Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Mixed

Termination w.r.t. Q of the given QTRS could be disproven:

0 QTRS

↳1 NonTerminationProof (⇒, 540 ms)

↳2 NO

(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

b(a(x)) → a(b(x))
c(c(x)) → a(b(c(x)))
c(b(x)) → b(c(x))
a(a(x)) → b(a(c(x)))

Q is empty.

(1) NonTerminationProof (COMPLETE transformation)

We used the non-termination processor [OPPELT08] to show that the SRS problem is infinite.

Found the self-embedding DerivationStructure:

a c (b)^k c → b a c (b)^k+1 c

a c (b)^k c → b a c (b)^k+1 c
by Overlap u with l (ol4)

c (b)^k c → a (b)^k+1 c
by Equivalent
c (b)^k c → a (b)^k b c
by Overlapping Derivationstructures
c (b)^k c → (b)^k a b c
by Overlap u with r (ol3)
c (b)^k → (b)^k c
by Selfoverlapping OC am2
c b → b c
by original rule (OC 1)
c c → a b c
by original rule (OC 1)
(b)^k a → a (b)^k
by Selfoverlapping OC am1
b a → a b
by original rule (OC 1)

a a → b a c
by original rule (OC 1)

(0) Obligation:

(1) NonTerminationProof (COMPLETE transformation)

(2) NO