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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 161 ms]
(2) NO


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

   a(L(x)) -> L(a(x))
   R(a(x)) -> a(R(x))
   b(L(x)) -> b(R(x))
   R(b(x)) -> L(a(b(x)))

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: 
"b R (a)^k b -> b R (a)^k+1 b"
b R (a)^k b -> b R (a)^k+1 b
by Overlap u with l (ol4)"R (a)^k b -> L (a)^k+1 b
by Equivalent"R (a)^k b -> L (a)^k a b
by Overlapping Derivationstructures"R (a)^k b -> (a)^k L a b
by Overlap u with r (ol3)"R (a)^k -> (a)^k R
by Selfoverlapping OC am2"R a -> a R
by original rule (OC 1)"""R b -> L a b
by original rule (OC 1)"""(a)^k L -> L (a)^k
by Selfoverlapping OC am1"a L -> L a
by original rule (OC 1)"""""b L -> b R
by original rule (OC 1)"

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(2)
NO