* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: active(b()) -> mark(c()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) g(mark(X)) -> mark(g(X)) g(ok(X)) -> ok(g(X)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/3,g/1,proper/1,top/1} / {b/0,c/0,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {b,c,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. active_0(2) -> 1 active_1(2) -> 5 active_2(3) -> 6 active_3(7) -> 9 active_3(8) -> 9 active_4(10) -> 11 active_5(12) -> 13 b_0() -> 2 b_1() -> 3 b_2() -> 8 c_0() -> 2 c_1() -> 3 c_2() -> 7 c_3() -> 10 c_4() -> 12 f_0(2,2,2) -> 1 f_1(2,2,2) -> 4 g_0(2) -> 1 g_1(2) -> 3 mark_0(2) -> 2 mark_1(3) -> 1 mark_1(3) -> 3 mark_1(3) -> 5 mark_2(7) -> 6 mark_3(10) -> 9 ok_0(2) -> 2 ok_1(3) -> 1 ok_1(3) -> 3 ok_1(3) -> 5 ok_1(4) -> 1 ok_1(4) -> 4 ok_2(7) -> 6 ok_2(8) -> 6 ok_3(10) -> 9 ok_4(12) -> 11 proper_0(2) -> 1 proper_1(2) -> 5 proper_2(3) -> 6 proper_3(7) -> 9 proper_4(10) -> 11 top_0(2) -> 1 top_1(5) -> 1 top_2(6) -> 1 top_3(9) -> 1 top_4(11) -> 1 top_5(13) -> 1 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: active(b()) -> mark(c()) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) g(mark(X)) -> mark(g(X)) g(ok(X)) -> ok(g(X)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/3,g/1,proper/1,top/1} / {b/0,c/0,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {b,c,mark,ok} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))