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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 123 ms]
(2) NO


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

   a(a(a(x1))) -> b(b(c(a(a(x1)))))
   b(b(x1)) -> c(a(b(x1)))
   c(x1) -> 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: 
"(b)^k+3 -> (b)^2k a a b"
(b)^k+3 -> (b)^2k a a b
by Overlapping Derivationstructures"(b)^k+3 -> (a)^k+2 b
by Equivalent"b (b)^k+2 -> (a)^k+2 b
by Overlap u with m (ol1)"b (b)^k+2 -> (c a)^k+2 b
by Operation lift"b (b)^k+1 -> (c a)^k+1 b
by Operation lift"b (b)^k -> (c a)^k b
by Selfoverlapping OC am2"b b -> c a b
by original rule (OC 1)"""""c -> 
by original rule (OC 1)""""(a)^k+2 -> (b)^2k a a
by Equivalent"a a (a)^k -> (b b)^k a a
by Overlap u with m (ol1)"a a (a)^k -> (b b c)^k a a
by Selfoverlapping OC am2"a a a -> b b c a a
by original rule (OC 1)"""c -> 
by original rule (OC 1)"""

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(2)
NO