* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: 0() -> n__0() activate(X) -> X activate(n__0()) -> 0() activate(n__adx(X)) -> adx(activate(X)) activate(n__incr(X)) -> incr(activate(X)) activate(n__s(X)) -> s(X) activate(n__zeros()) -> zeros() adx(X) -> n__adx(X) adx(cons(X,Y)) -> incr(cons(activate(X),n__adx(activate(Y)))) hd(cons(X,Y)) -> activate(X) incr(X) -> n__incr(X) incr(cons(X,Y)) -> cons(n__s(activate(X)),n__incr(activate(Y))) nats() -> adx(zeros()) s(X) -> n__s(X) tl(cons(X,Y)) -> activate(Y) zeros() -> cons(n__0(),n__zeros()) zeros() -> n__zeros() - Signature: {0/0,activate/1,adx/1,hd/1,incr/1,nats/0,s/1,tl/1,zeros/0} / {cons/2,n__0/0,n__adx/1,n__incr/1,n__s/1 ,n__zeros/0} - Obligation: innermost runtime complexity wrt. defined symbols {0,activate,adx,hd,incr,nats,s,tl ,zeros} and constructors {cons,n__0,n__adx,n__incr,n__s,n__zeros} + 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__adx(X)) -> adx(activate(X)) activate(n__incr(X)) -> incr(activate(X)) activate(n__s(X)) -> s(X) activate(n__zeros()) -> zeros() adx(X) -> n__adx(X) adx(cons(X,Y)) -> incr(cons(activate(X),n__adx(activate(Y)))) hd(cons(X,Y)) -> activate(X) incr(X) -> n__incr(X) incr(cons(X,Y)) -> cons(n__s(activate(X)),n__incr(activate(Y))) nats() -> adx(zeros()) s(X) -> n__s(X) tl(cons(X,Y)) -> activate(Y) zeros() -> cons(n__0(),n__zeros()) zeros() -> n__zeros() - Signature: {0/0,activate/1,adx/1,hd/1,incr/1,nats/0,s/1,tl/1,zeros/0} / {cons/2,n__0/0,n__adx/1,n__incr/1,n__s/1 ,n__zeros/0} - Obligation: innermost runtime complexity wrt. defined symbols {0,activate,adx,hd,incr,nats,s,tl ,zeros} and constructors {cons,n__0,n__adx,n__incr,n__s,n__zeros} + 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),?)