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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 338 ms]
(2) NO


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

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

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

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

(2)
NO