NO
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 110 ms]
(2) NO


----------------------------------------

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

   a(x1) -> x1
   a(b(x1)) -> b(a(c(b(c(x1)))))
   b(x1) -> a(x1)
   c(c(x1)) -> x1

Q is empty.

----------------------------------------

(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 c b -> a b c b c c"
a b c b -> a b c b c c
by OverlapClosure OC 3"a b c b -> a a b c
by OverlapClosure OC 3"a b c b -> a a c c b c
by OverlapClosure OC 2"a b c -> a a c b
by OverlapClosure OC 2"a b -> a a c b c
by OverlapClosure OC 3"a b -> b a c b c
by original rule (OC 1)""b -> a
by original rule (OC 1)"""c c -> 
by original rule (OC 1)"""b b -> c b c
by OverlapClosure OC 2"b -> a
by original rule (OC 1)""a b -> c b c
by OverlapClosure OC 3"a b -> b c b c
by OverlapClosure OC 3"a b -> b a c b c
by original rule (OC 1)""a -> 
by original rule (OC 1)"""b -> 
by OverlapClosure OC 2"b -> a
by original rule (OC 1)""a -> 
by original rule (OC 1)""""""c c -> 
by original rule (OC 1)"""a b -> b c b c
by OverlapClosure OC 3"a b -> b a c b c
by original rule (OC 1)""a -> 
by original rule (OC 1)""

----------------------------------------

(2)
NO