NO Termination w.r.t. Q proof of Zantema_15_ex04.ari

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

0 QTRS
↳1 NonTerminationProof (⇒, 956 ms)
↳2 NO

(0) Obligation:

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

a(L(x)) → L(a(x))
R(a(x)) → a(R(x))
a(L(L(x))) → a(L(R(x)))
R(R(a(x))) → L(a(R(a(x))))

Q is empty.

(1) NonTerminationProof (COMPLETE transformation)

We used the non-termination processor [OPPELT08] to show that the SRS problem is infinite.

Found the self-embedding DerivationStructure:
a L R (a)k R a → a L R (a)k+1 R a

a L R (a)k R a → a L R (a)k+1 R a
by Overlap u with l (ol4)
R (a)k R a → L (a)k+1 R a
by Equivalent
R (a)k R a → L (a)k a R a
by Overlapping Derivationstructures
R (a)k R a → (a)k L a R a
by Overlap u with r (ol3)
R (a)k → (a)k R
by Selfoverlapping OC am2
R a → a R
by original rule (OC 1)
R R a → L a R a
by original rule (OC 1)
(a)k L → L (a)k
by Selfoverlapping OC am1
a L → L a
by original rule (OC 1)
a L L → a L R
by original rule (OC 1)

(2) NO