```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
active(cons(X1,X2)) -> cons(active(X1),X2)
active(zeros()) -> mark(cons(0(),zeros()))
cons(mark(X1),X2) -> mark(cons(X1,X2))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
proper(0()) -> ok(0())
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(zeros()) -> ok(zeros())
tail(mark(X)) -> mark(tail(X))
tail(ok(X)) -> ok(tail(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{active/1,cons/2,proper/1,tail/1,top/1} / {0/0,mark/1,ok/1,zeros/0}
- Obligation:
runtime complexity wrt. defined symbols {active,cons,proper,tail,top} and constructors {0,mark,ok,zeros}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 5.
The enriched problem is compatible with follwoing automaton.
0_0() -> 1
0_1() -> 11
0_2() -> 18
0_3() -> 27
active_0(1) -> 2
active_0(4) -> 2
active_0(5) -> 2
active_0(9) -> 2
active_1(1) -> 15
active_1(4) -> 15
active_1(5) -> 15
active_1(9) -> 15
active_2(11) -> 16
active_2(12) -> 16
active_3(26) -> 22
active_4(18) -> 28
active_4(29) -> 30
active_5(27) -> 31
cons_0(1,1) -> 3
cons_0(1,4) -> 3
cons_0(1,5) -> 3
cons_0(1,9) -> 3
cons_0(4,1) -> 3
cons_0(4,4) -> 3
cons_0(4,5) -> 3
cons_0(4,9) -> 3
cons_0(5,1) -> 3
cons_0(5,4) -> 3
cons_0(5,5) -> 3
cons_0(5,9) -> 3
cons_0(9,1) -> 3
cons_0(9,4) -> 3
cons_0(9,5) -> 3
cons_0(9,9) -> 3
cons_1(1,1) -> 13
cons_1(1,4) -> 13
cons_1(1,5) -> 13
cons_1(1,9) -> 13
cons_1(4,1) -> 13
cons_1(4,4) -> 13
cons_1(4,5) -> 13
cons_1(4,9) -> 13
cons_1(5,1) -> 13
cons_1(5,4) -> 13
cons_1(5,5) -> 13
cons_1(5,9) -> 13
cons_1(9,1) -> 13
cons_1(9,4) -> 13
cons_1(9,5) -> 13
cons_1(9,9) -> 13
cons_1(11,12) -> 10
cons_2(18,19) -> 17
cons_2(20,21) -> 16
cons_3(18,19) -> 26
cons_3(23,24) -> 22
cons_4(27,25) -> 29
cons_4(28,19) -> 22
cons_5(31,25) -> 30
mark_0(1) -> 4
mark_0(4) -> 4
mark_0(5) -> 4
mark_0(9) -> 4
mark_1(10) -> 2
mark_1(10) -> 15
mark_1(13) -> 3
mark_1(13) -> 13
mark_1(14) -> 7
mark_1(14) -> 14
mark_2(17) -> 16
ok_0(1) -> 5
ok_0(4) -> 5
ok_0(5) -> 5
ok_0(9) -> 5
ok_1(11) -> 6
ok_1(11) -> 15
ok_1(12) -> 6
ok_1(12) -> 15
ok_1(13) -> 3
ok_1(13) -> 13
ok_1(14) -> 7
ok_1(14) -> 14
ok_2(18) -> 20
ok_2(19) -> 21
ok_3(25) -> 24
ok_3(26) -> 16
ok_3(27) -> 23
ok_4(29) -> 22
proper_0(1) -> 6
proper_0(4) -> 6
proper_0(5) -> 6
proper_0(9) -> 6
proper_1(1) -> 15
proper_1(4) -> 15
proper_1(5) -> 15
proper_1(9) -> 15
proper_2(10) -> 16
proper_2(11) -> 20
proper_2(12) -> 21
proper_3(17) -> 22
proper_3(18) -> 23
proper_3(19) -> 24
tail_0(1) -> 7
tail_0(4) -> 7
tail_0(5) -> 7
tail_0(9) -> 7
tail_1(1) -> 14
tail_1(4) -> 14
tail_1(5) -> 14
tail_1(9) -> 14
top_0(1) -> 8
top_0(4) -> 8
top_0(5) -> 8
top_0(9) -> 8
top_1(15) -> 8
top_2(16) -> 8
top_3(22) -> 8
top_4(30) -> 8
zeros_0() -> 9
zeros_1() -> 12
zeros_2() -> 19
zeros_3() -> 25
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
active(cons(X1,X2)) -> cons(active(X1),X2)
active(zeros()) -> mark(cons(0(),zeros()))
cons(mark(X1),X2) -> mark(cons(X1,X2))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
proper(0()) -> ok(0())
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(zeros()) -> ok(zeros())
tail(mark(X)) -> mark(tail(X))
tail(ok(X)) -> ok(tail(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{active/1,cons/2,proper/1,tail/1,top/1} / {0/0,mark/1,ok/1,zeros/0}
- Obligation:
runtime complexity wrt. defined symbols {active,cons,proper,tail,top} and constructors {0,mark,ok,zeros}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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