* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: active(a()) -> mark(b()) f(mark(X1),X2) -> mark(f(X1,X2)) f(ok(X1),ok(X2)) -> ok(f(X1,X2)) g(mark(X1),X2) -> mark(g(X1,X2)) g(ok(X1),ok(X2)) -> ok(g(X1,X2)) h(mark(X)) -> mark(h(X)) h(ok(X)) -> ok(h(X)) proper(a()) -> ok(a()) proper(b()) -> ok(b()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/2,g/2,h/1,proper/1,top/1} / {a/0,b/0,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,f,g,h,proper,top} and constructors {a,b,mark,ok} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 5. The enriched problem is compatible with follwoing automaton. a_0() -> 2 a_1() -> 3 a_2() -> 7 active_0(2) -> 1 active_1(2) -> 4 active_2(3) -> 5 active_3(6) -> 8 active_3(7) -> 8 active_4(9) -> 10 active_5(11) -> 12 b_0() -> 2 b_1() -> 3 b_2() -> 6 b_3() -> 9 b_4() -> 11 f_0(2,2) -> 1 f_1(2,2) -> 3 g_0(2,2) -> 1 g_1(2,2) -> 3 h_0(2) -> 1 h_1(2) -> 3 mark_0(2) -> 2 mark_1(3) -> 1 mark_1(3) -> 3 mark_1(3) -> 4 mark_2(6) -> 5 mark_3(9) -> 8 ok_0(2) -> 2 ok_1(3) -> 1 ok_1(3) -> 3 ok_1(3) -> 4 ok_2(6) -> 5 ok_2(7) -> 5 ok_3(9) -> 8 ok_4(11) -> 10 proper_0(2) -> 1 proper_1(2) -> 4 proper_2(3) -> 5 proper_3(6) -> 8 proper_4(9) -> 10 top_0(2) -> 1 top_1(4) -> 1 top_2(5) -> 1 top_3(8) -> 1 top_4(10) -> 1 top_5(12) -> 1 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: active(a()) -> mark(b()) f(mark(X1),X2) -> mark(f(X1,X2)) f(ok(X1),ok(X2)) -> ok(f(X1,X2)) g(mark(X1),X2) -> mark(g(X1,X2)) g(ok(X1),ok(X2)) -> ok(g(X1,X2)) h(mark(X)) -> mark(h(X)) h(ok(X)) -> ok(h(X)) proper(a()) -> ok(a()) proper(b()) -> ok(b()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/2,g/2,h/1,proper/1,top/1} / {a/0,b/0,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,f,g,h,proper,top} and constructors {a,b,mark,ok} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))