NO
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1321 ms]
(2) NO


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

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

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(2)
NO