Termination w.r.t. Q of the following Term Rewriting System could not be shown:

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.


QTRS
  ↳ DependencyPairsProof

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.

Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

CB
ACTIVATE(n__b) → B
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.

↳ QTRS
  ↳ DependencyPairsProof
QDP
      ↳ DependencyGraphProof

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

CB
ACTIVATE(n__b) → B
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.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 2 less nodes.

↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ DependencyGraphProof
QDP

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.