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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1739 ms]
(2) NO


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

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

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(2)
NO