(0) Obligation:

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

f(a, n__b, X) → f(X, X, X)
ca
cb
bn__b
activate(n__b) → b
activate(X) → X

Q is empty.

(1) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.

(2) Obligation:

Q DP problem:
The TRS P consists of the following rules:

F(a, n__b, X) → F(X, X, X)
CB
ACTIVATE(n__b) → B

The TRS R consists of the following rules:

f(a, n__b, X) → f(X, X, X)
ca
cb
bn__b
activate(n__b) → b
activate(X) → X

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(3) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.

(4) Obligation:

Q DP problem:
The TRS P consists of the following rules:

F(a, n__b, X) → F(X, X, X)

The TRS R consists of the following rules:

f(a, n__b, X) → f(X, X, X)
ca
cb
bn__b
activate(n__b) → b
activate(X) → X

Q is empty.
We have to consider all minimal (P,Q,R)-chains.