Termination w.r.t. Q proof of TRS/TRCSREx3_12_Luc96a

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:

from(X) → cons(X, n__from(s(X)))
sel(0, cons(X, Y)) → X
sel(s(X), cons(Y, Z)) → sel(X, activate(Z))
from(X) → n__from(X)
activate(n__from(X)) → from(X)
activate(X) → X

Q is empty.

↳ QTRS

  ↳ DirectTerminationProof

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

from(X) → cons(X, n__from(s(X)))
sel(0, cons(X, Y)) → X
sel(s(X), cons(Y, Z)) → sel(X, activate(Z))
from(X) → n__from(X)
activate(n__from(X)) → from(X)
activate(X) → X

Q is empty.

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

Lexicographic path order with status [19].
Quasi-Precedence:

sel₂ > [from₁, activate_1] > [cons₂, n_{_from₁}, s_1]
0 > [cons₂, n_{_from₁}, s_1]

Status:

sel₂: [1,2]
from₁: [1]
n_{_from₁}: [1]
0: multiset
s₁: [1]
cons₂: [2,1]
activate₁: [1]