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, activate1] > [cons2, nfrom1, s1]
0 > [cons2, nfrom1, s1]

Status:
sel2: [1,2]
from1: [1]
nfrom1: [1]
0: multiset
s1: [1]
cons2: [2,1]
activate1: [1]