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(h(x)) → f(i(x))
f(i(x)) → a
i(x) → h(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:

h(f(x)) → i(f(x))
i(f(x)) → a'(x)
i(x) → h(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:

i f → i f

i f → i f
by OverlapClosure OC 2

i → h
by original rule (OC 1)

h f → i f
by original rule (OC 1)

(4) NO