* Step 1: Sum 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: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: 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 = minimal, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. a_0() -> 2 a_1() -> 4 f_0(2) -> 1 f_1(2) -> 4 f_2(3) -> 6 g_0(2) -> 2 g_1(3) -> 1 g_1(3) -> 4 g_2(5) -> 3 h_0(2) -> 1 h_1(4) -> 3 h_2(6) -> 5 k_0(2,2,2) -> 1 * Step 3: 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))