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

0 QTRS
↳1 QTRS Reverse (⇔, 0 ms)
↳2 QTRS
↳3 NonTerminationProof (⇔, 5330 ms)
↳4 NO

(0) Obligation:

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

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

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:

b(a(a(a(a(x))))) → a(a(a(a(b(b(a(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:
b a a a a a a a a a a a a a a a a → a a a a b a a a a a a a a a a a a a a a a b b a b b a a b b a b b a a a b b a b b a a b b a b b a

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

(4) NO