```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
2ndsneg(X1,mark(X2)) -> mark(2ndsneg(X1,X2))
2ndsneg(mark(X1),X2) -> mark(2ndsneg(X1,X2))
2ndsneg(ok(X1),ok(X2)) -> ok(2ndsneg(X1,X2))
2ndspos(X1,mark(X2)) -> mark(2ndspos(X1,X2))
2ndspos(mark(X1),X2) -> mark(2ndspos(X1,X2))
2ndspos(ok(X1),ok(X2)) -> ok(2ndspos(X1,X2))
cons(mark(X1),X2) -> mark(cons(X1,X2))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
cons2(X1,mark(X2)) -> mark(cons2(X1,X2))
cons2(ok(X1),ok(X2)) -> ok(cons2(X1,X2))
from(mark(X)) -> mark(from(X))
from(ok(X)) -> ok(from(X))
negrecip(mark(X)) -> mark(negrecip(X))
negrecip(ok(X)) -> ok(negrecip(X))
pi(mark(X)) -> mark(pi(X))
pi(ok(X)) -> ok(pi(X))
plus(X1,mark(X2)) -> mark(plus(X1,X2))
plus(mark(X1),X2) -> mark(plus(X1,X2))
plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
posrecip(mark(X)) -> mark(posrecip(X))
posrecip(ok(X)) -> ok(posrecip(X))
proper(0()) -> ok(0())
proper(nil()) -> ok(nil())
proper(rnil()) -> ok(rnil())
rcons(X1,mark(X2)) -> mark(rcons(X1,X2))
rcons(mark(X1),X2) -> mark(rcons(X1,X2))
rcons(ok(X1),ok(X2)) -> ok(rcons(X1,X2))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
square(mark(X)) -> mark(square(X))
square(ok(X)) -> ok(square(X))
times(X1,mark(X2)) -> mark(times(X1,X2))
times(mark(X1),X2) -> mark(times(X1,X2))
times(ok(X1),ok(X2)) -> ok(times(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{2ndsneg/2,2ndspos/2,cons/2,cons2/2,from/1,negrecip/1,pi/1,plus/2,posrecip/1,proper/1,rcons/2,s/1,square/1
,times/2,top/1} / {0/0,active/1,mark/1,nil/0,ok/1,rnil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {2ndsneg,2ndspos,cons,cons2,from,negrecip,pi,plus,posrecip
,proper,rcons,s,square,times,top} and constructors {0,active,mark,nil,ok,rnil}
+ 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
2ndsneg_0(2,2) -> 1
2ndsneg_1(2,2) -> 3
2ndspos_0(2,2) -> 1
2ndspos_1(2,2) -> 3
active_0(2) -> 2
active_1(2) -> 4
active_2(3) -> 5
cons_0(2,2) -> 1
cons_1(2,2) -> 3
cons2_0(2,2) -> 1
cons2_1(2,2) -> 3
from_0(2) -> 1
from_1(2) -> 3
mark_0(2) -> 2
mark_1(3) -> 1
mark_1(3) -> 3
negrecip_0(2) -> 1
negrecip_1(2) -> 3
nil_0() -> 2
nil_1() -> 3
ok_0(2) -> 2
ok_1(3) -> 1
ok_1(3) -> 3
ok_1(3) -> 4
pi_0(2) -> 1
pi_1(2) -> 3
plus_0(2,2) -> 1
plus_1(2,2) -> 3
posrecip_0(2) -> 1
posrecip_1(2) -> 3
proper_0(2) -> 1
proper_1(2) -> 4
rcons_0(2,2) -> 1
rcons_1(2,2) -> 3
rnil_0() -> 2
rnil_1() -> 3
s_0(2) -> 1
s_1(2) -> 3
square_0(2) -> 1
square_1(2) -> 3
times_0(2,2) -> 1
times_1(2,2) -> 3
top_0(2) -> 1
top_1(4) -> 1
top_2(5) -> 1
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
2ndsneg(X1,mark(X2)) -> mark(2ndsneg(X1,X2))
2ndsneg(mark(X1),X2) -> mark(2ndsneg(X1,X2))
2ndsneg(ok(X1),ok(X2)) -> ok(2ndsneg(X1,X2))
2ndspos(X1,mark(X2)) -> mark(2ndspos(X1,X2))
2ndspos(mark(X1),X2) -> mark(2ndspos(X1,X2))
2ndspos(ok(X1),ok(X2)) -> ok(2ndspos(X1,X2))
cons(mark(X1),X2) -> mark(cons(X1,X2))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
cons2(X1,mark(X2)) -> mark(cons2(X1,X2))
cons2(ok(X1),ok(X2)) -> ok(cons2(X1,X2))
from(mark(X)) -> mark(from(X))
from(ok(X)) -> ok(from(X))
negrecip(mark(X)) -> mark(negrecip(X))
negrecip(ok(X)) -> ok(negrecip(X))
pi(mark(X)) -> mark(pi(X))
pi(ok(X)) -> ok(pi(X))
plus(X1,mark(X2)) -> mark(plus(X1,X2))
plus(mark(X1),X2) -> mark(plus(X1,X2))
plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
posrecip(mark(X)) -> mark(posrecip(X))
posrecip(ok(X)) -> ok(posrecip(X))
proper(0()) -> ok(0())
proper(nil()) -> ok(nil())
proper(rnil()) -> ok(rnil())
rcons(X1,mark(X2)) -> mark(rcons(X1,X2))
rcons(mark(X1),X2) -> mark(rcons(X1,X2))
rcons(ok(X1),ok(X2)) -> ok(rcons(X1,X2))
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
square(mark(X)) -> mark(square(X))
square(ok(X)) -> ok(square(X))
times(X1,mark(X2)) -> mark(times(X1,X2))
times(mark(X1),X2) -> mark(times(X1,X2))
times(ok(X1),ok(X2)) -> ok(times(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{2ndsneg/2,2ndspos/2,cons/2,cons2/2,from/1,negrecip/1,pi/1,plus/2,posrecip/1,proper/1,rcons/2,s/1,square/1
,times/2,top/1} / {0/0,active/1,mark/1,nil/0,ok/1,rnil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {2ndsneg,2ndspos,cons,cons2,from,negrecip,pi,plus,posrecip
,proper,rcons,s,square,times,top} and constructors {0,active,mark,nil,ok,rnil}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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