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 (⇒, 186 ms)

↳2 NO

(0) Obligation:

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

b(a(L(x))) → L(a(L(X(b(a(b(b(x))))))))
b(L(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 (b)^k L a L → L a L X b a (b)^k+1 L a L X b a b b

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

b a (b)^k L → L a L X b a (b)^k+1 b
by Operation expand
b a (b)^k L → L a L X b a (b)^k+2
by Equivalent
b a (b)^k L → L a L X b a b b (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)
b a L → L a L X b a b b
by original rule (OC 1)

b a L → L a L X b a b b
by original rule (OC 1)

(0) Obligation:

(1) NonTerminationProof (COMPLETE transformation)

(2) NO