* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__adx(X)) -> adx(activate(X)) activate(n__incr(X)) -> incr(activate(X)) activate(n__zeros()) -> zeros() adx(X) -> n__adx(X) adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L)))) adx(nil()) -> nil() head(cons(X,L)) -> X incr(X) -> n__incr(X) incr(cons(X,L)) -> cons(s(X),n__incr(activate(L))) incr(nil()) -> nil() nats() -> adx(zeros()) tail(cons(X,L)) -> activate(L) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {activate/1,adx/1,head/1,incr/1,nats/0,tail/1,zeros/0} / {0/0,cons/2,n__adx/1,n__incr/1,n__zeros/0,nil/0 ,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,adx,head,incr,nats,tail ,zeros} and constructors {0,cons,n__adx,n__incr,n__zeros,nil,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__adx(X)) -> adx(activate(X)) activate(n__incr(X)) -> incr(activate(X)) activate(n__zeros()) -> zeros() adx(X) -> n__adx(X) adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L)))) adx(nil()) -> nil() head(cons(X,L)) -> X incr(X) -> n__incr(X) incr(cons(X,L)) -> cons(s(X),n__incr(activate(L))) incr(nil()) -> nil() nats() -> adx(zeros()) tail(cons(X,L)) -> activate(L) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {activate/1,adx/1,head/1,incr/1,nats/0,tail/1,zeros/0} / {0/0,cons/2,n__adx/1,n__incr/1,n__zeros/0,nil/0 ,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,adx,head,incr,nats,tail ,zeros} and constructors {0,cons,n__adx,n__incr,n__zeros,nil,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: activate(x){x -> n__adx(x)} = activate(n__adx(x)) ->^+ adx(activate(x)) = C[activate(x) = activate(x){}] WORST_CASE(Omega(n^1),?)