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