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

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

0 QTRS

↳1 NonTerminationProof (⇒, 1207 ms)

↳2 NO

(0) Obligation:

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

a(l(x)) → l(a(x))
r(a(x)) → a(r(x))
b(l(x)) → b(a(r(x)))
r(b(x)) → l(b(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:

b (a)^k l b → b (a)^k+1 l b

b (a)^k l b → b (a)^k+1 l b
by Overlap u with r (ol3)

b (a)^k l → b (a)^k+1 r
by Equivalent
b (a)^k l → b a (a)^k r
by Overlapping Derivationstructures
b (a)^k l → b a r (a)^k
by Overlap u with l (ol4)
(a)^k l → l (a)^k
by Selfoverlapping OC am1
a l → l a
by original rule (OC 1)
b l → b a r
by original rule (OC 1)
r (a)^k → (a)^k r
by Selfoverlapping OC am2
r a → a r
by original rule (OC 1)

r b → l b
by original rule (OC 1)

(0) Obligation:

(1) NonTerminationProof (COMPLETE transformation)

(2) NO