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:

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

Q is empty.


QTRS
  ↳ DirectTerminationProof

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

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

Q is empty.

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

Lexicographic Path Order [19].
Precedence:
tail1 > activate1 > zeros > cons2
tail1 > activate1 > zeros > 0
tail1 > activate1 > zeros > nzeros