* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
active(c()) -> mark(f(g(c())))
active(f(g(X))) -> mark(g(X))
f(ok(X)) -> ok(f(X))
g(ok(X)) -> ok(g(X))
proper(c()) -> ok(c())
proper(f(X)) -> f(proper(X))
proper(g(X)) -> g(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{active/1,f/1,g/1,proper/1,top/1} / {c/0,mark/1,ok/1}
- Obligation:
runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {c,mark,ok}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 6.
The enriched problem is compatible with follwoing automaton.
active_0(2) -> 1
active_1(2) -> 7
active_2(5) -> 8
active_3(19) -> 14
active_4(22) -> 23
active_5(20) -> 26
active_6(29) -> 30
c_0() -> 2
c_1() -> 5
c_2() -> 11
c_3() -> 18
c_4() -> 28
f_0(2) -> 1
f_1(2) -> 6
f_1(4) -> 3
f_2(10) -> 9
f_2(12) -> 8
f_3(15) -> 14
f_3(17) -> 19
f_4(20) -> 22
g_0(2) -> 1
g_1(2) -> 6
g_1(5) -> 4
g_2(11) -> 10
g_2(13) -> 12
g_3(11) -> 17
g_3(16) -> 15
g_4(11) -> 21
g_4(18) -> 20
g_5(18) -> 24
g_5(25) -> 23
g_5(28) -> 29
g_6(27) -> 26
mark_0(2) -> 2
mark_1(3) -> 1
mark_1(3) -> 7
mark_2(9) -> 8
mark_4(21) -> 14
mark_5(24) -> 23
ok_0(2) -> 2
ok_1(5) -> 1
ok_1(5) -> 7
ok_1(6) -> 1
ok_1(6) -> 6
ok_2(11) -> 13
ok_3(17) -> 12
ok_3(18) -> 16
ok_3(18) -> 25
ok_3(19) -> 8
ok_4(20) -> 15
ok_4(20) -> 23
ok_4(22) -> 14
ok_4(28) -> 27
ok_5(29) -> 26
proper_0(2) -> 1
proper_1(2) -> 7
proper_2(3) -> 8
proper_2(4) -> 12
proper_2(5) -> 13
proper_3(9) -> 14
proper_3(10) -> 15
proper_3(11) -> 16
proper_4(21) -> 23
proper_5(11) -> 25
proper_5(24) -> 26
proper_6(18) -> 27
top_0(2) -> 1
top_1(7) -> 1
top_2(8) -> 1
top_3(14) -> 1
top_4(23) -> 1
top_5(26) -> 1
top_6(30) -> 1
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
active(c()) -> mark(f(g(c())))
active(f(g(X))) -> mark(g(X))
f(ok(X)) -> ok(f(X))
g(ok(X)) -> ok(g(X))
proper(c()) -> ok(c())
proper(f(X)) -> f(proper(X))
proper(g(X)) -> g(proper(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{active/1,f/1,g/1,proper/1,top/1} / {c/0,mark/1,ok/1}
- Obligation:
runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {c,mark,ok}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(?,O(n^1))