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 (⇒, 694 ms)

↳2 NO

(0) Obligation:

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

R(b(x)) → b(R(x))
R(c(x)) → L(c(x))
b(L(x)) → L(b(x))
a(L(x)) → a(b(R(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 (b)^k L c → a (b)^k+1 L c

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

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

R c → L c
by original rule (OC 1)

(0) Obligation:

(1) NonTerminationProof (COMPLETE transformation)

(2) NO