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(g(x, y), x, z) → f(z, z, z)
g(x, y) → x
g(x, y) → y

Q is empty.


QTRS
  ↳ DependencyPairsProof

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

f(g(x, y), x, z) → f(z, z, z)
g(x, y) → x
g(x, y) → y

Q is empty.

Using Dependency Pairs [1,13] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

F(g(x, y), x, z) → F(z, z, z)

The TRS R consists of the following rules:

f(g(x, y), x, z) → f(z, z, z)
g(x, y) → x
g(x, y) → y

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

↳ QTRS
  ↳ DependencyPairsProof
QDP

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

F(g(x, y), x, z) → F(z, z, z)

The TRS R consists of the following rules:

f(g(x, y), x, z) → f(z, z, z)
g(x, y) → x
g(x, y) → y

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