(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(f(a)) → f(g(n__f(n__a)))
f(X) → n__f(X)
a → n__a
activate(n__f(X)) → f(activate(X))
activate(n__a) → a
activate(X) → X
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Recursive Path Order [RPO].
Precedence:
[a, activate1] > [f1, nf1] > g1
[a, activate1] > [f1, nf1] > na
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
f(f(a)) → f(g(n__f(n__a)))
a → n__a
activate(n__f(X)) → f(activate(X))
activate(n__a) → a
activate(X) → X
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(X) → n__f(X)
Q is empty.
(3) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Recursive Path Order [RPO].
Precedence:
f1 > nf1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
f(X) → n__f(X)
(4) Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.
(5) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(6) TRUE