Termination w.r.t. Q proof of TRS/AG01#3.53a.trs

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:

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

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

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

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

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(s(x), y, y) → F(y, x, s(x))

The TRS R consists of the following rules:

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

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(s(x), y, y) → F(y, x, s(x))

The TRS R consists of the following rules:

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

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