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

0 QTRS
↳1 NonTerminationProof (⇔, 67 ms)
↳2 NO

(0) Obligation:

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

a(a(a(a(x1)))) → b(a(a(a(x1))))
b(b(x1)) → a(a(b(x1)))

Q is empty.

(1) NonTerminationProof (EQUIVALENT transformation)

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

Found the self-embedding DerivationStructure:
b b b b b → b b b b b a a a b

b b b b b → b b b b b a a a b
by OverlapClosure OC 3
b b b b b → b b b b a a a a b
by OverlapClosure OC 3
b b b b b → b b b a a a a a b
by OverlapClosure OC 2
b b b b → b b b a a a b
by OverlapClosure OC 3
b b b b → b b a a a a b
by OverlapClosure OC 3
b b b b → b a a a a a b
by OverlapClosure OC 2
b b b → b a a a b
by OverlapClosure OC 3
b b b → a a a a b
by OverlapClosure OC 2
b b → a a b
by original rule (OC 1)
b b → a a b
by original rule (OC 1)
a a a a → b a a a
by original rule (OC 1)
b b → a a b
by original rule (OC 1)
a a a a → b a a a
by original rule (OC 1)
a a a a → b a a a
by original rule (OC 1)
b b → a a b
by original rule (OC 1)
a a a a → b a a a
by original rule (OC 1)
a a a a → b a a a
by original rule (OC 1)

(2) NO