* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: f(x,g(x)) -> x f(x,h(y)) -> f(h(x),y) - Signature: {f/2} / {g/1,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {g,h} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(x,g(x)) -> x f(x,h(y)) -> f(h(x),y) - Signature: {f/2} / {g/1,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {g,h} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(x,y){y -> h(y)} = f(x,h(y)) ->^+ f(h(x),y) = C[f(h(x),y) = f(x,y){x -> h(x)}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x,g(x)) -> x f(x,h(y)) -> f(h(x),y) - Signature: {f/2} / {g/1,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {g,h} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. f_0(2,2) -> 1 f_1(3,2) -> 1 g_0(2) -> 1 g_0(2) -> 2 h_0(2) -> 1 h_0(2) -> 2 h_1(2) -> 1 h_1(2) -> 3 h_1(3) -> 1 h_1(3) -> 3 2 -> 1 3 -> 1 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: f(x,g(x)) -> x f(x,h(y)) -> f(h(x),y) - Signature: {f/2} / {g/1,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {g,h} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))