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:

c(c(x1)) → b(b(x1))
a(b(x1)) → a(c(b(x1)))
b(a(x1)) → b(b(x1))
b(c(x1)) → c(a(a(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 b b (a)^k c b → a b b (a)^2k+4 c b

a b b (a)^k c b → a b b (a)^2k+4 c b
by Overlap u with l (ol4)

b (a)^k c b → c (a)^2k+2 c b
by Overlapping Derivationstructures

b (a)^k c b → (b)^k c a a c b
by Overlap u with r (ol3)

b (a)^k → (b)^k b
by Selfoverlapping OC am2

b a → b b
by original rule (OC 1)

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

b c → c a a
by original rule (OC 1)

a b → a c b
by original rule (OC 1)

(b)^k c → c (a a)^k
by Selfoverlapping OC am1

b c → c a a
by original rule (OC 1)

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

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

a b → a c b
by original rule (OC 1)

b c → c a a
by original rule (OC 1)

c c → b b
by original rule (OC 1)

(2) NO