* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
goal(x) -> nestinc(x)
inc(Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),inc(xs))
inc(Nil()) -> Cons(Nil(),Nil())
nestinc(Cons(x,xs)) -> nestinc(inc(Cons(x,xs)))
nestinc(Nil()) -> number17(Nil())
number17(x) -> Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil())))))))))))))))))
- Signature:
{goal/1,inc/1,nestinc/1,number17/1} / {Cons/2,Nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {goal,inc,nestinc,number17} and constructors {Cons,Nil}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
goal(x) -> nestinc(x)
inc(Cons(x,xs)) -> Cons(Cons(Nil(),Nil()),inc(xs))
inc(Nil()) -> Cons(Nil(),Nil())
nestinc(Cons(x,xs)) -> nestinc(inc(Cons(x,xs)))
nestinc(Nil()) -> number17(Nil())
number17(x) -> Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Cons(Nil()
,Nil())))))))))))))))))
- Signature:
{goal/1,inc/1,nestinc/1,number17/1} / {Cons/2,Nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {goal,inc,nestinc,number17} and constructors {Cons,Nil}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
inc(y){y -> Cons(x,y)} =
inc(Cons(x,y)) ->^+ Cons(Cons(Nil(),Nil()),inc(y))
= C[inc(y) = inc(y){}]
WORST_CASE(Omega(n^1),?)