* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
+ Considered Problem:
- Strict TRS:
dbl(0(),y) -> y
dbl(S(0()),S(0())) -> S(S(S(S(0()))))
save(0()) -> 0()
save(S(x)) -> dbl(0(),save(x))
- Signature:
{dbl/2,save/1} / {0/0,S/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {dbl,save} and constructors {0,S}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
dbl(0(),y) -> y
dbl(S(0()),S(0())) -> S(S(S(S(0()))))
save(0()) -> 0()
save(S(x)) -> dbl(0(),save(x))
- Signature:
{dbl/2,save/1} / {0/0,S/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {dbl,save} and constructors {0,S}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
save(x){x -> S(x)} =
save(S(x)) ->^+ dbl(0(),save(x))
= C[save(x) = save(x){}]
** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
dbl(0(),y) -> y
dbl(S(0()),S(0())) -> S(S(S(S(0()))))
save(0()) -> 0()
save(S(x)) -> dbl(0(),save(x))
- Signature:
{dbl/2,save/1} / {0/0,S/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {dbl,save} and constructors {0,S}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
0_0() -> 1
0_0() -> 2
0_1() -> 1
0_1() -> 6
0_1() -> 7
S_0(2) -> 1
S_0(2) -> 2
S_1(3) -> 1
S_1(4) -> 3
S_1(5) -> 4
S_1(6) -> 5
dbl_0(2,2) -> 1
dbl_1(6,7) -> 1
dbl_1(7,7) -> 1
dbl_1(7,7) -> 7
save_0(2) -> 1
save_1(2) -> 1
save_1(2) -> 7
2 -> 1
7 -> 1
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
dbl(0(),y) -> y
dbl(S(0()),S(0())) -> S(S(S(S(0()))))
save(0()) -> 0()
save(S(x)) -> dbl(0(),save(x))
- Signature:
{dbl/2,save/1} / {0/0,S/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {dbl,save} and constructors {0,S}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(Omega(n^1),O(n^1))