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

0 QTRS
↳1 QTRS Reverse (⇔, 0 ms)
↳2 QTRS
↳3 NonTerminationProof (⇔, 4700 ms)
↳4 NO

(0) Obligation:

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

a(x1) → b(x1)
a(c(b(x1))) → c(a(b(a(c(x1)))))
b(c(x1)) → 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(x) → b(x)
b(c(a(x))) → c(a(b(a(c(x)))))
c(b(x)) → 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 a a a a → c b b c a a a a a c

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

(4) NO