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