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].
Quasi-Precedence:
from1 > [first2, cons1] > [0, nil]

Status:
from1: multiset
first2: multiset
0: multiset
s1: multiset
nil: multiset
cons1: [1]