(0) Obligation:

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

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

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Lexicographic Path Order [LPO].
Precedence:
f2 > [a, nb]
[b, activate1] > [a, nb]

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

ba
bn__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.