(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 with status [LPO].
Quasi-Precedence:
f2 > [a, nb]
[b, activate1] > [a, nb]

Status:
f2: [1,2]
a: []
nb: []
b: []
activate1: [1]

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.