Termination w.r.t. Q proof of TRS/TRCSREx1_Luc02b

Termination w.r.t. Q of the following Term Rewriting System could not be shown:

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

a__from(X) → cons(mark(X), from(s(X)))
a__first(0, Z) → nil
a__first(s(X), cons(Y, Z)) → cons(mark(Y), first(X, Z))
a__sel(0, cons(X, Z)) → mark(X)
a__sel(s(X), cons(Y, Z)) → a__sel(mark(X), mark(Z))
mark(from(X)) → a__from(mark(X))
mark(first(X1, X2)) → a__first(mark(X1), mark(X2))
mark(sel(X1, X2)) → a__sel(mark(X1), mark(X2))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))
mark(0) → 0
mark(nil) → nil
a__from(X) → from(X)
a__first(X1, X2) → first(X1, X2)
a__sel(X1, X2) → sel(X1, X2)

Q is empty.

↳ QTRS

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

a__from(X) → cons(mark(X), from(s(X)))
a__first(0, Z) → nil
a__first(s(X), cons(Y, Z)) → cons(mark(Y), first(X, Z))
a__sel(0, cons(X, Z)) → mark(X)
a__sel(s(X), cons(Y, Z)) → a__sel(mark(X), mark(Z))
mark(from(X)) → a__from(mark(X))
mark(first(X1, X2)) → a__first(mark(X1), mark(X2))
mark(sel(X1, X2)) → a__sel(mark(X1), mark(X2))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))
mark(0) → 0
mark(nil) → nil
a__from(X) → from(X)
a__first(X1, X2) → first(X1, X2)
a__sel(X1, X2) → sel(X1, X2)

Q is empty.