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 (⇒, 0 ms)

↳2 NO

(0) Obligation:

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

b(c(x)) → d(c(x))
b(d(x)) → d(b(x))
a(d(x)) → a(b(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:

a (b)^k d c → a (b)^k+1 d c

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

a (b)^k d → a (b)^k+1 b
by Operation expand
a (b)^k d → a (b)^k+2
by Equivalent
a (b)^k d → a b b (b)^k
by Overlap u with l (ol4)
(b)^k d → d (b)^k
by Selfoverlapping OC am1
b d → d b
by original rule (OC 1)
a d → a b b
by original rule (OC 1)

b c → d c
by original rule (OC 1)

(0) Obligation:

(1) NonTerminationProof (COMPLETE transformation)

(2) NO