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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 5405 ms]
(2) NO


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

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

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

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

(2)
NO