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 with status [LPO].
Quasi-Precedence:

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

Status:

a: []
f₂: [2,1]
b: []
activate₁: [1]
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.