons.0-1(X, Y), 0., M) → cons.0-0(0., n__filter.1-1-1(activate.1(Y), M, M))
activate.0(n__filter.1-0-0(X1, X2, X3)) → filter.1-0-0(activate.1(X1), activate.0(X2), activate.0(X3))
sieve.1(X) → n__sieve.1(X)
activate.0(n__sieve.0(X)) → sieve.0(activate.0(X))
filter.0-1-1(cons.0-1(X, Y), s.0(N), M) → cons.0-0(X, n__filter.1-0-1(activate.1(Y), N, M))
filter.1-1-0(X1, X2, X3) → n__filter.1-1-0(X1, X2, X3)
activate.0(n__sieve.1(X)) → sieve.1(activate.1(X))
filter.0-0-1(X1, X2, X3) → n__filter.0-0-1(X1, X2, X3)
filter.0-0-1(cons.0-0(X, Y), 0., M) → cons.0-0(0., n__filter.0-1-1(activate.0(Y), M, M))
activate.0(n__filter.0-1-0(X1, X2, X3)) → filter.0-1-0(activate.0(X1), activate.1(X2), activate.0(X3))
filter.0-1-1(X1, X2, X3) → n__filter.0-1-1(X1, X2, X3)
activate.0(n__filter.0-0-1(X1, X2, X3)) → filter.0-0-1(activate.0(X1), activate.0(X2), activate.1(X3))
filter.0-1-0(cons.1-1(X, Y), s.1(N), M) → cons.1-0(X, n__filter.1-1-0(activate.1(Y), N, M))
nats.0(X) → n__nats.0(X)
filter.0-1-0(X1, X2, X3) → n__filter.0-1-0(X1, X2, X3)
sieve.0(cons.1-0(s.0(N), Y)) → cons.1-0(s.0(N), n__sieve.0(n__filter.0-0-0(activate.0(Y), N, N)))
activate.0(n__filter.1-1-1(X1, X2, X3)) → filter.1-1-1(activate.1(X1), activate.1(X2), activate.1(X3))
sieve.0(cons.0-0(0., Y)) → cons.0-0(0., n__sieve.0(activate.0(Y)))
filter.0-1-0(cons.1-1(X, Y), s.0(N), M) → cons.1-0(X, n__filter.1-0-0(activate.1(Y), N, M))
sieve.0(cons.1-1(s.0(N), Y)) → cons.1-0(s.0(N), n__sieve.0(n__filter.1-0-0(activate.1(Y), N, N)))
filter.0-0-0(cons.0-0(X, Y), 0., M) → cons.0-0(0., n__filter.0-0-0(activate.0(Y), M, M))
filter.0-1-1(cons.1-0(X, Y), s.1(N), M) → cons.1-0(X, n__filter.0-1-1(activate.0(Y), N, M))
filter.0-1-1(cons.1-1(X, Y), s.0(N), M) → cons.1-0(X, n__filter.1-0-1(activate.1(Y), N, M))
sieve.0(cons.1-0(s.1(N), Y)) → cons.1-0(s.1(N), n__sieve.0(n__filter.0-1-1(activate.0(Y), N, N)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
As can be seen after transforming the QDP problem by semantic labelling [33] and then some rule deleting processors, only certain labelled rules and pairs can be used. Hence, we only have to consider all unlabelled pairs and rules (without the decreasing rules for quasi-models).

