* Step 1: ToInnermost 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: runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {n__a,n__f,n__g} + Applied Processor: ToInnermost + Details: switch to innermost, as the system is overlay and right linear and does not contain weak rules * Step 2: 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 = minimal, enrichment = match} + Details: The problem is match-bounded by 3. The enriched problem is compatible with follwoing automaton. a_0() -> 1 a_1() -> 1 a_1() -> 3 activate_0(2) -> 1 activate_1(2) -> 3 activate_1(4) -> 3 activate_2(4) -> 5 f_0(2) -> 1 f_1(2) -> 1 f_1(2) -> 3 f_1(3) -> 5 f_2(1) -> 3 f_2(1) -> 5 g_0(2) -> 1 g_1(3) -> 1 g_1(3) -> 3 g_2(5) -> 3 n__a_0() -> 1 n__a_0() -> 2 n__a_0() -> 3 n__a_1() -> 1 n__a_2() -> 1 n__a_2() -> 3 n__f_0(2) -> 1 n__f_0(2) -> 2 n__f_0(2) -> 3 n__f_1(1) -> 3 n__f_1(1) -> 4 n__f_1(1) -> 5 n__f_1(2) -> 1 n__f_2(2) -> 1 n__f_2(2) -> 3 n__f_2(3) -> 5 n__f_3(1) -> 3 n__f_3(1) -> 5 n__g_0(2) -> 1 n__g_0(2) -> 2 n__g_0(2) -> 3 n__g_1(2) -> 1 n__g_1(4) -> 1 n__g_1(4) -> 2 n__g_1(4) -> 3 n__g_2(3) -> 1 n__g_2(3) -> 3 n__g_2(5) -> 1 n__g_3(5) -> 3 2 -> 1 2 -> 3 4 -> 3 4 -> 5 * Step 3: 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))