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:

a__zeros → cons(0, zeros)
a__tail(cons(X, XS)) → mark(XS)
mark(zeros) → a__zeros
mark(tail(X)) → a__tail(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(0) → 0
a__zeros → zeros
a__tail(X) → tail(X)

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Lexicographic Path Order [LPO].
Precedence:

[a_tail1, mark₁, tail₁] > a_zeros > cons₂
[a_tail1, mark₁, tail₁] > a_zeros > 0
[a_tail1, mark₁, tail₁] > a_zeros > zeros

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

a__zeros → cons(0, zeros)
a__tail(cons(X, XS)) → mark(XS)
mark(zeros) → a__zeros
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(0) → 0
a__zeros → zeros

(2) Obligation:

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

mark(tail(X)) → a__tail(mark(X))
a__tail(X) → tail(X)

Q is empty.

(3) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Lexicographic Path Order [LPO].
Precedence:

mark₁ > a_tail1 > tail₁

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

mark(tail(X)) → a__tail(mark(X))
a__tail(X) → tail(X)

(4) Obligation:

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

(5) RisEmptyProof (EQUIVALENT transformation)

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

(6) TRUE