* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) f(X) -> cons(X,n__f(n__g(X))) f(X) -> n__f(X) g(X) -> n__g(X) g(0()) -> s(0()) g(s(X)) -> s(s(g(X))) sel(0(),cons(X,Y)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) - Signature: {activate/1,f/1,g/1,sel/2} / {0/0,cons/2,n__f/1,n__g/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,f,g,sel} and constructors {0,cons,n__f,n__g,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) f(X) -> cons(X,n__f(n__g(X))) f(X) -> n__f(X) g(X) -> n__g(X) g(0()) -> s(0()) g(s(X)) -> s(s(g(X))) sel(0(),cons(X,Y)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) - Signature: {activate/1,f/1,g/1,sel/2} / {0/0,cons/2,n__f/1,n__g/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,f,g,sel} and constructors {0,cons,n__f,n__g,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: activate(x){x -> n__f(x)} = activate(n__f(x)) ->^+ f(activate(x)) = C[activate(x) = activate(x){}] WORST_CASE(Omega(n^1),?)