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