```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
any(X) -> s(X)
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
eq(ok(X1),ok(X2)) -> ok(eq(X1,X2))
inf(mark(X)) -> mark(inf(X))
inf(ok(X)) -> ok(inf(X))
length(mark(X)) -> mark(length(X))
length(ok(X)) -> ok(length(X))
proper(0()) -> ok(0())
proper(false()) -> ok(false())
proper(nil()) -> ok(nil())
proper(true()) -> ok(true())
s(ok(X)) -> ok(s(X))
take(X1,mark(X2)) -> mark(take(X1,X2))
take(mark(X1),X2) -> mark(take(X1,X2))
take(ok(X1),ok(X2)) -> ok(take(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{any/1,cons/2,eq/2,inf/1,length/1,proper/1,s/1,take/2,top/1} / {0/0,active/1,false/0,mark/1,nil/0,ok/1
,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {any,cons,eq,inf,length,proper,s,take
,top} and constructors {0,active,false,mark,nil,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.
0_0() -> 2
0_1() -> 3
active_0(2) -> 2
active_1(2) -> 5
active_2(3) -> 6
any_0(2) -> 1
cons_0(2,2) -> 1
cons_1(2,2) -> 3
eq_0(2,2) -> 1
eq_1(2,2) -> 3
false_0() -> 2
false_1() -> 3
inf_0(2) -> 1
inf_1(2) -> 4
length_0(2) -> 1
length_1(2) -> 4
mark_0(2) -> 2
mark_1(4) -> 1
mark_1(4) -> 4
nil_0() -> 2
nil_1() -> 3
ok_0(2) -> 2
ok_1(1) -> 1
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
s_0(2) -> 1
s_1(2) -> 1
take_0(2,2) -> 1
take_1(2,2) -> 4
top_0(2) -> 1
top_1(5) -> 1
top_2(6) -> 1
true_0() -> 2
true_1() -> 3
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
any(X) -> s(X)
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
eq(ok(X1),ok(X2)) -> ok(eq(X1,X2))
inf(mark(X)) -> mark(inf(X))
inf(ok(X)) -> ok(inf(X))
length(mark(X)) -> mark(length(X))
length(ok(X)) -> ok(length(X))
proper(0()) -> ok(0())
proper(false()) -> ok(false())
proper(nil()) -> ok(nil())
proper(true()) -> ok(true())
s(ok(X)) -> ok(s(X))
take(X1,mark(X2)) -> mark(take(X1,X2))
take(mark(X1),X2) -> mark(take(X1,X2))
take(ok(X1),ok(X2)) -> ok(take(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{any/1,cons/2,eq/2,inf/1,length/1,proper/1,s/1,take/2,top/1} / {0/0,active/1,false/0,mark/1,nil/0,ok/1
,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {any,cons,eq,inf,length,proper,s,take
,top} and constructors {0,active,false,mark,nil,ok,true}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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