```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
active(c()) -> mark(d())
active(g(X)) -> mark(h(X))
active(h(d())) -> mark(g(c()))
g(ok(X)) -> ok(g(X))
h(ok(X)) -> ok(h(X))
proper(c()) -> ok(c())
proper(d()) -> ok(d())
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,g/1,h/1,proper/1,top/1} / {c/0,d/0,mark/1,ok/1}
- Obligation:
runtime complexity wrt. defined symbols {active,g,h,proper,top} and constructors {c,d,mark,ok}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 4.
The enriched problem is compatible with follwoing automaton.
active_0(2) -> 1
active_0(3) -> 1
active_0(6) -> 1
active_0(7) -> 1
active_1(2) -> 14
active_1(3) -> 14
active_1(6) -> 14
active_1(7) -> 14
active_2(10) -> 15
active_2(13) -> 15
active_3(16) -> 17
active_4(18) -> 19
c_0() -> 2
c_1() -> 13
d_0() -> 3
d_1() -> 10
d_2() -> 16
d_3() -> 18
g_0(2) -> 4
g_0(3) -> 4
g_0(6) -> 4
g_0(7) -> 4
g_1(2) -> 11
g_1(3) -> 11
g_1(6) -> 11
g_1(7) -> 11
h_0(2) -> 5
h_0(3) -> 5
h_0(6) -> 5
h_0(7) -> 5
h_1(2) -> 12
h_1(3) -> 12
h_1(6) -> 12
h_1(7) -> 12
mark_0(2) -> 6
mark_0(3) -> 6
mark_0(6) -> 6
mark_0(7) -> 6
mark_1(10) -> 1
mark_1(10) -> 14
mark_2(16) -> 15
ok_0(2) -> 7
ok_0(3) -> 7
ok_0(6) -> 7
ok_0(7) -> 7
ok_1(10) -> 8
ok_1(10) -> 14
ok_1(11) -> 4
ok_1(11) -> 11
ok_1(12) -> 5
ok_1(12) -> 12
ok_1(13) -> 8
ok_1(13) -> 14
ok_2(16) -> 15
ok_3(18) -> 17
proper_0(2) -> 8
proper_0(3) -> 8
proper_0(6) -> 8
proper_0(7) -> 8
proper_1(2) -> 14
proper_1(3) -> 14
proper_1(6) -> 14
proper_1(7) -> 14
proper_2(10) -> 15
proper_3(16) -> 17
top_0(2) -> 9
top_0(3) -> 9
top_0(6) -> 9
top_0(7) -> 9
top_1(14) -> 9
top_2(15) -> 9
top_3(17) -> 9
top_4(19) -> 9
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
active(c()) -> mark(d())
active(g(X)) -> mark(h(X))
active(h(d())) -> mark(g(c()))
g(ok(X)) -> ok(g(X))
h(ok(X)) -> ok(h(X))
proper(c()) -> ok(c())
proper(d()) -> ok(d())
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,g/1,h/1,proper/1,top/1} / {c/0,d/0,mark/1,ok/1}
- Obligation:
runtime complexity wrt. defined symbols {active,g,h,proper,top} and constructors {c,d,mark,ok}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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