* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__from(X)) -> from(activate(X)) activate(n__nil()) -> nil() activate(n__s(X)) -> s(activate(X)) cons(X1,X2) -> n__cons(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) length(n__cons(X,Y)) -> s(length1(activate(Y))) length(n__nil()) -> 0() length1(X) -> length(activate(X)) nil() -> n__nil() s(X) -> n__s(X) - Signature: {activate/1,cons/2,from/1,length/1,length1/1,nil/0,s/1} / {0/0,n__cons/2,n__from/1,n__nil/0,n__s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,cons,from,length,length1,nil ,s} and constructors {0,n__cons,n__from,n__nil,n__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__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__from(X)) -> from(activate(X)) activate(n__nil()) -> nil() activate(n__s(X)) -> s(activate(X)) cons(X1,X2) -> n__cons(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) length(n__cons(X,Y)) -> s(length1(activate(Y))) length(n__nil()) -> 0() length1(X) -> length(activate(X)) nil() -> n__nil() s(X) -> n__s(X) - Signature: {activate/1,cons/2,from/1,length/1,length1/1,nil/0,s/1} / {0/0,n__cons/2,n__from/1,n__nil/0,n__s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,cons,from,length,length1,nil ,s} and constructors {0,n__cons,n__from,n__nil,n__s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: activate(x){x -> n__cons(x,y)} = activate(n__cons(x,y)) ->^+ cons(activate(x),y) = C[activate(x) = activate(x){}] WORST_CASE(Omega(n^1),?)