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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 3595 ms]
(2) NO


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

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

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(2)
NO