* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a() -> n__a() activate(X) -> X activate(n__a()) -> a() activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) f(X) -> n__f(X) f(f(a())) -> c(n__f(n__g(n__f(n__a())))) g(X) -> n__g(X) - Signature: {a/0,activate/1,f/1,g/1} / {c/1,n__a/0,n__f/1,n__g/1} - Obligation: runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {c,n__a,n__f,n__g} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. a_0() -> 1 a_1() -> 2 a_1() -> 9 activate_0(3) -> 2 activate_0(6) -> 2 activate_0(7) -> 2 activate_0(8) -> 2 activate_1(3) -> 9 activate_1(6) -> 9 activate_1(7) -> 9 activate_1(8) -> 9 c_0(3) -> 2 c_0(3) -> 3 c_0(3) -> 9 c_0(6) -> 2 c_0(6) -> 3 c_0(6) -> 9 c_0(7) -> 2 c_0(7) -> 3 c_0(7) -> 9 c_0(8) -> 2 c_0(8) -> 3 c_0(8) -> 9 c_2(10) -> 2 c_2(10) -> 9 f_0(3) -> 4 f_0(6) -> 4 f_0(7) -> 4 f_0(8) -> 4 f_1(9) -> 2 f_1(9) -> 9 g_0(3) -> 5 g_0(6) -> 5 g_0(7) -> 5 g_0(8) -> 5 g_1(9) -> 2 g_1(9) -> 9 n__a_0() -> 2 n__a_0() -> 6 n__a_0() -> 9 n__a_1() -> 1 n__a_2() -> 2 n__a_2() -> 9 n__f_0(3) -> 2 n__f_0(3) -> 7 n__f_0(3) -> 9 n__f_0(6) -> 2 n__f_0(6) -> 7 n__f_0(6) -> 9 n__f_0(7) -> 2 n__f_0(7) -> 7 n__f_0(7) -> 9 n__f_0(8) -> 2 n__f_0(8) -> 7 n__f_0(8) -> 9 n__f_1(3) -> 4 n__f_1(6) -> 4 n__f_1(7) -> 4 n__f_1(8) -> 4 n__f_2(2) -> 12 n__f_2(9) -> 2 n__f_2(9) -> 9 n__f_2(11) -> 10 n__g_0(3) -> 2 n__g_0(3) -> 8 n__g_0(3) -> 9 n__g_0(6) -> 2 n__g_0(6) -> 8 n__g_0(6) -> 9 n__g_0(7) -> 2 n__g_0(7) -> 8 n__g_0(7) -> 9 n__g_0(8) -> 2 n__g_0(8) -> 8 n__g_0(8) -> 9 n__g_1(3) -> 5 n__g_1(6) -> 5 n__g_1(7) -> 5 n__g_1(8) -> 5 n__g_2(9) -> 2 n__g_2(9) -> 9 n__g_2(12) -> 11 3 -> 2 3 -> 9 6 -> 2 6 -> 9 7 -> 2 7 -> 9 8 -> 2 8 -> 9 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: a() -> n__a() activate(X) -> X activate(n__a()) -> a() activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) f(X) -> n__f(X) f(f(a())) -> c(n__f(n__g(n__f(n__a())))) g(X) -> n__g(X) - Signature: {a/0,activate/1,f/1,g/1} / {c/1,n__a/0,n__f/1,n__g/1} - Obligation: runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {c,n__a,n__f,n__g} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))