```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(mark(X)) -> mark(f(X))
f(ok(X)) -> ok(f(X))
if(X1,mark(X2),X3) -> mark(if(X1,X2,X3))
if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
proper(c()) -> ok(c())
proper(false()) -> ok(false())
proper(true()) -> ok(true())
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{f/1,if/3,proper/1,top/1} / {active/1,c/0,false/0,mark/1,ok/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,if,proper,top} and constructors {active,c,false,mark,ok
,true}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
active_0(2) -> 2
active_1(2) -> 4
active_2(3) -> 5
c_0() -> 2
c_1() -> 3
f_0(2) -> 1
f_1(2) -> 3
false_0() -> 2
false_1() -> 3
if_0(2,2,2) -> 1
if_1(2,2,2) -> 3
mark_0(2) -> 2
mark_1(3) -> 1
mark_1(3) -> 3
ok_0(2) -> 2
ok_1(3) -> 1
ok_1(3) -> 3
ok_1(3) -> 4
proper_0(2) -> 1
proper_1(2) -> 4
top_0(2) -> 1
top_1(4) -> 1
top_2(5) -> 1
true_0() -> 2
true_1() -> 3
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
f(mark(X)) -> mark(f(X))
f(ok(X)) -> ok(f(X))
if(X1,mark(X2),X3) -> mark(if(X1,X2,X3))
if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
proper(c()) -> ok(c())
proper(false()) -> ok(false())
proper(true()) -> ok(true())
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{f/1,if/3,proper/1,top/1} / {active/1,c/0,false/0,mark/1,ok/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,if,proper,top} and constructors {active,c,false,mark,ok
,true}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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