* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
+ Considered Problem:
- Strict TRS:
h(f(x,y)) -> f(y,f(h(h(x)),a()))
- Signature:
{h/1} / {a/0,f/2}
- Obligation:
innermost runtime complexity wrt. defined symbols {h} and constructors {a,f}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
h(f(x,y)) -> f(y,f(h(h(x)),a()))
- Signature:
{h/1} / {a/0,f/2}
- Obligation:
innermost runtime complexity wrt. defined symbols {h} and constructors {a,f}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
h(x){x -> f(x,y)} =
h(f(x,y)) ->^+ f(y,f(h(h(x)),a()))
= C[h(x) = h(x){}]
** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
h(f(x,y)) -> f(y,f(h(h(x)),a()))
- Signature:
{h/1} / {a/0,f/2}
- Obligation:
innermost runtime complexity wrt. defined symbols {h} and constructors {a,f}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
a_0() -> 2
a_1() -> 5
a_2() -> 9
f_0(2,2) -> 2
f_1(2,3) -> 1
f_1(2,3) -> 6
f_1(2,3) -> 10
f_1(4,5) -> 3
f_2(3,7) -> 4
f_2(3,7) -> 8
f_2(8,9) -> 7
h_0(2) -> 1
h_1(2) -> 6
h_1(6) -> 4
h_2(2) -> 10
h_2(10) -> 8
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
h(f(x,y)) -> f(y,f(h(h(x)),a()))
- Signature:
{h/1} / {a/0,f/2}
- Obligation:
innermost runtime complexity wrt. defined symbols {h} and constructors {a,f}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(Omega(n^1),O(n^1))