```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
active(a()) -> mark(b())
f(mark(X1),X2) -> mark(f(X1,X2))
f(ok(X1),ok(X2)) -> ok(f(X1,X2))
g(mark(X1),X2) -> mark(g(X1,X2))
g(ok(X1),ok(X2)) -> ok(g(X1,X2))
h(mark(X)) -> mark(h(X))
h(ok(X)) -> ok(h(X))
proper(a()) -> ok(a())
proper(b()) -> ok(b())
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{active/1,f/2,g/2,h/1,proper/1,top/1} / {a/0,b/0,mark/1,ok/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {active,f,g,h,proper,top} and constructors {a,b,mark,ok}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 5.
The enriched problem is compatible with follwoing automaton.
a_0() -> 2
a_1() -> 3
a_2() -> 7
active_0(2) -> 1
active_1(2) -> 4
active_2(3) -> 5
active_3(6) -> 8
active_3(7) -> 8
active_4(9) -> 10
active_5(11) -> 12
b_0() -> 2
b_1() -> 3
b_2() -> 6
b_3() -> 9
b_4() -> 11
f_0(2,2) -> 1
f_1(2,2) -> 3
g_0(2,2) -> 1
g_1(2,2) -> 3
h_0(2) -> 1
h_1(2) -> 3
mark_0(2) -> 2
mark_1(3) -> 1
mark_1(3) -> 3
mark_1(3) -> 4
mark_2(6) -> 5
mark_3(9) -> 8
ok_0(2) -> 2
ok_1(3) -> 1
ok_1(3) -> 3
ok_1(3) -> 4
ok_2(6) -> 5
ok_2(7) -> 5
ok_3(9) -> 8
ok_4(11) -> 10
proper_0(2) -> 1
proper_1(2) -> 4
proper_2(3) -> 5
proper_3(6) -> 8
proper_4(9) -> 10
top_0(2) -> 1
top_1(4) -> 1
top_2(5) -> 1
top_3(8) -> 1
top_4(10) -> 1
top_5(12) -> 1
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
active(a()) -> mark(b())
f(mark(X1),X2) -> mark(f(X1,X2))
f(ok(X1),ok(X2)) -> ok(f(X1,X2))
g(mark(X1),X2) -> mark(g(X1,X2))
g(ok(X1),ok(X2)) -> ok(g(X1,X2))
h(mark(X)) -> mark(h(X))
h(ok(X)) -> ok(h(X))
proper(a()) -> ok(a())
proper(b()) -> ok(b())
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{active/1,f/2,g/2,h/1,proper/1,top/1} / {a/0,b/0,mark/1,ok/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {active,f,g,h,proper,top} and constructors {a,b,mark,ok}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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