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

(0) Obligation:

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

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

b a a a a → b a a a a b b
by OverlapClosure OC 3

b a a a a → b a a a c b
by OverlapClosure OC 3

b a a a a → c a a a c b
by OverlapClosure OC 3

b a a a a → c a a a b c c b
by OverlapClosure OC 3

b a a a a → c a a c c c b
by OverlapClosure OC 3

b a a a a → c a a b a a b
by OverlapClosure OC 3

b a a a a → c a c a a b
by OverlapClosure OC 2

b a a a a → c a c a c
by OverlapClosure OC 3

b a a a a → c a c a b c c
by OverlapClosure OC 3

b a a a a → c a c c c c
by OverlapClosure OC 3

b a a a a → c a b a a c
by OverlapClosure OC 3

b a a a a → c c a a c
by OverlapClosure OC 2

b a a → c c c
by original rule (OC 1)

c a a → a a c
by OverlapClosure OC 2

c → a b
by original rule (OC 1)

b a a → a c
by OverlapClosure OC 3

b a a → a b c c
by OverlapClosure OC 3

b a a → c c c
by original rule (OC 1)

c → a b
by original rule (OC 1)

b c →
by original rule (OC 1)

c → a b
by original rule (OC 1)

b a a → c c c
by original rule (OC 1)

c → a b
by original rule (OC 1)

b c →
by original rule (OC 1)

c → a b
by original rule (OC 1)

c → a b
by original rule (OC 1)

b a a → c c c
by original rule (OC 1)

c → a b
by original rule (OC 1)

b c →
by original rule (OC 1)

c → b
by OverlapClosure OC 3

c → a b
by original rule (OC 1)

a →
by original rule (OC 1)

c → a b
by original rule (OC 1)

(4) NO