```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
active(c()) -> mark(f(g(c())))
active(f(g(X))) -> mark(g(X))
f(ok(X)) -> ok(f(X))
g(ok(X)) -> ok(g(X))
proper(c()) -> ok(c())
proper(f(X)) -> f(proper(X))
proper(g(X)) -> g(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{active/1,f/1,g/1,proper/1,top/1} / {c/0,mark/1,ok/1}
- Obligation:
runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {c,mark,ok}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 6.
The enriched problem is compatible with follwoing automaton.
active_0(2) -> 1
active_0(5) -> 1
active_0(6) -> 1
active_1(2) -> 14
active_1(5) -> 14
active_1(6) -> 14
active_2(11) -> 15
active_3(26) -> 21
active_4(29) -> 30
active_5(27) -> 33
active_6(36) -> 37
c_0() -> 2
c_1() -> 11
c_2() -> 18
c_3() -> 25
c_4() -> 35
f_0(2) -> 3
f_0(5) -> 3
f_0(6) -> 3
f_1(2) -> 12
f_1(5) -> 12
f_1(6) -> 12
f_1(10) -> 9
f_2(17) -> 16
f_2(19) -> 15
f_3(22) -> 21
f_3(24) -> 26
f_4(27) -> 29
g_0(2) -> 4
g_0(5) -> 4
g_0(6) -> 4
g_1(2) -> 13
g_1(5) -> 13
g_1(6) -> 13
g_1(11) -> 10
g_2(18) -> 17
g_2(20) -> 19
g_3(18) -> 24
g_3(23) -> 22
g_4(18) -> 28
g_4(25) -> 27
g_5(25) -> 31
g_5(32) -> 30
g_5(35) -> 36
g_6(34) -> 33
mark_0(2) -> 5
mark_0(5) -> 5
mark_0(6) -> 5
mark_1(9) -> 1
mark_1(9) -> 14
mark_2(16) -> 15
mark_4(28) -> 21
mark_5(31) -> 30
ok_0(2) -> 6
ok_0(5) -> 6
ok_0(6) -> 6
ok_1(11) -> 7
ok_1(11) -> 14
ok_1(12) -> 3
ok_1(12) -> 12
ok_1(13) -> 4
ok_1(13) -> 13
ok_2(18) -> 20
ok_3(24) -> 19
ok_3(25) -> 23
ok_3(25) -> 32
ok_3(26) -> 15
ok_4(27) -> 22
ok_4(27) -> 30
ok_4(29) -> 21
ok_4(35) -> 34
ok_5(36) -> 33
proper_0(2) -> 7
proper_0(5) -> 7
proper_0(6) -> 7
proper_1(2) -> 14
proper_1(5) -> 14
proper_1(6) -> 14
proper_2(9) -> 15
proper_2(10) -> 19
proper_2(11) -> 20
proper_3(16) -> 21
proper_3(17) -> 22
proper_3(18) -> 23
proper_4(28) -> 30
proper_5(18) -> 32
proper_5(31) -> 33
proper_6(25) -> 34
top_0(2) -> 8
top_0(5) -> 8
top_0(6) -> 8
top_1(14) -> 8
top_2(15) -> 8
top_3(21) -> 8
top_4(30) -> 8
top_5(33) -> 8
top_6(37) -> 8
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
active(c()) -> mark(f(g(c())))
active(f(g(X))) -> mark(g(X))
f(ok(X)) -> ok(f(X))
g(ok(X)) -> ok(g(X))
proper(c()) -> ok(c())
proper(f(X)) -> f(proper(X))
proper(g(X)) -> g(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{active/1,f/1,g/1,proper/1,top/1} / {c/0,mark/1,ok/1}
- Obligation:
runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {c,mark,ok}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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