* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: active(c()) -> mark(d()) active(g(X)) -> mark(h(X)) active(h(d())) -> mark(g(c())) g(ok(X)) -> ok(g(X)) h(ok(X)) -> ok(h(X)) proper(c()) -> ok(c()) proper(d()) -> ok(d()) proper(g(X)) -> g(proper(X)) proper(h(X)) -> h(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,g/1,h/1,proper/1,top/1} / {c/0,d/0,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,g,h,proper,top} and constructors {c,d,mark,ok} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: active(c()) -> mark(d()) active(g(X)) -> mark(h(X)) active(h(d())) -> mark(g(c())) g(ok(X)) -> ok(g(X)) h(ok(X)) -> ok(h(X)) proper(c()) -> ok(c()) proper(d()) -> ok(d()) proper(g(X)) -> g(proper(X)) proper(h(X)) -> h(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,g/1,h/1,proper/1,top/1} / {c/0,d/0,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,g,h,proper,top} and constructors {c,d,mark,ok} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: g(x){x -> ok(x)} = g(ok(x)) ->^+ ok(g(x)) = C[g(x) = g(x){}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: active(c()) -> mark(d()) active(g(X)) -> mark(h(X)) active(h(d())) -> mark(g(c())) g(ok(X)) -> ok(g(X)) h(ok(X)) -> ok(h(X)) proper(c()) -> ok(c()) proper(d()) -> ok(d()) proper(g(X)) -> g(proper(X)) proper(h(X)) -> h(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,g/1,h/1,proper/1,top/1} / {c/0,d/0,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,g,h,proper,top} and constructors {c,d,mark,ok} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 4. The enriched problem is compatible with follwoing automaton. active_0(2) -> 1 active_0(3) -> 1 active_0(6) -> 1 active_0(7) -> 1 active_1(2) -> 14 active_1(3) -> 14 active_1(6) -> 14 active_1(7) -> 14 active_2(10) -> 15 active_2(13) -> 15 active_3(16) -> 17 active_4(18) -> 19 c_0() -> 2 c_1() -> 13 d_0() -> 3 d_1() -> 10 d_2() -> 16 d_3() -> 18 g_0(2) -> 4 g_0(3) -> 4 g_0(6) -> 4 g_0(7) -> 4 g_1(2) -> 11 g_1(3) -> 11 g_1(6) -> 11 g_1(7) -> 11 h_0(2) -> 5 h_0(3) -> 5 h_0(6) -> 5 h_0(7) -> 5 h_1(2) -> 12 h_1(3) -> 12 h_1(6) -> 12 h_1(7) -> 12 mark_0(2) -> 6 mark_0(3) -> 6 mark_0(6) -> 6 mark_0(7) -> 6 mark_1(10) -> 1 mark_1(10) -> 14 mark_2(16) -> 15 ok_0(2) -> 7 ok_0(3) -> 7 ok_0(6) -> 7 ok_0(7) -> 7 ok_1(10) -> 8 ok_1(10) -> 14 ok_1(11) -> 4 ok_1(11) -> 11 ok_1(12) -> 5 ok_1(12) -> 12 ok_1(13) -> 8 ok_1(13) -> 14 ok_2(16) -> 15 ok_3(18) -> 17 proper_0(2) -> 8 proper_0(3) -> 8 proper_0(6) -> 8 proper_0(7) -> 8 proper_1(2) -> 14 proper_1(3) -> 14 proper_1(6) -> 14 proper_1(7) -> 14 proper_2(10) -> 15 proper_3(16) -> 17 top_0(2) -> 9 top_0(3) -> 9 top_0(6) -> 9 top_0(7) -> 9 top_1(14) -> 9 top_2(15) -> 9 top_3(17) -> 9 top_4(19) -> 9 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: active(c()) -> mark(d()) active(g(X)) -> mark(h(X)) active(h(d())) -> mark(g(c())) g(ok(X)) -> ok(g(X)) h(ok(X)) -> ok(h(X)) proper(c()) -> ok(c()) proper(d()) -> ok(d()) proper(g(X)) -> g(proper(X)) proper(h(X)) -> h(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,g/1,h/1,proper/1,top/1} / {c/0,d/0,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,g,h,proper,top} and constructors {c,d,mark,ok} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))