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

          ↳ Narrowing

            ↳ QDP

              ↳ Narrowing

                ↳ QDP

                  ↳ Narrowing

                    ↳ QDP

                      ↳ Narrowing

                        ↳ QDP

                          ↳ Narrowing

                            ↳ QDP

                              ↳ Narrowing

                                ↳ QDP

                                  ↳ Narrowing

                                    ↳ QDP

                                      ↳ SemLabProof

                                      ↳ SemLabProof2

                                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

ACTIVATE(n__filter(n__filter(y0, y1, y2), n__sieve(x0), y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), sieve(activate(x0)), activate(y4))
ACTIVATE(n__filter(n__sieve(y0), n__filter(x0, x1, x2), y2)) → FILTER(sieve(activate(y0)), filter(activate(x0), activate(x1), activate(x2)), activate(y2))
ACTIVATE(n__sieve(n__filter(x0, x1, x2))) → SIEVE(filter(activate(x0), activate(x1), activate(x2)))
ACTIVATE(n__filter(y0, n__sieve(x0), y2)) → FILTER(y0, sieve(activate(x0)), activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X1)
ACTIVATE(n__s(X)) → ACTIVATE(X)
FILTER(cons(X, Y), 0, M) → ACTIVATE(Y)
ACTIVATE(n__filter(n__nats(y0), n__filter(x0, x1, x2), y2)) → FILTER(nats(activate(y0)), filter(activate(x0), activate(x1), activate(x2)), activate(y2))
ACTIVATE(n__filter(n__filter(y0, y1, y2), n__nats(x0), y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), nats(activate(x0)), activate(y4))
ACTIVATE(n__filter(y0, n__filter(x0, x1, x2), y2)) → FILTER(y0, filter(activate(x0), activate(x1), activate(x2)), activate(y2))
FILTER(cons(X, Y), s(N), M) → ACTIVATE(Y)
ACTIVATE(n__filter(n__filter(y0, y1, y2), x0, y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), x0, activate(y4))
ACTIVATE(n__filter(n__filter(y0, y1, y2), n__filter(x0, x1, x2), y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), filter(activate(x0), activate(x1), activate(x2)), activate(y4))
SIEVE(cons(0, Y)) → ACTIVATE(Y)
ACTIVATE(n__filter(n__nats(y0), n__nats(x0), y2)) → FILTER(nats(activate(y0)), nats(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__nats(y0), n__s(x0), y2)) → FILTER(nats(activate(y0)), s(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__nats(y0), x0, y2)) → FILTER(nats(activate(y0)), x0, activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X3)
ACTIVATE(n__sieve(X)) → ACTIVATE(X)
ACTIVATE(n__sieve(x0)) → SIEVE(x0)
ACTIVATE(n__filter(n__sieve(y0), n__sieve(x0), y2)) → FILTER(sieve(activate(y0)), sieve(activate(x0)), activate(y2))
SIEVE(cons(s(N), Y)) → ACTIVATE(Y)
ACTIVATE(n__filter(y0, x0, y2)) → FILTER(y0, x0, activate(y2))
ACTIVATE(n__filter(n__sieve(y0), n__s(x0), y2)) → FILTER(sieve(activate(y0)), s(activate(x0)), activate(y2))
ACTIVATE(n__filter(X1, X2, X3)) → ACTIVATE(X2)
ACTIVATE(n__filter(n__sieve(y0), x0, y2)) → FILTER(sieve(activate(y0)), x0, activate(y2))
ACTIVATE(n__filter(y0, n__s(x0), y2)) → FILTER(y0, s(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__nats(y0), n__sieve(x0), y2)) → FILTER(nats(activate(y0)), sieve(activate(x0)), activate(y2))
ACTIVATE(n__filter(n__sieve(y0), n__nats(x0), y2)) → FILTER(sieve(activate(y0)), nats(activate(x0)), activate(y2))
ACTIVATE(n__sieve(n__sieve(x0))) → SIEVE(sieve(activate(x0)))
ACTIVATE(n__nats(X)) → ACTIVATE(X)
ACTIVATE(n__filter(n__filter(y0, y1, y2), n__s(x0), y4)) → FILTER(filter(activate(y0), activate(y1), activate(y2)), s(activate(x0)), activate(y4))
ACTIVATE(n__filter(y0, n__nats(x0), y2)) → FILTER(y0, nats(activate(x0)), activate(y2))
ACTIVATE(n__sieve(n__nats(x0))) → SIEVE(nats(activate(x0)))

The TRS R consists of the following rules:

filter(cons(X, Y), 0, M) → cons(0, n__filter(activate(Y), M, M))
filter(cons(X, Y), s(N), M) → cons(X, n__filter(activate(Y), N, M))
sieve(cons(0, Y)) → cons(0, n__sieve(activate(Y)))
sieve(cons(s(N), Y)) → cons(s(N), n__sieve(n__filter(activate(Y), N, N)))
nats(N) → cons(N, n__nats(n__s(N)))
zprimes → sieve(nats(s(s(0))))
filter(X1, X2, X3) → n__filter(X1, X2, X3)
sieve(X) → n__sieve(X)
nats(X) → n__nats(X)
s(X) → n__s(X)
activate(n__filter(X1, X2, X3)) → filter(activate(X1), activate(X2), activate(X3))
activate(n__sieve(X)) → sieve(activate(X))
activate(n__nats(X)) → nats(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X

Q is empty.
We have to consider all minimal (P,Q,R)-chains.