* 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(X) activate(n__g(X)) -> g(activate(X)) f(X) -> n__f(X) f(n__f(n__a())) -> f(n__g(n__f(n__a()))) g(X) -> n__g(X) - Signature: {a/0,activate/1,f/1,g/1} / {n__a/0,n__f/1,n__g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {n__a,n__f,n__g} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 3. The enriched problem is compatible with follwoing automaton. a_0() -> 1 a_1() -> 2 a_1() -> 8 activate_0(5) -> 2 activate_0(6) -> 2 activate_0(7) -> 2 activate_1(5) -> 8 activate_1(6) -> 8 activate_1(7) -> 8 activate_1(9) -> 8 activate_2(9) -> 12 f_0(5) -> 3 f_0(6) -> 3 f_0(7) -> 3 f_1(5) -> 2 f_1(5) -> 3 f_1(5) -> 8 f_1(6) -> 2 f_1(6) -> 8 f_1(7) -> 2 f_1(7) -> 8 f_2(1) -> 8 f_2(1) -> 12 g_0(5) -> 4 g_0(6) -> 4 g_0(7) -> 4 g_1(8) -> 2 g_1(8) -> 8 g_2(12) -> 8 n__a_0() -> 2 n__a_0() -> 5 n__a_0() -> 8 n__a_1() -> 1 n__a_2() -> 2 n__a_2() -> 8 n__f_0(5) -> 2 n__f_0(5) -> 6 n__f_0(5) -> 8 n__f_0(6) -> 2 n__f_0(6) -> 6 n__f_0(6) -> 8 n__f_0(7) -> 2 n__f_0(7) -> 6 n__f_0(7) -> 8 n__f_1(1) -> 8 n__f_1(1) -> 9 n__f_1(1) -> 12 n__f_1(5) -> 3 n__f_1(6) -> 3 n__f_1(7) -> 3 n__f_2(5) -> 2 n__f_2(5) -> 3 n__f_2(5) -> 8 n__f_2(6) -> 2 n__f_2(6) -> 8 n__f_2(7) -> 2 n__f_2(7) -> 8 n__f_3(1) -> 8 n__f_3(1) -> 12 n__g_0(5) -> 2 n__g_0(5) -> 7 n__g_0(5) -> 8 n__g_0(6) -> 2 n__g_0(6) -> 7 n__g_0(6) -> 8 n__g_0(7) -> 2 n__g_0(7) -> 7 n__g_0(7) -> 8 n__g_1(5) -> 4 n__g_1(6) -> 4 n__g_1(7) -> 4 n__g_1(9) -> 2 n__g_1(9) -> 5 n__g_1(9) -> 8 n__g_2(8) -> 2 n__g_2(8) -> 8 n__g_3(12) -> 8 5 -> 2 5 -> 8 6 -> 2 6 -> 8 7 -> 2 7 -> 8 9 -> 8 9 -> 12 * 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(X) activate(n__g(X)) -> g(activate(X)) f(X) -> n__f(X) f(n__f(n__a())) -> f(n__g(n__f(n__a()))) g(X) -> n__g(X) - Signature: {a/0,activate/1,f/1,g/1} / {n__a/0,n__f/1,n__g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {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))