Termination w.r.t. Q proof of TRS/TRCSREx9_BLR02

Termination w.r.t. Q of the following Term Rewriting System could be proven:

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

filter(cons(X), 0, M) → cons(0)
filter(cons(X), s(N), M) → cons(X)
sieve(cons(0)) → cons(0)
sieve(cons(s(N))) → cons(s(N))
nats(N) → cons(N)
zprimes → sieve(nats(s(s(0))))

Q is empty.

↳ QTRS

  ↳ DirectTerminationProof

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

filter(cons(X), 0, M) → cons(0)
filter(cons(X), s(N), M) → cons(X)
sieve(cons(0)) → cons(0)
sieve(cons(s(N))) → cons(s(N))
nats(N) → cons(N)
zprimes → sieve(nats(s(s(0))))

Q is empty.

We use [23] with the following order to prove termination.

Recursive path order with status [2].
Precedence:

filter₃ > 0
zprimes > sieve₁ > s₁ > cons₁ > 0
zprimes > nats₁ > cons₁ > 0

Status:

filter₃: multiset
sieve₁: multiset
zprimes: multiset
s₁: multiset
0: multiset
cons₁: multiset
nats₁: multiset