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:

h(X) → g(X)
g(a) → f(b)
f(X) → h(a)
a → b

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:

h(x) → g(x)
a'(g(x)) → b'(f(x))
f(x) → a'(h(x))
a'(x) → b'(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:

f → b' f

f → b' f
by OverlapClosure OC 2

f → a' g
by OverlapClosure OC 2

f → a' h
by original rule (OC 1)

h → g
by original rule (OC 1)

a' g → b' f
by original rule (OC 1)

(4) NO