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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 ms]
(2) NO


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

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

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(2)
NO