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

(0) Obligation:

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

b(a(L(x1))) → L(a(L(X(b(a(b(b(x1))))))))
b(L(x1)) → L(b(x1))

Q is empty.

(1) QTRS Reverse (EQUIVALENT transformation)

We applied the QTRS Reverse Processor [REVERSE].

(2) Obligation:

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

L(a(b(x))) → b(b(a(b(X(L(a(L(x))))))))
L(b(x)) → b(L(x))

Q is empty.

(3) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [OPPELT08] to show that the SRS problem is infinite.

Found the self-embedding DerivationStructure:

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

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

L (b)^k a b → b (b)^k+1 a b X L a L
by Operation expand

L (b)^k a b → (b)^k+2 a b X L a L
by Overlap u with r (ol3)

L (b)^k → (b)^k L
by Selfoverlapping OC am2

L b → b L
by original rule (OC 1)

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

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

(4) NO