NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Trafo_06/hom02-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 486 ms)
↳2 NO

(0) Obligation:

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

Begin(b(b(x))) → Wait(Right1(x))
Begin(b(x)) → Wait(Right2(x))
Begin(b(x)) → Wait(Right3(x))
Begin(c(c(b(b(x))))) → Wait(Right4(x))
Begin(c(b(b(x)))) → Wait(Right5(x))
Begin(b(b(x))) → Wait(Right6(x))
Begin(b(x)) → Wait(Right7(x))
Right1(a(End(x))) → Left(b(b(c(c(c(a(End(x))))))))
Right2(a(b(End(x)))) → Left(b(b(c(c(c(a(End(x))))))))
Right3(b(End(x))) → Left(c(c(c(End(x)))))
Right4(c(End(x))) → Left(a(End(x)))
Right5(c(c(End(x)))) → Left(a(End(x)))
Right6(c(c(c(End(x))))) → Left(a(End(x)))
Right7(c(c(c(b(End(x)))))) → Left(a(End(x)))
Right1(a(x)) → Aa(Right1(x))
Right2(a(x)) → Aa(Right2(x))
Right3(a(x)) → Aa(Right3(x))
Right4(a(x)) → Aa(Right4(x))
Right5(a(x)) → Aa(Right5(x))
Right6(a(x)) → Aa(Right6(x))
Right7(a(x)) → Aa(Right7(x))
Right1(b(x)) → Ab(Right1(x))
Right2(b(x)) → Ab(Right2(x))
Right3(b(x)) → Ab(Right3(x))
Right4(b(x)) → Ab(Right4(x))
Right5(b(x)) → Ab(Right5(x))
Right6(b(x)) → Ab(Right6(x))
Right7(b(x)) → Ab(Right7(x))
Right1(c(x)) → Ac(Right1(x))
Right2(c(x)) → Ac(Right2(x))
Right3(c(x)) → Ac(Right3(x))
Right4(c(x)) → Ac(Right4(x))
Right5(c(x)) → Ac(Right5(x))
Right6(c(x)) → Ac(Right6(x))
Right7(c(x)) → Ac(Right7(x))
Aa(Left(x)) → Left(a(x))
Ab(Left(x)) → Left(b(x))
Ac(Left(x)) → Left(c(x))
Wait(Left(x)) → Begin(x)
a(x) → b(b(x))
a(b(b(x))) → b(b(c(c(c(a(x))))))
b(b(x)) → c(c(c(x)))
c(c(c(b(b(x))))) → 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:
Wait Left b b a End → Wait Left b b a End

Wait Left b b a End → Wait Left b b a End
by OverlapClosure OC 2
Wait Left b b → Wait Right1
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin b b → Wait Right1
by original rule (OC 1)
Right1 a End → Left b b a End
by OverlapClosure OC 3
Right1 a End → Left b b c c c b b End
by OverlapClosure OC 3
Right1 a End → Left b b c c c a End
by original rule (OC 1)
a → b b
by original rule (OC 1)
c c c b b → a
by original rule (OC 1)

(2) NO