```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
dbl(mark(X)) -> mark(dbl(X))
dbl(ok(X)) -> ok(dbl(X))
dbl1(mark(X)) -> mark(dbl1(X))
dbl1(ok(X)) -> ok(dbl1(X))
dbls(mark(X)) -> mark(dbls(X))
dbls(ok(X)) -> ok(dbls(X))
from(ok(X)) -> ok(from(X))
indx(mark(X1),X2) -> mark(indx(X1,X2))
indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
proper(0()) -> ok(0())
proper(01()) -> ok(01())
proper(nil()) -> ok(nil())
quote(mark(X)) -> mark(quote(X))
quote(ok(X)) -> ok(quote(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))
- Signature:
{cons/2,dbl/1,dbl1/1,dbls/1,from/1,indx/2,proper/1,quote/1,s/1,s1/1,sel/2,sel1/2,top/1} / {0/0,01/0,active/1
,mark/1,nil/0,ok/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {cons,dbl,dbl1,dbls,from,indx,proper,quote,s,s1,sel,sel1
,top} and constructors {0,01,active,mark,nil,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) -> 5
active_2(3) -> 6
cons_0(2,2) -> 1
cons_1(2,2) -> 3
dbl_0(2) -> 1
dbl_1(2) -> 4
dbl1_0(2) -> 1
dbl1_1(2) -> 4
dbls_0(2) -> 1
dbls_1(2) -> 4
from_0(2) -> 1
from_1(2) -> 3
indx_0(2,2) -> 1
indx_1(2,2) -> 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(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
quote_0(2) -> 1
quote_1(2) -> 4
s_0(2) -> 1
s_1(2) -> 3
s1_0(2) -> 1
s1_1(2) -> 4
sel_0(2,2) -> 1
sel_1(2,2) -> 4
sel1_0(2,2) -> 1
sel1_1(2,2) -> 4
top_0(2) -> 1
top_1(5) -> 1
top_2(6) -> 1
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
dbl(mark(X)) -> mark(dbl(X))
dbl(ok(X)) -> ok(dbl(X))
dbl1(mark(X)) -> mark(dbl1(X))
dbl1(ok(X)) -> ok(dbl1(X))
dbls(mark(X)) -> mark(dbls(X))
dbls(ok(X)) -> ok(dbls(X))
from(ok(X)) -> ok(from(X))
indx(mark(X1),X2) -> mark(indx(X1,X2))
indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
proper(0()) -> ok(0())
proper(01()) -> ok(01())
proper(nil()) -> ok(nil())
quote(mark(X)) -> mark(quote(X))
quote(ok(X)) -> ok(quote(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))
- Signature:
{cons/2,dbl/1,dbl1/1,dbls/1,from/1,indx/2,proper/1,quote/1,s/1,s1/1,sel/2,sel1/2,top/1} / {0/0,01/0,active/1
,mark/1,nil/0,ok/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {cons,dbl,dbl1,dbls,from,indx,proper,quote,s,s1,sel,sel1
,top} and constructors {0,01,active,mark,nil,ok}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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