Termination w.r.t. Q of the given QTRS could be disproven:

(0) Obligation:

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

f(g(a)) → f(s(g(b)))
f(f(x)) → b
g(x) → f(g(x))

Q is empty.

(1) QTRS Reverse (EQUIVALENT transformation)

We applied the QTRS Reverse Processor [REVERSE].

(2) Obligation:

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

a'(g(f(x))) → b'(g(s(f(x))))
f(f(x)) → b'(x)
g(x) → g(f(x))

Q is empty.

(3) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [OPPELT08] to show that the SRS problem is infinite.

Found the self-embedding DerivationStructure:

g → g f

g → g f
by original rule (OC 1)

(4) NO