Termination w.r.t. Q of the given QTRS could be proven:

(0) Obligation:

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

f(f(X)) → c(n__f(g(n__f(X))))
c(X) → d(activate(X))
h(X) → c(n__d(X))
f(X) → n__f(X)
d(X) → n__d(X)
activate(n__f(X)) → f(X)
activate(n__d(X)) → d(X)
activate(X) → X

Q is empty.

(1) DirectTerminationProof (EQUIVALENT transformation)

We use [DIRECT_TERMINATION] with the following order to prove termination.

Knuth-Bendix order [KBO] with precedence:

n_f1 > n_d1 > h₁ > activate₁ > c₁ > d₁ > f₁ > g₁

and weight map:

f_1=10
c_1=8
n__f_1=5
g_1=1
d_1=2
activate_1=6
h_1=9
n__d_1=1

The variable weight is 1

(2) TRUE