* 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 = perSymbol, enrichment = match} + Details: The problem is match-bounded by 6. The enriched problem is compatible with follwoing automaton. active_0(2) -> 1 active_0(5) -> 1 active_0(6) -> 1 active_1(2) -> 14 active_1(5) -> 14 active_1(6) -> 14 active_2(11) -> 15 active_3(26) -> 21 active_4(29) -> 30 active_5(27) -> 33 active_6(36) -> 37 c_0() -> 2 c_1() -> 11 c_2() -> 18 c_3() -> 25 c_4() -> 35 f_0(2) -> 3 f_0(5) -> 3 f_0(6) -> 3 f_1(2) -> 12 f_1(5) -> 12 f_1(6) -> 12 f_1(10) -> 9 f_2(17) -> 16 f_2(19) -> 15 f_3(22) -> 21 f_3(24) -> 26 f_4(27) -> 29 g_0(2) -> 4 g_0(5) -> 4 g_0(6) -> 4 g_1(2) -> 13 g_1(5) -> 13 g_1(6) -> 13 g_1(11) -> 10 g_2(18) -> 17 g_2(20) -> 19 g_3(18) -> 24 g_3(23) -> 22 g_4(18) -> 28 g_4(25) -> 27 g_5(25) -> 31 g_5(32) -> 30 g_5(35) -> 36 g_6(34) -> 33 mark_0(2) -> 5 mark_0(5) -> 5 mark_0(6) -> 5 mark_1(9) -> 1 mark_1(9) -> 14 mark_2(16) -> 15 mark_4(28) -> 21 mark_5(31) -> 30 ok_0(2) -> 6 ok_0(5) -> 6 ok_0(6) -> 6 ok_1(11) -> 7 ok_1(11) -> 14 ok_1(12) -> 3 ok_1(12) -> 12 ok_1(13) -> 4 ok_1(13) -> 13 ok_2(18) -> 20 ok_3(24) -> 19 ok_3(25) -> 23 ok_3(25) -> 32 ok_3(26) -> 15 ok_4(27) -> 22 ok_4(27) -> 30 ok_4(29) -> 21 ok_4(35) -> 34 ok_5(36) -> 33 proper_0(2) -> 7 proper_0(5) -> 7 proper_0(6) -> 7 proper_1(2) -> 14 proper_1(5) -> 14 proper_1(6) -> 14 proper_2(9) -> 15 proper_2(10) -> 19 proper_2(11) -> 20 proper_3(16) -> 21 proper_3(17) -> 22 proper_3(18) -> 23 proper_4(28) -> 30 proper_5(18) -> 32 proper_5(31) -> 33 proper_6(25) -> 34 top_0(2) -> 8 top_0(5) -> 8 top_0(6) -> 8 top_1(14) -> 8 top_2(15) -> 8 top_3(21) -> 8 top_4(30) -> 8 top_5(33) -> 8 top_6(37) -> 8 * 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))