* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
+ Considered Problem:
- Strict TRS:
r1(cons(x,k),a) -> r1(k,cons(x,a))
r1(empty(),a) -> a
rev(ls) -> r1(ls,empty())
- Signature:
{r1/2,rev/1} / {cons/2,empty/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
r1(cons(x,k),a) -> r1(k,cons(x,a))
r1(empty(),a) -> a
rev(ls) -> r1(ls,empty())
- Signature:
{r1/2,rev/1} / {cons/2,empty/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
r1(y,z){y -> cons(x,y)} =
r1(cons(x,y),z) ->^+ r1(y,cons(x,z))
= C[r1(y,cons(x,z)) = r1(y,z){z -> cons(x,z)}]
** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
r1(cons(x,k),a) -> r1(k,cons(x,a))
r1(empty(),a) -> a
rev(ls) -> r1(ls,empty())
- Signature:
{r1/2,rev/1} / {cons/2,empty/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
cons_0(2,2) -> 1
cons_0(2,2) -> 2
cons_1(2,2) -> 1
cons_1(2,2) -> 3
cons_1(2,3) -> 1
cons_1(2,3) -> 3
empty_0() -> 1
empty_0() -> 2
empty_1() -> 1
empty_1() -> 3
r1_0(2,2) -> 1
r1_1(2,3) -> 1
rev_0(2) -> 1
2 -> 1
3 -> 1
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
r1(cons(x,k),a) -> r1(k,cons(x,a))
r1(empty(),a) -> a
rev(ls) -> r1(ls,empty())
- Signature:
{r1/2,rev/1} / {cons/2,empty/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(Omega(n^1),O(n^1))