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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1161 ms]
(2) NO


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

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

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

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

(2)
NO