Termination w.r.t. Q proof of Zantema_15

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

0 QTRS

↳1 NonTerminationProof (⇒, 72 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(R(x))
R(b(x)) → L(a(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 R (a)^k b → b R (a)^k+1 b

b R (a)^k b → b R (a)^k+1 b
by Overlap u with l (ol4)

R (a)^k b → L (a)^k+1 b
by Equivalent
R (a)^k b → L (a)^k a b
by Overlapping Derivationstructures
R (a)^k b → (a)^k L a b
by Overlap u with r (ol3)
R (a)^k → (a)^k R
by Selfoverlapping OC am2
R a → a R
by original rule (OC 1)
R b → L a b
by original rule (OC 1)
(a)^k L → L (a)^k
by Selfoverlapping OC am1
a L → L a
by original rule (OC 1)

b L → b R
by original rule (OC 1)

(0) Obligation:

(1) NonTerminationProof (COMPLETE transformation)

(2) NO