* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__add(X1,X2)) -> add(activate(X1),X2) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(X) activate(n__s(X)) -> s(X) add(X1,X2) -> n__add(X1,X2) add(0(),X) -> activate(X) add(s(X),Y) -> s(n__add(activate(X),activate(Y))) and(false(),Y) -> false() and(true(),X) -> activate(X) first(X1,X2) -> n__first(X1,X2) first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(activate(Y),n__first(activate(X),activate(Z))) from(X) -> cons(activate(X),n__from(n__s(activate(X)))) from(X) -> n__from(X) if(false(),X,Y) -> activate(Y) if(true(),X,Y) -> activate(X) s(X) -> n__s(X) - Signature: {activate/1,add/2,and/2,first/2,from/1,if/3,s/1} / {0/0,cons/2,false/0,n__add/2,n__first/2,n__from/1,n__s/1 ,nil/0,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate,add,and,first,from,if,s} and constructors {0 ,cons,false,n__add,n__first,n__from,n__s,nil,true} + 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__add(X1,X2)) -> add(activate(X1),X2) activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(X) activate(n__s(X)) -> s(X) add(X1,X2) -> n__add(X1,X2) add(0(),X) -> activate(X) add(s(X),Y) -> s(n__add(activate(X),activate(Y))) and(false(),Y) -> false() and(true(),X) -> activate(X) first(X1,X2) -> n__first(X1,X2) first(0(),X) -> nil() first(s(X),cons(Y,Z)) -> cons(activate(Y),n__first(activate(X),activate(Z))) from(X) -> cons(activate(X),n__from(n__s(activate(X)))) from(X) -> n__from(X) if(false(),X,Y) -> activate(Y) if(true(),X,Y) -> activate(X) s(X) -> n__s(X) - Signature: {activate/1,add/2,and/2,first/2,from/1,if/3,s/1} / {0/0,cons/2,false/0,n__add/2,n__first/2,n__from/1,n__s/1 ,nil/0,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate,add,and,first,from,if,s} and constructors {0 ,cons,false,n__add,n__first,n__from,n__s,nil,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: activate(x){x -> n__add(x,y)} = activate(n__add(x,y)) ->^+ add(activate(x),y) = C[activate(x) = activate(x){}] WORST_CASE(Omega(n^1),?)