* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
a__a() -> a()
a__a() -> b()
a__f(X,X) -> a__h(a__a())
a__f(X1,X2) -> f(X1,X2)
a__g(X1,X2) -> g(X1,X2)
a__g(a(),X) -> a__f(b(),X)
a__h(X) -> a__g(mark(X),X)
a__h(X) -> h(X)
mark(a()) -> a__a()
mark(b()) -> b()
mark(f(X1,X2)) -> a__f(mark(X1),X2)
mark(g(X1,X2)) -> a__g(mark(X1),X2)
mark(h(X)) -> a__h(mark(X))
- Signature:
{a__a/0,a__f/2,a__g/2,a__h/1,mark/1} / {a/0,b/0,f/2,g/2,h/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a__a,a__f,a__g,a__h,mark} and constructors {a,b,f,g,h}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
a__a() -> a()
a__a() -> b()
a__f(X,X) -> a__h(a__a())
a__f(X1,X2) -> f(X1,X2)
a__g(X1,X2) -> g(X1,X2)
a__g(a(),X) -> a__f(b(),X)
a__h(X) -> a__g(mark(X),X)
a__h(X) -> h(X)
mark(a()) -> a__a()
mark(b()) -> b()
mark(f(X1,X2)) -> a__f(mark(X1),X2)
mark(g(X1,X2)) -> a__g(mark(X1),X2)
mark(h(X)) -> a__h(mark(X))
- Signature:
{a__a/0,a__f/2,a__g/2,a__h/1,mark/1} / {a/0,b/0,f/2,g/2,h/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a__a,a__f,a__g,a__h,mark} and constructors {a,b,f,g,h}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
mark(x){x -> f(x,y)} =
mark(f(x,y)) ->^+ a__f(mark(x),y)
= C[mark(x) = mark(x){}]
WORST_CASE(Omega(n^1),?)