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

(0) Obligation:

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

w(r(x)) → r(w(x))
b(r(x)) → r(b(x))
b(w(x)) → w(b(x))

Q is empty.

(1) DirectTerminationProof (EQUIVALENT transformation)

We use [DIRECT_TERMINATION] with the following order to prove termination.

Knuth-Bendix order [KBO] with precedence:

b₁ > w₁ > r₁

and weight map:

w_1=2
r_1=1
b_1=3

The variable weight is 1

(2) TRUE