* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: active(c(X)) -> mark(d(X)) active(f(X)) -> f(active(X)) active(f(f(X))) -> mark(c(f(g(f(X))))) active(h(X)) -> h(active(X)) active(h(X)) -> mark(c(d(X))) c(ok(X)) -> ok(c(X)) d(ok(X)) -> ok(d(X)) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) g(ok(X)) -> ok(g(X)) h(mark(X)) -> mark(h(X)) h(ok(X)) -> ok(h(X)) proper(c(X)) -> c(proper(X)) proper(d(X)) -> d(proper(X)) proper(f(X)) -> f(proper(X)) 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,c/1,d/1,f/1,g/1,h/1,proper/1,top/1} / {mark/1,ok/1} - Obligation: runtime complexity wrt. defined symbols {active,c,d,f,g,h,proper,top} and constructors {mark,ok} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. active_0(7) -> 1 active_0(8) -> 1 active_1(7) -> 16 active_1(8) -> 16 c_0(7) -> 2 c_0(8) -> 2 c_1(7) -> 11 c_1(8) -> 11 d_0(7) -> 3 d_0(8) -> 3 d_1(7) -> 12 d_1(8) -> 12 f_0(7) -> 4 f_0(8) -> 4 f_1(7) -> 13 f_1(8) -> 13 g_0(7) -> 5 g_0(8) -> 5 g_1(7) -> 14 g_1(8) -> 14 h_0(7) -> 6 h_0(8) -> 6 h_1(7) -> 15 h_1(8) -> 15 mark_0(7) -> 7 mark_0(8) -> 7 mark_1(13) -> 4 mark_1(13) -> 13 mark_1(15) -> 6 mark_1(15) -> 15 ok_0(7) -> 8 ok_0(8) -> 8 ok_1(11) -> 2 ok_1(11) -> 11 ok_1(12) -> 3 ok_1(12) -> 12 ok_1(13) -> 4 ok_1(13) -> 13 ok_1(14) -> 5 ok_1(14) -> 14 ok_1(15) -> 6 ok_1(15) -> 15 proper_0(7) -> 9 proper_0(8) -> 9 proper_1(7) -> 16 proper_1(8) -> 16 top_0(7) -> 10 top_0(8) -> 10 top_1(16) -> 10 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: active(c(X)) -> mark(d(X)) active(f(X)) -> f(active(X)) active(f(f(X))) -> mark(c(f(g(f(X))))) active(h(X)) -> h(active(X)) active(h(X)) -> mark(c(d(X))) c(ok(X)) -> ok(c(X)) d(ok(X)) -> ok(d(X)) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) g(ok(X)) -> ok(g(X)) h(mark(X)) -> mark(h(X)) h(ok(X)) -> ok(h(X)) proper(c(X)) -> c(proper(X)) proper(d(X)) -> d(proper(X)) proper(f(X)) -> f(proper(X)) 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,c/1,d/1,f/1,g/1,h/1,proper/1,top/1} / {mark/1,ok/1} - Obligation: runtime complexity wrt. defined symbols {active,c,d,f,g,h,proper,top} and constructors {mark,ok} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))