```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
active(f(X)) -> f(active(X))
active(f(f(a()))) -> mark(c(f(g(f(a())))))
active(g(X)) -> g(active(X))
c(ok(X)) -> ok(c(X))
f(mark(X)) -> mark(f(X))
f(ok(X)) -> ok(f(X))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
proper(a()) -> ok(a())
proper(c(X)) -> c(proper(X))
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,c/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1}
- Obligation:
runtime complexity wrt. defined symbols {active,c,f,g,proper,top} and constructors {a,mark,ok}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
a_0() -> 2
a_1() -> 3
active_0(2) -> 1
active_1(2) -> 5
active_2(3) -> 6
c_0(2) -> 1
c_1(2) -> 3
f_0(2) -> 1
f_1(2) -> 4
g_0(2) -> 1
g_1(2) -> 4
mark_0(2) -> 2
mark_1(4) -> 1
mark_1(4) -> 4
ok_0(2) -> 2
ok_1(3) -> 1
ok_1(3) -> 3
ok_1(3) -> 5
ok_1(4) -> 1
ok_1(4) -> 4
proper_0(2) -> 1
proper_1(2) -> 5
top_0(2) -> 1
top_1(5) -> 1
top_2(6) -> 1
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
active(f(X)) -> f(active(X))
active(f(f(a()))) -> mark(c(f(g(f(a())))))
active(g(X)) -> g(active(X))
c(ok(X)) -> ok(c(X))
f(mark(X)) -> mark(f(X))
f(ok(X)) -> ok(f(X))
g(mark(X)) -> mark(g(X))
g(ok(X)) -> ok(g(X))
proper(a()) -> ok(a())
proper(c(X)) -> c(proper(X))
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,c/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1}
- Obligation:
runtime complexity wrt. defined symbols {active,c,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))
```