(0) Obligation:

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.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Recursive path order with status [RPO].
Quasi-Precedence:
[tail1, activate1] > zeros > cons2
[tail1, activate1] > zeros > 0
[tail1, activate1] > zeros > nzeros

Status:
zeros: multiset
cons2: multiset
0: multiset
nzeros: multiset
tail1: multiset
activate1: multiset

With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

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


(2) Obligation:

Q restricted rewrite system:
R is empty.
Q is empty.

(3) RisEmptyProof (EQUIVALENT transformation)

The TRS R is empty. Hence, termination is trivially proven.

(4) TRUE