* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
eq(X,Y) -> false()
eq(0(),0()) -> true()
eq(s(X),s(Y)) -> eq(X,Y)
inf(X) -> cons(X,inf(s(X)))
length(cons(X,L)) -> s(length(L))
length(nil()) -> 0()
take(0(),X) -> nil()
take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
- Signature:
{eq/2,inf/1,length/1,take/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {eq,inf,length,take} and constructors {0,cons,false,nil,s
,true}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
eq(X,Y) -> false()
eq(0(),0()) -> true()
eq(s(X),s(Y)) -> eq(X,Y)
inf(X) -> cons(X,inf(s(X)))
length(cons(X,L)) -> s(length(L))
length(nil()) -> 0()
take(0(),X) -> nil()
take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
- Signature:
{eq/2,inf/1,length/1,take/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {eq,inf,length,take} and constructors {0,cons,false,nil,s
,true}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
eq(x,y){x -> s(x),y -> s(y)} =
eq(s(x),s(y)) ->^+ eq(x,y)
= C[eq(x,y) = eq(x,y){}]
WORST_CASE(Omega(n^1),?)