* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
+ Considered Problem:
- Strict TRS:
minus(f(x,y)) -> f(minus(y),minus(x))
minus(h(x)) -> h(minus(x))
minus(minus(x)) -> x
- Signature:
{minus/1} / {f/2,h/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {minus} and constructors {f,h}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
minus(f(x,y)) -> f(minus(y),minus(x))
minus(h(x)) -> h(minus(x))
minus(minus(x)) -> x
- Signature:
{minus/1} / {f/2,h/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {minus} and constructors {f,h}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
minus(y){y -> f(x,y)} =
minus(f(x,y)) ->^+ f(minus(y),minus(x))
= C[minus(y) = minus(y){}]
** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
minus(f(x,y)) -> f(minus(y),minus(x))
minus(h(x)) -> h(minus(x))
minus(minus(x)) -> x
- Signature:
{minus/1} / {f/2,h/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {minus} and constructors {f,h}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
f_0(2,2) -> 2
f_1(3,4) -> 1
f_1(4,4) -> 3
f_1(4,4) -> 4
h_0(2) -> 2
h_1(4) -> 1
h_1(4) -> 3
h_1(4) -> 4
minus_0(2) -> 1
minus_1(2) -> 3
minus_1(2) -> 4
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
minus(f(x,y)) -> f(minus(y),minus(x))
minus(h(x)) -> h(minus(x))
minus(minus(x)) -> x
- Signature:
{minus/1} / {f/2,h/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {minus} and constructors {f,h}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(Omega(n^1),O(n^1))