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

0 QTRS
↳1 NonTerminationProof (⇔, 9479 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO