NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Gebhardt_06/08.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 1402 ms)
↳2 NO

(0) Obligation:

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

0(0(0(0(x)))) → 0(1(1(0(x))))
1(0(0(1(x)))) → 0(0(1(0(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:
0 0 0 0 0 1 0 1 0 1 0 0 → 0 0 0 0 0 1 0 1 0 1 0 0

0 0 0 0 0 1 0 1 0 1 0 0 → 0 0 0 0 0 1 0 1 0 1 0 0
by OverlapClosure OC 3
0 0 0 0 0 1 0 1 0 1 0 0 → 0 0 0 1 0 0 1 1 0 1 0 0
by OverlapClosure OC 3
0 0 0 0 0 1 0 1 0 1 0 0 → 0 1 0 0 1 0 1 1 0 1 0 0
by OverlapClosure OC 2
0 0 0 0 → 0 1 1 0
by original rule (OC 1)
1 0 0 1 0 1 0 1 0 0 → 0 0 1 0 1 1 0 1 0 0
by OverlapClosure OC 3
1 0 0 1 0 1 0 1 0 0 → 0 0 1 0 0 0 0 1 0 0
by OverlapClosure OC 3
1 0 0 1 0 1 0 1 0 0 → 0 0 1 0 0 1 0 0 1 0
by OverlapClosure OC 3
1 0 0 1 0 1 0 1 0 0 → 0 0 1 1 0 0 1 0 1 0
by OverlapClosure OC 3
1 0 0 1 0 1 0 1 0 0 → 0 0 0 0 0 0 1 0 1 0
by OverlapClosure OC 3
1 0 0 1 0 1 0 1 0 0 → 0 0 0 0 1 0 0 1 1 0
by OverlapClosure OC 2
1 0 0 1 0 1 0 1 → 0 0 0 0 1 0 0 0
by OverlapClosure OC 3
1 0 0 1 0 1 0 1 → 0 0 1 0 0 1 0 0
by OverlapClosure OC 3
1 0 0 1 0 1 0 1 → 0 0 1 1 0 0 1 0
by OverlapClosure OC 3
1 0 0 1 0 1 0 1 → 0 0 0 0 0 0 1 0
by OverlapClosure OC 2
1 0 0 1 → 0 0 1 0
by original rule (OC 1)
1 0 0 1 0 1 → 0 0 0 0 1 0
by OverlapClosure OC 2
1 0 0 1 → 0 0 1 0
by original rule (OC 1)
1 0 0 1 → 0 0 1 0
by original rule (OC 1)
0 0 0 0 → 0 1 1 0
by original rule (OC 1)
1 0 0 1 → 0 0 1 0
by original rule (OC 1)
1 0 0 1 → 0 0 1 0
by original rule (OC 1)
0 0 0 0 → 0 1 1 0
by original rule (OC 1)
1 0 0 1 → 0 0 1 0
by original rule (OC 1)
0 0 0 0 → 0 1 1 0
by original rule (OC 1)
1 0 0 1 → 0 0 1 0
by original rule (OC 1)
1 0 0 1 → 0 0 1 0
by original rule (OC 1)
0 0 0 0 → 0 1 1 0
by original rule (OC 1)
1 0 0 1 → 0 0 1 0
by original rule (OC 1)
1 0 0 1 → 0 0 1 0
by original rule (OC 1)

(2) NO