* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
dbl(0()) -> 0()
dbl(s(X)) -> s(s(dbl(X)))
dbl1(0()) -> 01()
dbl1(s(X)) -> s1(s1(dbl1(X)))
dbls(cons(X,Y)) -> cons(dbl(X),dbls(Y))
dbls(nil()) -> nil()
from(X) -> cons(X,from(s(X)))
indx(cons(X,Y),Z) -> cons(sel(X,Z),indx(Y,Z))
indx(nil(),X) -> nil()
quote(0()) -> 01()
quote(dbl(X)) -> dbl1(X)
quote(s(X)) -> s1(quote(X))
quote(sel(X,Y)) -> sel1(X,Y)
sel(0(),cons(X,Y)) -> X
sel(s(X),cons(Y,Z)) -> sel(X,Z)
sel1(0(),cons(X,Y)) -> X
sel1(s(X),cons(Y,Z)) -> sel1(X,Z)
- Signature:
{dbl/1,dbl1/1,dbls/1,from/1,indx/2,quote/1,sel/2,sel1/2} / {0/0,01/0,cons/2,nil/0,s/1,s1/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {dbl,dbl1,dbls,from,indx,quote,sel
,sel1} and constructors {0,01,cons,nil,s,s1}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
dbl(0()) -> 0()
dbl(s(X)) -> s(s(dbl(X)))
dbl1(0()) -> 01()
dbl1(s(X)) -> s1(s1(dbl1(X)))
dbls(cons(X,Y)) -> cons(dbl(X),dbls(Y))
dbls(nil()) -> nil()
from(X) -> cons(X,from(s(X)))
indx(cons(X,Y),Z) -> cons(sel(X,Z),indx(Y,Z))
indx(nil(),X) -> nil()
quote(0()) -> 01()
quote(dbl(X)) -> dbl1(X)
quote(s(X)) -> s1(quote(X))
quote(sel(X,Y)) -> sel1(X,Y)
sel(0(),cons(X,Y)) -> X
sel(s(X),cons(Y,Z)) -> sel(X,Z)
sel1(0(),cons(X,Y)) -> X
sel1(s(X),cons(Y,Z)) -> sel1(X,Z)
- Signature:
{dbl/1,dbl1/1,dbls/1,from/1,indx/2,quote/1,sel/2,sel1/2} / {0/0,01/0,cons/2,nil/0,s/1,s1/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {dbl,dbl1,dbls,from,indx,quote,sel
,sel1} and constructors {0,01,cons,nil,s,s1}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
dbl(x){x -> s(x)} =
dbl(s(x)) ->^+ s(s(dbl(x)))
= C[dbl(x) = dbl(x){}]
WORST_CASE(Omega(n^1),?)