* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
a__f(X) -> a__if(mark(X),c(),f(true()))
a__f(X) -> f(X)
a__if(X1,X2,X3) -> if(X1,X2,X3)
a__if(false(),X,Y) -> mark(Y)
a__if(true(),X,Y) -> mark(X)
mark(c()) -> c()
mark(f(X)) -> a__f(mark(X))
mark(false()) -> false()
mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
mark(true()) -> true()
- Signature:
{a__f/1,a__if/3,mark/1} / {c/0,f/1,false/0,if/3,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {a__f,a__if,mark} and constructors {c,f,false,if,true}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
a__f(X) -> a__if(mark(X),c(),f(true()))
a__f(X) -> f(X)
a__if(X1,X2,X3) -> if(X1,X2,X3)
a__if(false(),X,Y) -> mark(Y)
a__if(true(),X,Y) -> mark(X)
mark(c()) -> c()
mark(f(X)) -> a__f(mark(X))
mark(false()) -> false()
mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3)
mark(true()) -> true()
- Signature:
{a__f/1,a__if/3,mark/1} / {c/0,f/1,false/0,if/3,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {a__f,a__if,mark} and constructors {c,f,false,if,true}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
mark(x){x -> f(x)} =
mark(f(x)) ->^+ a__f(mark(x))
= C[mark(x) = mark(x){}]
WORST_CASE(Omega(n^1),?)