WORST_CASE(?,O(n^1)) * Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: filter(cons(X),0(),M) -> cons(0()) filter(cons(X),s(N),M) -> cons(X) nats(N) -> cons(N) sieve(cons(0())) -> cons(0()) sieve(cons(s(N))) -> cons(s(N)) zprimes() -> sieve(nats(s(s(0())))) - Signature: {filter/3,nats/1,sieve/1,zprimes/0} / {0/0,cons/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {filter,nats,sieve,zprimes} and constructors {0,cons,s} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. 0_0() -> 2 0_1() -> 3 cons_0(2) -> 2 cons_1(2) -> 1 cons_1(3) -> 1 cons_2(5) -> 4 cons_2(7) -> 1 filter_0(2,2,2) -> 1 nats_0(2) -> 1 nats_1(5) -> 4 s_0(2) -> 2 s_1(2) -> 2 s_1(3) -> 6 s_1(6) -> 5 s_2(6) -> 7 sieve_0(2) -> 1 sieve_1(4) -> 1 zprimes_0() -> 1 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: filter(cons(X),0(),M) -> cons(0()) filter(cons(X),s(N),M) -> cons(X) nats(N) -> cons(N) sieve(cons(0())) -> cons(0()) sieve(cons(s(N))) -> cons(s(N)) zprimes() -> sieve(nats(s(s(0())))) - Signature: {filter/3,nats/1,sieve/1,zprimes/0} / {0/0,cons/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {filter,nats,sieve,zprimes} and constructors {0,cons,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))