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