Termination w.r.t. Q of the given QTRS could be proven:

(0) Obligation:

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.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Recursive path order with status [RPO].
Quasi-Precedence:

0 > nil
s₁ > cons₁
from₁ > cons₁

Status:

from₁: [1]
cons₁: [1]
s₁: multiset
first₂: [1,2]
0: multiset
nil: multiset

With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

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

(2) Obligation:

Q restricted rewrite system:
R is empty.
Q is empty.

(3) RisEmptyProof (EQUIVALENT transformation)

The TRS R is empty. Hence, termination is trivially proven.

(4) TRUE