* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
+ Considered Problem:
- Strict TRS:
b(r(x)) -> r(b(x))
b(w(x)) -> w(b(x))
w(r(x)) -> r(w(x))
- Signature:
{b/1,w/1} / {r/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {b,w} and constructors {r}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
b(r(x)) -> r(b(x))
b(w(x)) -> w(b(x))
w(r(x)) -> r(w(x))
- Signature:
{b/1,w/1} / {r/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {b,w} and constructors {r}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
b(x){x -> r(x)} =
b(r(x)) ->^+ r(b(x))
= C[b(x) = b(x){}]
** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
b(r(x)) -> r(b(x))
b(w(x)) -> w(b(x))
w(r(x)) -> r(w(x))
- Signature:
{b/1,w/1} / {r/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {b,w} and constructors {r}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
b_0(2) -> 1
b_1(2) -> 3
r_0(2) -> 2
r_1(3) -> 1
r_1(3) -> 3
w_0(2) -> 1
w_1(2) -> 3
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
b(r(x)) -> r(b(x))
b(w(x)) -> w(b(x))
w(r(x)) -> r(w(x))
- Signature:
{b/1,w/1} / {r/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {b,w} and constructors {r}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(Omega(n^1),O(n^1))