/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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NO
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

(0) QTRS
(1) NonTerminationProof [COMPLETE, 718 ms]
(2) NO


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

   a(x1) -> b(x1)
   a(c(x1)) -> x1
   c(b(b(x1))) -> a(a(a(c(c(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: 
"c b b b b b b -> a a a c b b b b b b c c c"
c b b b b b b -> a a a c b b b b b b c c c
by OverlapClosure OC 3"c b b b b b b -> a a a c b b b a b b c c c
by OverlapClosure OC 2"c b b -> a a a c c
by original rule (OC 1)""c b b b b -> b b b a b b c c c
by OverlapClosure OC 3"c b b b b -> b b b c b b c
by OverlapClosure OC 2"c b b -> b b b c c
by OverlapClosure OC 3"c b b -> b b a c c
by OverlapClosure OC 3"c b b -> b a a c c
by OverlapClosure OC 3"c b b -> a a a c c
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)"""c b b -> b b c
by OverlapClosure OC 3"c b b -> b b a c c
by OverlapClosure OC 3"c b b -> b a a c c
by OverlapClosure OC 3"c b b -> a a a c c
by original rule (OC 1)""a -> b
by original rule (OC 1)"""a -> b
by original rule (OC 1)"""a c -> 
by original rule (OC 1)""""c b b -> a b b c c
by OverlapClosure OC 3"c b b -> a b a c c
by OverlapClosure OC 3"c b b -> a a a c c
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)"

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(2)
NO