(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) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Lexicographic path order with status [LPO].
Precedence:
b1 > w1 > r1
Status:
trivial
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
w(r(x)) → r(w(x))
b(r(x)) → r(b(x))
b(w(x)) → w(b(x))
(2) Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.
(3) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(4) TRUE