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:

zeros → cons(0, n__zeros)
tail(cons(X, XS)) → activate(XS)
zeros → n__zeros
activate(n__zeros) → zeros
activate(X) → X

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Polynomial interpretation [POLO]:

POL(0) = 0   
POL(activate(x₁)) = 2 + x₁   
POL(cons(x₁, x₂)) = x₁ + x₂   
POL(n__zeros) = 0   
POL(tail(x₁)) = 3 + x₁   
POL(zeros) = 1   

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

zeros → cons(0, n__zeros)
tail(cons(X, XS)) → activate(XS)
zeros → n__zeros
activate(n__zeros) → zeros
activate(X) → 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

(5) RisEmptyProof (EQUIVALENT transformation)

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

(6) TRUE