* 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),?)