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

0 QTRS
↳1 QTRS Reverse (⇔, 0 ms)
↳2 QTRS
↳3 NonTerminationProof (⇔, 17.0 s)
↳4 NO

(0) Obligation:

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

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

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

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

(4) NO