```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
active(d()) -> m(b())
active(d()) -> mark(c())
f(x,y,mark(z)) -> mark(f(x,y,z))
f(ok(x),ok(y),ok(z)) -> ok(f(x,y,z))
proper(b()) -> ok(b())
proper(c()) -> ok(c())
proper(d()) -> ok(d())
top(mark(x)) -> top(proper(x))
top(ok(x)) -> top(active(x))
- Signature:
{active/1,f/3,proper/1,top/1} / {b/0,c/0,d/0,m/1,mark/1,ok/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {active,f,proper,top} and constructors {b,c,d,m,mark,ok}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 4.
The enriched problem is compatible with follwoing automaton.
active_0(2) -> 1
active_1(2) -> 5
active_2(3) -> 6
active_2(4) -> 6
active_3(8) -> 9
active_4(10) -> 11
b_0() -> 2
b_1() -> 3
b_2() -> 7
c_0() -> 2
c_1() -> 4
c_2() -> 8
c_3() -> 10
d_0() -> 2
d_1() -> 3
f_0(2,2,2) -> 1
f_1(2,2,2) -> 4
m_0(2) -> 2
m_1(3) -> 1
m_1(3) -> 5
m_2(7) -> 6
mark_0(2) -> 2
mark_1(4) -> 1
mark_1(4) -> 4
mark_1(4) -> 5
mark_2(8) -> 6
ok_0(2) -> 2
ok_1(3) -> 1
ok_1(3) -> 5
ok_1(4) -> 1
ok_1(4) -> 4
ok_1(4) -> 5
ok_2(8) -> 6
ok_3(10) -> 9
proper_0(2) -> 1
proper_1(2) -> 5
proper_2(4) -> 6
proper_3(8) -> 9
top_0(2) -> 1
top_1(5) -> 1
top_2(6) -> 1
top_3(9) -> 1
top_4(11) -> 1
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
active(d()) -> m(b())
active(d()) -> mark(c())
f(x,y,mark(z)) -> mark(f(x,y,z))
f(ok(x),ok(y),ok(z)) -> ok(f(x,y,z))
proper(b()) -> ok(b())
proper(c()) -> ok(c())
proper(d()) -> ok(d())
top(mark(x)) -> top(proper(x))
top(ok(x)) -> top(active(x))
- Signature:
{active/1,f/3,proper/1,top/1} / {b/0,c/0,d/0,m/1,mark/1,ok/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {active,f,proper,top} and constructors {b,c,d,m,mark,ok}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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