```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
cons(mark(X1),X2) -> mark(cons(X1,X2))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
cons1(mark(X1),X2) -> mark(cons1(X1,X2))
cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
fcons(X1,mark(X2)) -> mark(fcons(X1,X2))
fcons(mark(X1),X2) -> mark(fcons(X1,X2))
fcons(ok(X1),ok(X2)) -> ok(fcons(X1,X2))
first(X1,mark(X2)) -> mark(first(X1,X2))
first(mark(X1),X2) -> mark(first(X1,X2))
first(ok(X1),ok(X2)) -> ok(first(X1,X2))
first1(X1,mark(X2)) -> mark(first1(X1,X2))
first1(mark(X1),X2) -> mark(first1(X1,X2))
first1(ok(X1),ok(X2)) -> ok(first1(X1,X2))
from(mark(X)) -> mark(from(X))
from(ok(X)) -> ok(from(X))
proper(0()) -> ok(0())
proper(01()) -> ok(01())
proper(nil()) -> ok(nil())
proper(nil1()) -> ok(nil1())
quote(ok(X)) -> ok(quote(X))
quote1(ok(X)) -> ok(quote1(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
s1(mark(X)) -> mark(s1(X))
s1(ok(X)) -> ok(s1(X))
sel(X1,mark(X2)) -> mark(sel(X1,X2))
sel(mark(X1),X2) -> mark(sel(X1,X2))
sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
sel1(X1,mark(X2)) -> mark(sel1(X1,X2))
sel1(mark(X1),X2) -> mark(sel1(X1,X2))
sel1(ok(X1),ok(X2)) -> ok(sel1(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
unquote(mark(X)) -> mark(unquote(X))
unquote(ok(X)) -> ok(unquote(X))
unquote1(mark(X)) -> mark(unquote1(X))
unquote1(ok(X)) -> ok(unquote1(X))
- Signature:
{cons/2,cons1/2,fcons/2,first/2,first1/2,from/1,proper/1,quote/1,quote1/1,s/1,s1/1,sel/2,sel1/2,top/1
,unquote/1,unquote1/1} / {0/0,01/0,active/1,mark/1,nil/0,nil1/0,ok/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {cons,cons1,fcons,first,first1,from,proper,quote,quote1,s
,s1,sel,sel1,top,unquote,unquote1} and constructors {0,01,active,mark,nil,nil1,ok}
+ 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
01_0() -> 2
01_1() -> 3
active_0(2) -> 2
active_1(2) -> 4
active_2(3) -> 5
cons_0(2,2) -> 1
cons_1(2,2) -> 3
cons1_0(2,2) -> 1
cons1_1(2,2) -> 3
fcons_0(2,2) -> 1
fcons_1(2,2) -> 3
first_0(2,2) -> 1
first_1(2,2) -> 3
first1_0(2,2) -> 1
first1_1(2,2) -> 3
from_0(2) -> 1
from_1(2) -> 3
mark_0(2) -> 2
mark_1(3) -> 1
mark_1(3) -> 3
nil_0() -> 2
nil_1() -> 3
nil1_0() -> 2
nil1_1() -> 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
quote_0(2) -> 1
quote_1(2) -> 3
quote1_0(2) -> 1
quote1_1(2) -> 3
s_0(2) -> 1
s_1(2) -> 3
s1_0(2) -> 1
s1_1(2) -> 3
sel_0(2,2) -> 1
sel_1(2,2) -> 3
sel1_0(2,2) -> 1
sel1_1(2,2) -> 3
top_0(2) -> 1
top_1(4) -> 1
top_2(5) -> 1
unquote_0(2) -> 1
unquote_1(2) -> 3
unquote1_0(2) -> 1
unquote1_1(2) -> 3
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
cons(mark(X1),X2) -> mark(cons(X1,X2))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
cons1(mark(X1),X2) -> mark(cons1(X1,X2))
cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
fcons(X1,mark(X2)) -> mark(fcons(X1,X2))
fcons(mark(X1),X2) -> mark(fcons(X1,X2))
fcons(ok(X1),ok(X2)) -> ok(fcons(X1,X2))
first(X1,mark(X2)) -> mark(first(X1,X2))
first(mark(X1),X2) -> mark(first(X1,X2))
first(ok(X1),ok(X2)) -> ok(first(X1,X2))
first1(X1,mark(X2)) -> mark(first1(X1,X2))
first1(mark(X1),X2) -> mark(first1(X1,X2))
first1(ok(X1),ok(X2)) -> ok(first1(X1,X2))
from(mark(X)) -> mark(from(X))
from(ok(X)) -> ok(from(X))
proper(0()) -> ok(0())
proper(01()) -> ok(01())
proper(nil()) -> ok(nil())
proper(nil1()) -> ok(nil1())
quote(ok(X)) -> ok(quote(X))
quote1(ok(X)) -> ok(quote1(X))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
s1(mark(X)) -> mark(s1(X))
s1(ok(X)) -> ok(s1(X))
sel(X1,mark(X2)) -> mark(sel(X1,X2))
sel(mark(X1),X2) -> mark(sel(X1,X2))
sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
sel1(X1,mark(X2)) -> mark(sel1(X1,X2))
sel1(mark(X1),X2) -> mark(sel1(X1,X2))
sel1(ok(X1),ok(X2)) -> ok(sel1(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
unquote(mark(X)) -> mark(unquote(X))
unquote(ok(X)) -> ok(unquote(X))
unquote1(mark(X)) -> mark(unquote1(X))
unquote1(ok(X)) -> ok(unquote1(X))
- Signature:
{cons/2,cons1/2,fcons/2,first/2,first1/2,from/1,proper/1,quote/1,quote1/1,s/1,s1/1,sel/2,sel1/2,top/1
,unquote/1,unquote1/1} / {0/0,01/0,active/1,mark/1,nil/0,nil1/0,ok/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {cons,cons1,fcons,first,first1,from,proper,quote,quote1,s
,s1,sel,sel1,top,unquote,unquote1} and constructors {0,01,active,mark,nil,nil1,ok}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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