NO
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) QTRS
(1) NonTerminationProof [COMPLETE, 362 ms]
(2) NO


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(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   0(0(0(0(x1)))) -> 0(0(1(1(x1))))
   1(0(0(1(x1)))) -> 0(0(1(0(x1))))

Q is empty.

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(1) NonTerminationProof (COMPLETE)
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 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
by OverlapClosure OC 3"0 0 0 0 0 0 1 0 1 0 1 0 -> 0 0 0 0 1 0 0 1 1 0 1 0
by OverlapClosure OC 3"0 0 0 0 0 0 1 0 1 0 1 0 -> 0 0 0 0 1 0 0 0 0 0 1 0
by OverlapClosure OC 3"0 0 0 0 0 0 1 0 1 0 1 0 -> 0 0 1 0 0 1 0 0 0 0 1 0
by OverlapClosure OC 2"0 0 0 0 -> 0 0 1 1
by original rule (OC 1)""1 0 0 1 0 1 0 1 0 -> 0 0 1 0 0 0 0 1 0
by OverlapClosure OC 2"1 0 0 1 0 1 0 1 0 -> 0 0 1 0 0 1 0 0 1
by OverlapClosure OC 3"1 0 0 1 0 1 0 1 0 -> 0 0 1 1 0 0 1 0 1
by OverlapClosure OC 3"1 0 0 1 0 1 0 1 0 -> 0 0 1 1 1 0 0 1 1
by OverlapClosure OC 2"1 0 0 1 0 1 0 1 -> 0 0 1 1 1 0 0 0
by OverlapClosure OC 3"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 2"1 0 0 1 0 1 -> 0 0 1 1 1 0
by OverlapClosure OC 3"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 0 1 1
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)"""1 0 0 1 -> 0 0 1 0
by original rule (OC 1)"""0 0 0 0 -> 0 0 1 1
by original rule (OC 1)"""0 0 0 0 -> 0 0 1 1
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)"""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 0 1 1
by original rule (OC 1)"""1 0 0 1 -> 0 0 1 0
by original rule (OC 1)"

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(2)
NO