* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: active(d()) -> m(b()) active(d()) -> mark(c()) f(x,y,mark(z)) -> mark(f(x,y,z)) f(ok(x),ok(y),ok(z)) -> ok(f(x,y,z)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) proper(d()) -> ok(d()) top(mark(x)) -> top(proper(x)) top(ok(x)) -> top(active(x)) - Signature: {active/1,f/3,proper/1,top/1} / {b/0,c/0,d/0,m/1,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,f,proper,top} and constructors {b,c,d,m,mark,ok} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 4. The enriched problem is compatible with follwoing automaton. active_0(2) -> 1 active_1(2) -> 5 active_2(3) -> 6 active_2(4) -> 6 active_3(8) -> 9 active_4(10) -> 11 b_0() -> 2 b_1() -> 3 b_2() -> 7 c_0() -> 2 c_1() -> 4 c_2() -> 8 c_3() -> 10 d_0() -> 2 d_1() -> 3 f_0(2,2,2) -> 1 f_1(2,2,2) -> 4 m_0(2) -> 2 m_1(3) -> 1 m_1(3) -> 5 m_2(7) -> 6 mark_0(2) -> 2 mark_1(4) -> 1 mark_1(4) -> 4 mark_1(4) -> 5 mark_2(8) -> 6 ok_0(2) -> 2 ok_1(3) -> 1 ok_1(3) -> 5 ok_1(4) -> 1 ok_1(4) -> 4 ok_1(4) -> 5 ok_2(8) -> 6 ok_3(10) -> 9 proper_0(2) -> 1 proper_1(2) -> 5 proper_2(4) -> 6 proper_3(8) -> 9 top_0(2) -> 1 top_1(5) -> 1 top_2(6) -> 1 top_3(9) -> 1 top_4(11) -> 1 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: active(d()) -> m(b()) active(d()) -> mark(c()) f(x,y,mark(z)) -> mark(f(x,y,z)) f(ok(x),ok(y),ok(z)) -> ok(f(x,y,z)) proper(b()) -> ok(b()) proper(c()) -> ok(c()) proper(d()) -> ok(d()) top(mark(x)) -> top(proper(x)) top(ok(x)) -> top(active(x)) - Signature: {active/1,f/3,proper/1,top/1} / {b/0,c/0,d/0,m/1,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,f,proper,top} and constructors {b,c,d,m,mark,ok} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))