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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 8515 ms]
(2) NO


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

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

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

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

(2)
NO