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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 149 ms]
(2) NO


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

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

   a(x1) -> x1
   a(b(x1)) -> b(c(a(a(x1))))
   b(x1) -> a(x1)
   c(c(x1)) -> b(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 b c -> a b b c a a"
a b b c -> a b b c a a
by OverlapClosure OC 2"a b b c -> a b a b
by OverlapClosure OC 2"a b b -> a b a c
by OverlapClosure OC 3"a b b -> b b a c
by OverlapClosure OC 3"a b b -> b c c a c
by OverlapClosure OC 3"a b b -> b c b c a c
by OverlapClosure OC 3"a b b -> b c b c a a c
by OverlapClosure OC 3"a b b -> b c a b c
by OverlapClosure OC 2"a b -> b c a a
by original rule (OC 1)""a b -> b c
by OverlapClosure OC 2"a b -> b c a
by OverlapClosure OC 2"a b -> b c a a
by original rule (OC 1)""a -> 
by original rule (OC 1)"""a -> 
by original rule (OC 1)""""a b -> b c a a
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 -> b
by original rule (OC 1)"""b -> a
by original rule (OC 1)"""c c -> b
by original rule (OC 1)"""a b -> b c a a
by original rule (OC 1)"

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

(2)
NO