```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
active(f(f(a()))) -> mark(f(g(f(a()))))
active(g(X)) -> g(active(X))
f(ok(X)) -> ok(f(X))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
proper(a()) -> ok(a())
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} / {a/0,mark/1,ok/1}
- Obligation:
runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {a,mark,ok}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
a_0() -> 1
a_1() -> 11
active_0(1) -> 2
active_0(5) -> 2
active_0(6) -> 2
active_1(1) -> 12
active_1(5) -> 12
active_1(6) -> 12
active_2(11) -> 13
f_0(1) -> 3
f_0(5) -> 3
f_0(6) -> 3
f_1(1) -> 9
f_1(5) -> 9
f_1(6) -> 9
g_0(1) -> 4
g_0(5) -> 4
g_0(6) -> 4
g_1(1) -> 10
g_1(5) -> 10
g_1(6) -> 10
mark_0(1) -> 5
mark_0(5) -> 5
mark_0(6) -> 5
mark_1(10) -> 4
mark_1(10) -> 10
ok_0(1) -> 6
ok_0(5) -> 6
ok_0(6) -> 6
ok_1(9) -> 3
ok_1(9) -> 9
ok_1(10) -> 4
ok_1(10) -> 10
ok_1(11) -> 7
ok_1(11) -> 12
proper_0(1) -> 7
proper_0(5) -> 7
proper_0(6) -> 7
proper_1(1) -> 12
proper_1(5) -> 12
proper_1(6) -> 12
top_0(1) -> 8
top_0(5) -> 8
top_0(6) -> 8
top_1(12) -> 8
top_2(13) -> 8
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
active(f(f(a()))) -> mark(f(g(f(a()))))
active(g(X)) -> g(active(X))
f(ok(X)) -> ok(f(X))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
proper(a()) -> ok(a())
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} / {a/0,mark/1,ok/1}
- Obligation:
runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {a,mark,ok}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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