Termination w.r.t. Q proof of TRS/TRCSREx4_7_77_Bor03

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:

zeros → cons(0, n__zeros)
tail(cons(X, XS)) → activate(XS)
zeros → n__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:

zeros → cons(0, n__zeros)
tail(cons(X, XS)) → activate(XS)
zeros → n__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 > n_{_zeros}

Status:

trivial