(0) Obligation:

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

f(n__b, X, n__c) → f(X, c, X)
cb
bn__b
cn__c
activate(n__b) → b
activate(n__c) → c
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(n__b, X, n__c) → F(X, c, X)
F(n__b, X, n__c) → C
CB
ACTIVATE(n__b) → B
ACTIVATE(n__c) → C

The TRS R consists of the following rules:

f(n__b, X, n__c) → f(X, c, X)
cb
bn__b
cn__c
activate(n__b) → b
activate(n__c) → c
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 4 less nodes.

(4) Obligation:

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

F(n__b, X, n__c) → F(X, c, X)

The TRS R consists of the following rules:

f(n__b, X, n__c) → f(X, c, X)
cb
bn__b
cn__c
activate(n__b) → b
activate(n__c) → c
activate(X) → X

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