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

c a b b b b b b b b → a b a c a b b b b b b b b c c a c c a a c c a c c a

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

c a b b → a b a c c a
by original rule (OC 1)

c a b b → a b a c c a
by original rule (OC 1)

c a b b → a b a c c a
by original rule (OC 1)

a → b
by original rule (OC 1)

c a b b → a b a c c a
by original rule (OC 1)

a → b
by original rule (OC 1)

a → b
by original rule (OC 1)

c a b b → a b a c c a
by original rule (OC 1)

a → b
by original rule (OC 1)

c a b b → a b a c c a
by original rule (OC 1)

a → b
by original rule (OC 1)

c a b b → a b a c c a
by original rule (OC 1)

a → b
by original rule (OC 1)

c a b b → a b a c c a
by original rule (OC 1)

a → b
by original rule (OC 1)

a → b
by original rule (OC 1)

a → b
by original rule (OC 1)

(4) NO