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(n__s(X)))
after(0, XS) → XS
after(s(N), cons(X, XS)) → after(N, activate(XS))
from(X) → n__from(X)
s(X) → n__s(X)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(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(n__s(X)))
after(0, XS) → XS
after(s(N), cons(X, XS)) → after(N, activate(XS))
from(X) → n__from(X)
s(X) → n__s(X)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(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:
after2 > activate1 > from1 > [cons2, nfrom1, ns1]
after2 > activate1 > s1 > [cons2, nfrom1, ns1]
0 > [cons2, nfrom1, ns1]
Status: from1: [1]
nfrom1: [1]
after2: [1,2]
ns1: [1]
s1: [1]
0: multiset
cons2: [1,2]
activate1: [1]