* 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),?)