* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
add0(x,Nil()) -> x
add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
goal(x,y) -> power(x,y)
mult(x,Nil()) -> Nil()
mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
power(x,Nil()) -> Cons(Nil(),Nil())
power(x',Cons(x,xs)) -> mult(x',power(x',xs))
- Signature:
{add0/2,goal/2,mult/2,power/2} / {Cons/2,Nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {add0,goal,mult,power} and constructors {Cons,Nil}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
add0(x,Nil()) -> x
add0(x',Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),add0(x',xs))
goal(x,y) -> power(x,y)
mult(x,Nil()) -> Nil()
mult(x',Cons(x,xs)) -> add0(x',mult(x',xs))
power(x,Nil()) -> Cons(Nil(),Nil())
power(x',Cons(x,xs)) -> mult(x',power(x',xs))
- Signature:
{add0/2,goal/2,mult/2,power/2} / {Cons/2,Nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {add0,goal,mult,power} and constructors {Cons,Nil}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
add0(x,z){z -> Cons(y,z)} =
add0(x,Cons(y,z)) ->^+ Cons(Cons(Nil(),Nil()),add0(x,z))
= C[add0(x,z) = add0(x,z){}]
WORST_CASE(Omega(n^1),?)