* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: active(f(f(a()))) -> mark(f(g(f(a())))) active(g(X)) -> g(active(X)) f(ok(X)) -> ok(f(X)) g(mark(X)) -> mark(g(X)) g(ok(X)) -> ok(g(X)) proper(a()) -> ok(a()) proper(f(X)) -> f(proper(X)) proper(g(X)) -> g(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1} - Obligation: runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {a,mark,ok} + 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() -> 11 active_0(1) -> 2 active_0(5) -> 2 active_0(6) -> 2 active_1(1) -> 12 active_1(5) -> 12 active_1(6) -> 12 active_2(11) -> 13 f_0(1) -> 3 f_0(5) -> 3 f_0(6) -> 3 f_1(1) -> 9 f_1(5) -> 9 f_1(6) -> 9 g_0(1) -> 4 g_0(5) -> 4 g_0(6) -> 4 g_1(1) -> 10 g_1(5) -> 10 g_1(6) -> 10 mark_0(1) -> 5 mark_0(5) -> 5 mark_0(6) -> 5 mark_1(10) -> 4 mark_1(10) -> 10 ok_0(1) -> 6 ok_0(5) -> 6 ok_0(6) -> 6 ok_1(9) -> 3 ok_1(9) -> 9 ok_1(10) -> 4 ok_1(10) -> 10 ok_1(11) -> 7 ok_1(11) -> 12 proper_0(1) -> 7 proper_0(5) -> 7 proper_0(6) -> 7 proper_1(1) -> 12 proper_1(5) -> 12 proper_1(6) -> 12 top_0(1) -> 8 top_0(5) -> 8 top_0(6) -> 8 top_1(12) -> 8 top_2(13) -> 8 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: active(f(f(a()))) -> mark(f(g(f(a())))) active(g(X)) -> g(active(X)) f(ok(X)) -> ok(f(X)) g(mark(X)) -> mark(g(X)) g(ok(X)) -> ok(g(X)) proper(a()) -> ok(a()) proper(f(X)) -> f(proper(X)) proper(g(X)) -> g(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1} - Obligation: runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {a,mark,ok} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))