(0) Obligation:

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

f(f(a)) → c(n__f(g(f(a))))
f(X) → n__f(X)
activate(n__f(X)) → f(X)
activate(X) → X

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Lexicographic path order with status [LPO].
Precedence:
a > f1 > c1
a > f1 > nf1
a > f1 > g1
activate1 > f1 > c1
activate1 > f1 > nf1
activate1 > f1 > g1

Status:
f1: [1]
a: []
c1: [1]
g1: [1]
nf1: [1]
activate1: [1]
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

f(f(a)) → c(n__f(g(f(a))))
f(X) → n__f(X)
activate(n__f(X)) → f(X)
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