* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: active(c()) -> mark(f(g(c()))) active(f(g(X))) -> mark(g(X)) f(ok(X)) -> ok(f(X)) g(ok(X)) -> ok(g(X)) proper(c()) -> ok(c()) 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} / {c/0,mark/1,ok/1} - Obligation: runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {c,mark,ok} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 6. The enriched problem is compatible with follwoing automaton. active_0(2) -> 1 active_1(2) -> 7 active_2(5) -> 8 active_3(19) -> 14 active_4(22) -> 23 active_5(20) -> 26 active_6(29) -> 30 c_0() -> 2 c_1() -> 5 c_2() -> 11 c_3() -> 18 c_4() -> 28 f_0(2) -> 1 f_1(2) -> 6 f_1(4) -> 3 f_2(10) -> 9 f_2(12) -> 8 f_3(15) -> 14 f_3(17) -> 19 f_4(20) -> 22 g_0(2) -> 1 g_1(2) -> 6 g_1(5) -> 4 g_2(11) -> 10 g_2(13) -> 12 g_3(11) -> 17 g_3(16) -> 15 g_4(11) -> 21 g_4(18) -> 20 g_5(18) -> 24 g_5(25) -> 23 g_5(28) -> 29 g_6(27) -> 26 mark_0(2) -> 2 mark_1(3) -> 1 mark_1(3) -> 7 mark_2(9) -> 8 mark_4(21) -> 14 mark_5(24) -> 23 ok_0(2) -> 2 ok_1(5) -> 1 ok_1(5) -> 7 ok_1(6) -> 1 ok_1(6) -> 6 ok_2(11) -> 13 ok_3(17) -> 12 ok_3(18) -> 16 ok_3(18) -> 25 ok_3(19) -> 8 ok_4(20) -> 15 ok_4(20) -> 23 ok_4(22) -> 14 ok_4(28) -> 27 ok_5(29) -> 26 proper_0(2) -> 1 proper_1(2) -> 7 proper_2(3) -> 8 proper_2(4) -> 12 proper_2(5) -> 13 proper_3(9) -> 14 proper_3(10) -> 15 proper_3(11) -> 16 proper_4(21) -> 23 proper_5(11) -> 25 proper_5(24) -> 26 proper_6(18) -> 27 top_0(2) -> 1 top_1(7) -> 1 top_2(8) -> 1 top_3(14) -> 1 top_4(23) -> 1 top_5(26) -> 1 top_6(30) -> 1 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: active(c()) -> mark(f(g(c()))) active(f(g(X))) -> mark(g(X)) f(ok(X)) -> ok(f(X)) g(ok(X)) -> ok(g(X)) proper(c()) -> ok(c()) 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} / {c/0,mark/1,ok/1} - Obligation: runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {c,mark,ok} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))