* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: active(cons(X1,X2)) -> cons(active(X1),X2) active(f(X)) -> f(active(X)) active(f(0())) -> mark(cons(0(),f(s(0())))) active(f(s(0()))) -> mark(f(p(s(0())))) active(p(X)) -> p(active(X)) active(p(s(X))) -> mark(X) active(s(X)) -> s(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) p(mark(X)) -> mark(p(X)) p(ok(X)) -> ok(p(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(f(X)) -> f(proper(X)) proper(p(X)) -> p(proper(X)) proper(s(X)) -> s(proper(X)) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,cons/2,f/1,p/1,proper/1,s/1,top/1} / {0/0,mark/1,ok/1} - Obligation: runtime complexity wrt. defined symbols {active,cons,f,p,proper,s,top} and constructors {0,mark,ok} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. 0_0() -> 1 0_1() -> 14 active_0(1) -> 2 active_0(5) -> 2 active_0(6) -> 2 active_1(1) -> 16 active_1(5) -> 16 active_1(6) -> 16 active_2(14) -> 17 cons_0(1,1) -> 3 cons_0(1,5) -> 3 cons_0(1,6) -> 3 cons_0(5,1) -> 3 cons_0(5,5) -> 3 cons_0(5,6) -> 3 cons_0(6,1) -> 3 cons_0(6,5) -> 3 cons_0(6,6) -> 3 cons_1(1,1) -> 11 cons_1(1,5) -> 11 cons_1(1,6) -> 11 cons_1(5,1) -> 11 cons_1(5,5) -> 11 cons_1(5,6) -> 11 cons_1(6,1) -> 11 cons_1(6,5) -> 11 cons_1(6,6) -> 11 f_0(1) -> 4 f_0(5) -> 4 f_0(6) -> 4 f_1(1) -> 12 f_1(5) -> 12 f_1(6) -> 12 mark_0(1) -> 5 mark_0(5) -> 5 mark_0(6) -> 5 mark_1(11) -> 3 mark_1(11) -> 11 mark_1(12) -> 4 mark_1(12) -> 12 mark_1(13) -> 7 mark_1(13) -> 13 mark_1(15) -> 9 mark_1(15) -> 15 ok_0(1) -> 6 ok_0(5) -> 6 ok_0(6) -> 6 ok_1(11) -> 3 ok_1(11) -> 11 ok_1(12) -> 4 ok_1(12) -> 12 ok_1(13) -> 7 ok_1(13) -> 13 ok_1(14) -> 8 ok_1(14) -> 16 ok_1(15) -> 9 ok_1(15) -> 15 p_0(1) -> 7 p_0(5) -> 7 p_0(6) -> 7 p_1(1) -> 13 p_1(5) -> 13 p_1(6) -> 13 proper_0(1) -> 8 proper_0(5) -> 8 proper_0(6) -> 8 proper_1(1) -> 16 proper_1(5) -> 16 proper_1(6) -> 16 s_0(1) -> 9 s_0(5) -> 9 s_0(6) -> 9 s_1(1) -> 15 s_1(5) -> 15 s_1(6) -> 15 top_0(1) -> 10 top_0(5) -> 10 top_0(6) -> 10 top_1(16) -> 10 top_2(17) -> 10 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: active(cons(X1,X2)) -> cons(active(X1),X2) active(f(X)) -> f(active(X)) active(f(0())) -> mark(cons(0(),f(s(0())))) active(f(s(0()))) -> mark(f(p(s(0())))) active(p(X)) -> p(active(X)) active(p(s(X))) -> mark(X) active(s(X)) -> s(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) p(mark(X)) -> mark(p(X)) p(ok(X)) -> ok(p(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(f(X)) -> f(proper(X)) proper(p(X)) -> p(proper(X)) proper(s(X)) -> s(proper(X)) s(mark(X)) -> mark(s(X)) s(ok(X)) -> ok(s(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,cons/2,f/1,p/1,proper/1,s/1,top/1} / {0/0,mark/1,ok/1} - Obligation: runtime complexity wrt. defined symbols {active,cons,f,p,proper,s,top} and constructors {0,mark,ok} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))