(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
active(g(X)) → mark(h(X))
active(c) → mark(d)
active(h(d)) → mark(g(c))
mark(g(X)) → active(g(X))
mark(h(X)) → active(h(X))
mark(c) → active(c)
mark(d) → active(d)
g(mark(X)) → g(X)
g(active(X)) → g(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Recursive Path Order [RPO].
Precedence:
[active1, mark1] > [c, d] > [g1, h1]
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
g(mark(X)) → g(X)
g(active(X)) → g(X)
h(mark(X)) → h(X)
h(active(X)) → h(X)
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
active(g(X)) → mark(h(X))
active(c) → mark(d)
active(h(d)) → mark(g(c))
mark(g(X)) → active(g(X))
mark(h(X)) → active(h(X))
mark(c) → active(c)
mark(d) → active(d)
Q is empty.