* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: 0() -> n__0() activate(X) -> X activate(n__0()) -> 0() activate(n__inf(X)) -> inf(activate(X)) activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(X) activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) eq(X,Y) -> false() eq(n__0(),n__0()) -> true() eq(n__s(X),n__s(Y)) -> eq(activate(X),activate(Y)) inf(X) -> cons(X,n__inf(n__s(X))) inf(X) -> n__inf(X) length(X) -> n__length(X) length(cons(X,L)) -> s(n__length(activate(L))) length(nil()) -> 0() s(X) -> n__s(X) take(X1,X2) -> n__take(X1,X2) take(0(),X) -> nil() take(s(X),cons(Y,L)) -> cons(activate(Y),n__take(activate(X),activate(L))) - Signature: {0/0,activate/1,eq/2,inf/1,length/1,s/1,take/2} / {cons/2,false/0,n__0/0,n__inf/1,n__length/1,n__s/1 ,n__take/2,nil/0,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {0,activate,eq,inf,length,s,take} and constructors {cons ,false,n__0,n__inf,n__length,n__s,n__take,nil,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: 0() -> n__0() activate(X) -> X activate(n__0()) -> 0() activate(n__inf(X)) -> inf(activate(X)) activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(X) activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) eq(X,Y) -> false() eq(n__0(),n__0()) -> true() eq(n__s(X),n__s(Y)) -> eq(activate(X),activate(Y)) inf(X) -> cons(X,n__inf(n__s(X))) inf(X) -> n__inf(X) length(X) -> n__length(X) length(cons(X,L)) -> s(n__length(activate(L))) length(nil()) -> 0() s(X) -> n__s(X) take(X1,X2) -> n__take(X1,X2) take(0(),X) -> nil() take(s(X),cons(Y,L)) -> cons(activate(Y),n__take(activate(X),activate(L))) - Signature: {0/0,activate/1,eq/2,inf/1,length/1,s/1,take/2} / {cons/2,false/0,n__0/0,n__inf/1,n__length/1,n__s/1 ,n__take/2,nil/0,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {0,activate,eq,inf,length,s,take} and constructors {cons ,false,n__0,n__inf,n__length,n__s,n__take,nil,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: activate(x){x -> n__inf(x)} = activate(n__inf(x)) ->^+ inf(activate(x)) = C[activate(x) = activate(x){}] WORST_CASE(Omega(n^1),?)