* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
+ Considered Problem:
- Strict TRS:
a(b(x)) -> b(b(a(x)))
- Signature:
{a/1} / {b/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a} and constructors {b}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
a(b(x)) -> b(b(a(x)))
- Signature:
{a/1} / {b/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a} and constructors {b}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
a(x){x -> b(x)} =
a(b(x)) ->^+ b(b(a(x)))
= C[a(x) = a(x){}]
** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
a(b(x)) -> b(b(a(x)))
- Signature:
{a/1} / {b/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a} and constructors {b}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
a_0(2) -> 1
a_1(2) -> 4
b_0(2) -> 2
b_1(3) -> 1
b_1(3) -> 4
b_1(4) -> 3
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
a(b(x)) -> b(b(a(x)))
- Signature:
{a/1} / {b/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a} and constructors {b}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(Omega(n^1),O(n^1))