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