Termination w.r.t. Q proof of /tmp/aprove_benchmark_example

Termination w.r.t. Q of the following Term Rewriting System could be proven:

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

active(f(X)) → mark(g(h(f(X))))
active(f(X)) → f(active(X))
active(h(X)) → h(active(X))
f(mark(X)) → mark(f(X))
h(mark(X)) → mark(h(X))
proper(f(X)) → f(proper(X))
proper(g(X)) → g(proper(X))
proper(h(X)) → h(proper(X))
f(ok(X)) → ok(f(X))
g(ok(X)) → ok(g(X))
h(ok(X)) → ok(h(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

Q is empty.

↳ QTRS

  ↳ DirectTerminationProof

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

active(f(X)) → mark(g(h(f(X))))
active(f(X)) → f(active(X))
active(h(X)) → h(active(X))
f(mark(X)) → mark(f(X))
h(mark(X)) → mark(h(X))
proper(f(X)) → f(proper(X))
proper(g(X)) → g(proper(X))
proper(h(X)) → h(proper(X))
f(ok(X)) → ok(f(X))
g(ok(X)) → ok(g(X))
h(ok(X)) → ok(h(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

Q is empty.

We use [27] with the following order to prove termination.

Knuth-Bendix order [24] with precedence:

active₁ > f₁ > ok₁
active₁ > f₁ > mark₁
active₁ > h₁ > ok₁
active₁ > h₁ > mark₁
proper₁ > f₁ > ok₁
proper₁ > f₁ > mark₁
proper₁ > g₁ > ok₁
proper₁ > h₁ > ok₁
proper₁ > h₁ > mark₁

and weight map:

top_1=1
active_1=5
f_1=1
g_1=1
h_1=1
mark_1=2
ok_1=6
proper_1=1
dummyConstant=1