Termination w.r.t. Q proof of TRS/TRCSREx6_Luc98

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:

first(0, X) → nil
first(s(X), cons(Y)) → cons(Y)
from(X) → cons(X)

Q is empty.

↳ QTRS

  ↳ DirectTerminationProof

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

first(0, X) → nil
first(s(X), cons(Y)) → cons(Y)
from(X) → cons(X)

Q is empty.

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

Recursive path order with status [2].
Precedence:

first₂ > nil
s₁ > cons₁
from₁ > cons₁

Status:

from₁: multiset
first₂: multiset
0: multiset
s₁: multiset
nil: multiset
cons₁: multiset