```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
active(f(X)) -> f(active(X))
active(f(X)) -> mark(g(h(f(X))))
active(h(X)) -> h(active(X))
f(mark(X)) -> mark(f(X))
f(ok(X)) -> ok(f(X))
g(ok(X)) -> ok(g(X))
h(mark(X)) -> mark(h(X))
h(ok(X)) -> ok(h(X))
proper(f(X)) -> f(proper(X))
proper(g(X)) -> g(proper(X))
proper(h(X)) -> h(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{active/1,f/1,g/1,h/1,proper/1,top/1} / {mark/1,ok/1}
- Obligation:
runtime complexity wrt. defined symbols {active,f,g,h,proper,top} and constructors {mark,ok}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
active_0(2) -> 1
active_1(2) -> 4
f_0(2) -> 1
f_1(2) -> 3
g_0(2) -> 1
g_1(2) -> 3
h_0(2) -> 1
h_1(2) -> 3
mark_0(2) -> 2
mark_1(3) -> 1
mark_1(3) -> 3
ok_0(2) -> 2
ok_1(3) -> 1
ok_1(3) -> 3
proper_0(2) -> 1
proper_1(2) -> 4
top_0(2) -> 1
top_1(4) -> 1
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
active(f(X)) -> f(active(X))
active(f(X)) -> mark(g(h(f(X))))
active(h(X)) -> h(active(X))
f(mark(X)) -> mark(f(X))
f(ok(X)) -> ok(f(X))
g(ok(X)) -> ok(g(X))
h(mark(X)) -> mark(h(X))
h(ok(X)) -> ok(h(X))
proper(f(X)) -> f(proper(X))
proper(g(X)) -> g(proper(X))
proper(h(X)) -> h(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{active/1,f/1,g/1,h/1,proper/1,top/1} / {mark/1,ok/1}
- Obligation:
runtime complexity wrt. defined symbols {active,f,g,h,proper,top} and constructors {mark,ok}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))
```