WORST_CASE(?,O(n^1)) * Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(a()) -> g(h(a())) h(g(x)) -> g(h(f(x))) k(x,h(x),a()) -> h(x) k(f(x),y,x) -> f(x) - Signature: {f/1,h/1,k/3} / {a/0,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,h,k} and constructors {a,g} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. a_0() -> 1 a_1() -> 7 f_0(1) -> 2 f_0(3) -> 2 f_1(1) -> 9 f_1(3) -> 9 f_2(6) -> 11 g_0(1) -> 3 g_0(3) -> 3 g_1(6) -> 2 g_1(6) -> 9 g_1(8) -> 4 g_2(10) -> 8 h_0(1) -> 4 h_0(3) -> 4 h_1(7) -> 6 h_1(9) -> 8 h_2(11) -> 10 k_0(1,1,1) -> 5 k_0(1,1,3) -> 5 k_0(1,3,1) -> 5 k_0(1,3,3) -> 5 k_0(3,1,1) -> 5 k_0(3,1,3) -> 5 k_0(3,3,1) -> 5 k_0(3,3,3) -> 5 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: f(a()) -> g(h(a())) h(g(x)) -> g(h(f(x))) k(x,h(x),a()) -> h(x) k(f(x),y,x) -> f(x) - Signature: {f/1,h/1,k/3} / {a/0,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,h,k} and constructors {a,g} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))