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 with status [19].
Quasi-Precedence:
tail1 > activate1 > zeros > cons2
tail1 > activate1 > zeros > 0
tail1 > activate1 > zeros > nzeros

Status:
zeros: multiset
0: multiset
tail1: [1]
cons2: [2,1]
nzeros: multiset
activate1: [1]