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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 2713 ms]
(2) NO


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

   c(c(x1)) -> b(b(x1))
   a(b(x1)) -> a(c(b(x1)))
   b(a(x1)) -> b(b(x1))
   b(c(x1)) -> c(a(a(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: 
"a b b (a)^k c b -> a b b (a)^2k+4 c b"
a b b (a)^k c b -> a b b (a)^2k+4 c b
by Equivalent"a b b (a)^k c b -> a b b a a (a)^2k+2 c b
by Overlap u with l (ol4)"b (a)^k c b -> c (a)^2k+2 c b
by Equivalent"b (a)^k c b -> c (a a)^k a a c b
by Overlapping Derivationstructures"b (a)^k c b -> (b)^k c a a c b
by Overlap u with r (ol3)"b (a)^k -> (b)^k b
by Selfoverlapping OC am2"b a -> b b
by original rule (OC 1)"""b c b -> c a a c b
by OverlapClosure OC 2"b c -> c a a
by original rule (OC 1)""a b -> a c b
by original rule (OC 1)""""(b)^k c -> c (a a)^k
by Selfoverlapping OC am1"b c -> c a a
by original rule (OC 1)"""""a b c -> a b b a a
by OverlapClosure OC 3"a b c -> a c c a a
by OverlapClosure OC 2"a b -> a c b
by original rule (OC 1)""b c -> c a a
by original rule (OC 1)"""c c -> b b
by original rule (OC 1)"""

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(2)
NO