* Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(X) c(X) -> d(activate(X)) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(g(n__f(X)))) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,h/1} / {g/1,n__d/1,n__f/1} - Obligation: runtime complexity wrt. defined symbols {activate,c,d,f,h} and constructors {g,n__d,n__f} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 3. The enriched problem is compatible with follwoing automaton. activate_0(5) -> 1 activate_0(7) -> 1 activate_0(8) -> 1 activate_1(5) -> 9 activate_1(7) -> 9 activate_1(8) -> 9 activate_2(3) -> 10 c_0(5) -> 2 c_0(7) -> 2 c_0(8) -> 2 c_1(3) -> 6 d_0(5) -> 3 d_0(5) -> 10 d_0(7) -> 3 d_0(7) -> 10 d_0(8) -> 3 d_0(8) -> 10 d_1(5) -> 1 d_1(5) -> 9 d_1(7) -> 1 d_1(7) -> 9 d_1(8) -> 1 d_1(8) -> 9 d_1(9) -> 2 d_2(5) -> 10 d_2(7) -> 10 d_2(8) -> 10 d_2(10) -> 6 f_0(5) -> 4 f_0(7) -> 4 f_0(8) -> 4 f_1(5) -> 1 f_1(5) -> 9 f_1(7) -> 1 f_1(7) -> 9 f_1(8) -> 1 f_1(8) -> 9 g_0(5) -> 1 g_0(5) -> 5 g_0(5) -> 9 g_0(7) -> 1 g_0(7) -> 5 g_0(7) -> 9 g_0(8) -> 1 g_0(8) -> 5 g_0(8) -> 9 h_0(5) -> 6 h_0(7) -> 6 h_0(8) -> 6 n__d_0(5) -> 1 n__d_0(5) -> 7 n__d_0(5) -> 9 n__d_0(7) -> 1 n__d_0(7) -> 7 n__d_0(7) -> 9 n__d_0(8) -> 1 n__d_0(8) -> 7 n__d_0(8) -> 9 n__d_1(5) -> 3 n__d_1(5) -> 10 n__d_1(7) -> 3 n__d_1(7) -> 10 n__d_1(8) -> 3 n__d_1(8) -> 10 n__d_2(5) -> 1 n__d_2(5) -> 9 n__d_2(7) -> 1 n__d_2(7) -> 9 n__d_2(8) -> 1 n__d_2(8) -> 9 n__d_2(9) -> 2 n__d_3(5) -> 10 n__d_3(7) -> 10 n__d_3(8) -> 10 n__d_3(10) -> 6 n__f_0(5) -> 1 n__f_0(5) -> 8 n__f_0(5) -> 9 n__f_0(7) -> 1 n__f_0(7) -> 8 n__f_0(7) -> 9 n__f_0(8) -> 1 n__f_0(8) -> 8 n__f_0(8) -> 9 n__f_1(5) -> 4 n__f_1(7) -> 4 n__f_1(8) -> 4 n__f_2(5) -> 1 n__f_2(5) -> 9 n__f_2(7) -> 1 n__f_2(7) -> 9 n__f_2(8) -> 1 n__f_2(8) -> 9 3 -> 10 5 -> 1 5 -> 9 7 -> 1 7 -> 9 8 -> 1 8 -> 9 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(X) c(X) -> d(activate(X)) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(g(n__f(X)))) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,h/1} / {g/1,n__d/1,n__f/1} - Obligation: runtime complexity wrt. defined symbols {activate,c,d,f,h} and constructors {g,n__d,n__f} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))