Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Waldmann_06

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

0 QTRS

↳1 NonTerminationProof (⇒, 802 ms)

↳2 NO

(0) Obligation:

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

a(a(a(x))) → b(b(c(a(a(x)))))
b(b(x)) → c(a(b(x)))
c(x) → 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)^k+3 → (b)^2k a a b

(b)^k+3 → (b)^2k a a b
by Overlapping Derivationstructures

(b)^k+3 → (a)^k+2 b
by Equivalent
b (b)^k+2 → (a)^k+2 b
by Overlap u with m (ol1)
b (b)^k+2 → (c a)^k+2 b
by Operation lift
b (b)^k+1 → (c a)^k+1 b
by Operation lift
b (b)^k → (c a)^k b
by Selfoverlapping OC am2
b b → c a b
by original rule (OC 1)
c →
by original rule (OC 1)

(a)^k+2 → (b)^2k a a
by Equivalent
a a (a)^k → (b b)^k a a
by Overlap u with m (ol1)
a a (a)^k → (b b c)^k a a
by Selfoverlapping OC am2
a a a → b b c a a
by original rule (OC 1)
c →
by original rule (OC 1)

(0) Obligation:

(1) NonTerminationProof (COMPLETE transformation)

(2) NO