* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
activate(X) -> X
activate(n__f(X)) -> f(activate(X))
activate(n__g(X)) -> g(activate(X))
f(X) -> cons(X,n__f(n__g(X)))
f(X) -> n__f(X)
g(X) -> n__g(X)
g(0()) -> s(0())
g(s(X)) -> s(s(g(X)))
sel(0(),cons(X,Y)) -> X
sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
- Signature:
{activate/1,f/1,g/1,sel/2} / {0/0,cons/2,n__f/1,n__g/1,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate,f,g,sel} and constructors {0,cons,n__f,n__g,s}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
activate(X) -> X
activate(n__f(X)) -> f(activate(X))
activate(n__g(X)) -> g(activate(X))
f(X) -> cons(X,n__f(n__g(X)))
f(X) -> n__f(X)
g(X) -> n__g(X)
g(0()) -> s(0())
g(s(X)) -> s(s(g(X)))
sel(0(),cons(X,Y)) -> X
sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
- Signature:
{activate/1,f/1,g/1,sel/2} / {0/0,cons/2,n__f/1,n__g/1,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate,f,g,sel} and constructors {0,cons,n__f,n__g,s}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
activate(x){x -> n__f(x)} =
activate(n__f(x)) ->^+ f(activate(x))
= C[activate(x) = activate(x){}]
WORST_CASE(Omega(n^1),?)