Termination w.r.t. Q of the given QTRS could not be shown:

(0) Obligation:

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

f(X, X) → f(a, n__b)
b → a
b → n__b
activate(n__b) → b
activate(X) → X

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Lexicographic Path Order [LPO].
Precedence:

f₂ > [a, n_b]
[b, activate₁] > [a, n_b]

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

b → a
b → n__b
activate(n__b) → b
activate(X) → X

(2) Obligation:

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

f(X, X) → f(a, n__b)

Q is empty.